Adaptive feedforward control for dynamic positioning of ships

基于⾃适应模糊反步法的永磁同步电机位置跟踪控制_于⾦鹏第25卷第10期V ol.25No.10控制与决策Control and Decision2010年10⽉Oct.2010基于⾃适应模糊反步法的永磁同步电机位置跟踪控制⽂章编号:1001-0920(2010)10-1547-05于⾦鹏,陈兵,于海⽣,⾼军伟(青岛⼤学复杂性科学研究所，⼭东青岛266071)摘要:研究具有参数不确定性的永磁同步电动机位置跟踪控制问题.利⽤模糊逻辑系统逼近系统中⾮线性函数,采⽤反步设计⽅法实现永磁同步电动机的⾃适应模糊控制.所提出的⾃适应模糊控制器在电机参数不确定和负载扰动的情况下,实现了永磁同步电动机的⾼性能位置跟踪控制.仿真结果表明了所提出⽅法的有效性.关键词:永磁同步电动机；⾮线性系统；⾃适应控制；模糊控制；位置跟踪；反步中图分类号:TM351⽂献标识码:AAdaptive fuzzy backstepping position tracking control for permanent magnet synchronous motorYU Jin-peng,CHEN Bing,YU Hai-sheng,GAO Jun-wei(Institute of Complexity Science，Qingdao University，Qingdao266071，China.Correspondent：YU Jin-peng，E-mail:yjp1109@/doc/b4ee8a9cbe23482fb4da4cf9.html)Abstract：This paper studies the problem of position tracking control for permanent magnet synchronous motors with parameter uncertainties and load torque disturbance.Based on backstepping technique,an adaptive fuzzy control method is proposed by using fuzzy logic systems to approximate unknown nonlinearities of permanent magnet synchronousmotor(PMSM)drive system.The proposed controller guarantees the good tracking performance even with the existence of the parameter uncertainties and load torque disturbance.Simulation results show the effectiveness of the proposed method. Key words：Permanent magnet synchronous motor；Nonlinear system；Adaptive control；Fuzzy control；Position tracking；Backstepping1引⾔永磁同步电机(PMSM)以其优越的性能⼴泛应⽤于交流伺服系统中.永磁同步电机是⼀个多变量、强耦合的⾮线性控制对象,并受电机参数变化、外部负载扰动等不确定性因素的影响.⽮量控制、直接转矩控制等传统控制策略,使PMSM系统的性能有了较⼤的提⾼,但这些⽅法都建⽴在⼯程的基础上,并未从理论上给出完整的证明,也没有从本质上解决电机的⾮线性问题.因此,研究先进的控制策略,提⾼PMSM系统的动静态性能具有重要意义.近年来, PMSM⾮线性控制⽅法的研究获得了很⼤进展,如状态反馈线性化控制[1]、滑模变结构控制[2,3]、⽆源性⽅法[4]、⾃适应控制[5]、模糊控制[6]和反步控制[7-11]等.其中反步设计⽅法以其易于与⾃适应控制技术相结合,消除参数时变和外界扰动对系统性能的影响⽽受到了⼴泛的重视.⾃适应反步控制⽅法将复杂的⾮线性系统分解成多个简单低阶的⼦系统,通过引⼊虚拟控制变量来逐步进⾏控制器设计,最终确定控制律以及参数⾃适应律,从⽽实现对系统的有效控制.⾃1965年美国学者Zadeh⾸次提出模糊集理论后,模糊逻辑控制便受到国内外控制界的⼴泛关注,并⽤于对具有⾼度⾮线性和不确定性的复杂系统的控制设计.在发展形成的各种模糊控制技术中,基于反步法的⾃适应模糊控制是⼀种有效的⾮线性控制⽅法.该⽅法通过利⽤模糊逻辑系统逼近系统中的⾼度⾮线性函数,并结合⾃适应和反步技术构造控制器.本⽂根据永磁同步电动机的结构特点,将⾃适应模糊反步控制应⽤于永磁同步电动机的位置控制.利收稿⽇期:2009-09-14；修回⽇期:2009-11-13.基⾦项⽬:国家⾃然科学基⾦项⽬(60674055,60774027,60774047)；国家863计划项⽬(2007AA11Z247)；⼭东省⾃然科学基⾦项⽬(ZR2009GM034)；⼭东省⼯业控制技术重点实验室(青岛⼤学)开放课题基⾦项⽬.作者简介:于⾦鹏(1978?),男,⼭东威海⼈,讲师,博⼠,从事电机控制、⾮线性控制的研究；陈兵(1958?),男,辽宁锦州⼈,教授,博⼠⽣导师,从事复杂系统、⾮线性系统等研究.DOI：10.13195/j.cd.2010.10.110.yujp.0061548控制与决策第25卷⽤模糊逻辑系统逼近系统中的⾮线性函数,结合⾃适应技术对系统中未知参数进⾏估计,同时基于反步⽅法构造系统的控制器,实现对PMSM的有效控制.相⽐现有经典的基于反步⽅法的永磁同步电机⾃适应控制,利⽤⾃适应模糊设计⽅法构造的控制律具有结构简单、易于⼯程实现的特点.实例仿真研究表明,所设计的模糊控制律可以确保系统很好地跟踪永磁同步电机的位置信号,⽽且对电机参数变化及负载扰动具有较强的鲁棒性.2永磁同步电机的数学模型在同步旋转坐标(d-q)下,PMSM系统的模型可表⽰为J dωd t=T?T L?Bω=32n p[(L d?L q)i d i q+Φi q]?Bω?T L,L d d i dd t=?R s i d+n pωL q i q+u d,L q d i qd t=?R s i q?n pωL d i d?n pωΦ+u q,dθ=ω.式中:u d,u q表⽰永磁同步电动机d,q轴定⼦电压,为系统的控制输⼊;i d,i q,ω和θ分别表⽰d,q轴电流、电动机的转⼦⾓速度和转⼦⾓度,为系统的状态变量;J为转动惯量;n p为极对数,B为摩擦系数;L d和L q为d-q坐标系下的定⼦电感;R s为定⼦电阻;T L为负载转矩;Φ为永磁体产⽣的磁链.为更简便地表⽰电机模型,定义新的变量如下:x1=θ,x2=ω,x3=i q,x4=i d,a1=3n pΦ23n p(L d?L q)2,b1=?R sL q,b2=?n p L dL q,b3=?n pΦL q,b4=1L q,c1=?R sL d,c2=n p L qL d,c3=1L d.则永磁同步电机的数学模型可表⽰为˙x1=x2,(1)˙x2=a1Jx3+a2Jx3x4?BJJ,(2)˙x3=b1x3+b2x2x4+b3x2+b4u q,(3)˙x4=c1x4+c2x2x3+c3u d.(4) 3永磁同步电动机的模糊⾃适应反步控制器设计根据反步法原理,永磁同步电动机的⾃适应模糊控制器的设计步骤如下: Step1定义系统误差变量如下:{z1=x1?x d,z2=x2?α1, z3=x3?α2,z4=x4.(5)其中:x d为期望的位置信号;α1和α2为所期望的虚拟控制信号,其具体结构将在下⾯的设计过程中给出.为此,对于第1个⼦系统,选取Lyapunov控制函数V1=12z21.(6)对式(6)求导,可得˙V1=z1˙z1=z1(x2?˙x d).(7)将x2视为第1个⼦系统的控制输⼊,选取虚拟控制函数α1=?k1z1+˙x d,则˙V1=?k1z21+z1z2.(8) Step2选取Lyapunov函数V2=V1+J2z22.对V2求导,并利⽤式(8),得˙V2=˙V1+Jz2˙z2=k1z21+z2(a1x3+z1+a2x3x4Bx2?T L?J˙α1).(9)注意到实际系统中负载不可能⽆穷⼤,假定0?T L?d,其中d为正数.利⽤熟知的平⽅和公式,有z2T L?z22+12ε22d2,(10)其中ε2为任意⼩的正数.取虚拟控制函数α2=1a1(¯k2z2z112ε22z2+?Bx2+?J˙α1)=1a1(?k2z2?z1+?Bx2+?J˙α1).(11)其中:k2=¯k2+12ε22>0,?B和?J分别为B和J的估计值.将式(10)和(11)代⼊(9),得˙V2?k1z21k2z22+a1z2z3+a2z2x3x4++z2(?B?B)x2+z2(?J?J)˙α1+12ε22d2.(12) Step3选取Lyapunov函数V3=V2+12z23.(13)对式(13)求导,并利⽤(12),得˙V3?k1z21k2z22+a2z2x3x4+z2(BB)x2+z2(?J?J)˙α1+12ε22d2+z3(f3+b4u q),(14)其中f3=b1x3+b2x2x4+b3x2+a1z2?˙α2.由万能逼近定理[12],对于任意⼩的正数ε3,存在模糊逻辑系统W T3S3使得f3=W T3S3+δ3,其中δ3表⽰逼近误差,并满⾜不等式∣δ3∣?ε3.从⽽z3f3=z3(W T3S3+δ3)?z3(∥W3∥S3W T3l3l3∥W3∥+ε3)第10期于⾦鹏等:基于⾃适应模糊反步法的永磁同步电机位置跟踪控制154912l 23z 23∥W 3∥2S T 3S 3+12l 23+12z 23+12ε23,(15)其中∥W 3∥为向量W 3的范数.将上式代⼊式(14),得˙V 3??k 1z 21?k 2z 22+a 2z 2x 3x 4+z 2(?BB )x 2+z 2(J J )˙α1+12l 23z 23∥W 3∥2S T 3S 3+12l 23+12z 23+12ε23+12ε22d 2+z 3b 4u q .(16)现在选取真实的控制率u q =1b 4(?k 3z 3?12z 3?12l 23z 3?θS T 3S 3),(17)其中?θ为θ的估计值,θ将在后⾯定义.将式(17)代⼊(16),得˙V3??3∑i =1k i z 2i +a 2z 2x 3x 4+z 2(?BB )x 2+z 2(J J )˙α1+12l 23z 23(∥W 3∥2??θ)S T 3S 3+12l 23+12ε23+12ε22d 2.(18)注1在构造控制率u q 的过程中,直接利⽤模糊逻辑系统作为函数逼近算⼦来逼近⾮线性函数f 3,⽆需计算˙α2和¨α1,从⽽避免了控制器设计过程的繁琐性,所设计的⾃适应控制律具有结构简单的特点.为设计控制律u d ,选取Lyapunov 函数V 4=V 3+12z 24,于是得到˙V 4=˙V 3+z 4˙z 4??3∑i =1k i z 2i +z 2(?B ?B )x 2+z 2(?J ?J )˙α1+12l 23z 23(∥W 3∥2??θ)S T 3S 3+12l 23+12ε23+12ε22d 2+z 4(f 4+c 3u d ),(19)其中f 4=a 2z 2x 3+c 1x 4+c 2x 2x 3.再⼀次利⽤模糊逻辑系统逼近⾮线性函数f 4,使得f 4=W T4S 4+δ4,其中∣δ4∣?ε4.与式(15)同理,可得z 4f 4?12l 24z 24∥W 4∥2S T4S 4+12l 24+12z 24+12ε24.(20)进⽽,由式(19)和(20),得˙V 4=˙V 3+z 4˙z 4??3∑i =1k i z 2i +12l 23z 23(∥W 3∥2??θ)S T 3S 3+4∑i =312(l 2i +ε2i)+12ε22d 2+z 2(?B ?B )x 2+z 2(?J ?J )˙α1+12l 24z 24∥W 4∥2S T4S 4+12z 24+c 3z 4u d .(21)取u d =?1c 3(k 4z 4+12z 4+12l 24z 4?θS T 4S 4).(22)现在定义θ=max {∥W 3∥2,∥W 4∥2}.由式(21)和(22),可得˙V 4??4∑i =1k i z 2i+4∑i =312(l 2i +ε2i )+z 2(?J ?J )˙α1+4∑i =312l 2i z 2i S T i S i (θ??θ)+z 2(?B ?B )x 2+12ε22d 2.(23)Step 4定义B,J 和θ,3个物理量的估计误差分别为?B =?B ?B,?J =?J ?J,?θ=?θ?θ.选取系统的Lyapunov 函数V =V 4+12r 1?B 2+12r 2?J 2+12r 3θ2,其中r i (i =1,2,3)为正数.⼜˙?B =˙?B,˙?J =˙?J,˙?θ=˙?θ,则˙V ??4∑i =1k i z 2i +4∑i =312(l 2i +ε2i )+12ε22d 2+1r 1?B (r 1z 2x 2+˙?B )+1r 2J (r 2z 2˙α1+˙?J )+1r 3?θ[?4∑i =3r 32l 2iz 2i S T i S i +˙?θ].(24)选取⾃适应律˙?B =?r 1z 2x 2?m 1?B,˙?J =?r 2z 2˙α1?m 2?J,˙?θ=4∑i =3r 32l 2iz 2i S T i S i ?m 3?θ,其中m i (i =1,2,3,4)和l i (i =3,4)皆为正数.4稳定性分析将上述⾃适应率代⼊式(24),可得˙V ??4∑i =1k i z 2i +4∑i =312(l 2i +ε2i)+12ε22d 2?m 1r 1?B ?B ?m 2r 2?J ?J ?m 3r 3θ?θ.对于?BB ,有??B ?B B (?B +B )??12?B 2+12B 2,同理,可得到下述不等式:JJ 12J 2+12J 2,θ?θ??12?θ2+12θ2.进⽽˙V ??4∑i =1k i z 2i +12ε22d 2?m 12r 1?B 2?m 22r 2?J 2?m 32r 3θ2+4∑i =312(l 2i +ε2i )+m 12r 1B 2+m 22r 2J 2+m 32r 3θ2a 0V +b 0.(25)其中a 0=min {2k 1,2k 2J,2k 3,2k 4,m 1,m 2,m 3},b 0=4∑i =312(l 2i +ε2i)+12ε22d 2+m 12r 1B 2+m 22r 2J 2+m 32r 3θ2.1550控制与决策第25卷由式(25),容易得到V (t )?(V (t 0)?b 0/a 0)e ?a 0(t ?t 0)+b 0/a 0?V (t 0)+b 0/a 0,?t ?t 0.(26)式(26)表明,变量z i (i =1,2,3,4),?B,J 和?θ属于紧集Ω={(z i ,?B,J,θ)∣V ?V (t 0)+b 0/a 0,?t ?t 0}.显然有lim t →∞z 21?2b 0/a 0.(27)由上述分析可得如下结论:结论1永磁同步电动机在控制律u d ,u q 的作⽤下,系统的跟踪误差能够收敛到原点的⼀个充分⼩的邻域内,同时其他信号保持有界.注2式(27)给出了跟踪误差的上限.由a 0和b 0的定义可见,当选定合适的控制参数k i ,m i 后,a 0保持不变.通过选择充分⼤的r i ,充分⼩的l i 和εi ,可以保证2b 0/a 0充分⼩,进⽽确保跟踪误差充分⼩.5系统仿真分析为验证所提出的PMSM ⾃适应模糊反步控制⽅法的有效性,在Matlab7环境下进⾏仿真分析,电机及负载的参数为J =0.003798Kg ?m 2,R s =0.68Ω,B =0.001158N ?m /(rad /s),L d =0.00285H ,L q =0.00315H ,Φ=0.1245H ,n p =3.选择模糊集如下:µF 1i =exp [?(x +5)22],µF 2i =exp [?(x +4)22],µF 3i =exp [?(x +3)22],µF 4i =exp [?(x +2)22],µF 5i =exp [?(x +1)22],µF 6i =exp [?(x ?0)22],µF 7i =exp [?(x ?1)22],µF 8i =exp [?(x ?2)22],µF 9i =exp[?(x ?3)22],µF 10i =exp [?(x ?4)22],µF 11i =exp [?(x ?5)22].选择控制律参数为k 1=75,k 2=30,k 3=40,k 4=50,r 1=r 2=r 3=0.25,m 1=m 2=m 3=0.005,l 3=l 4=0.5.在x T (0)=0和?J(0)=?B (0)=?θ(0)=0的初始条件下,对于上述同⼀组控制参数按两组⽅案进⾏仿真研究.第1组⽅案中,给定x d =sin t,T L =1.5N ?m ;第2组⽅案中,给定x d =2sin(2t );T L ={1.5N ?m ,0?t ?1;3N ?m ,t ?1.仿真结果如图1和图2所⽰.图1为第1组⽅案仿真结果,图2为第2组⽅案仿真结果.从两组仿真结果可以看出,在电机参数不确定及负载⼒矩存在扰动的情况下,电机位置信号可以迅速跟踪给定信号,⽽且对电机参数变化及负载扰动具有较强的鲁棒性.x 11.50.50.0-0.5P o s i t i o n /r a d246810t /s1.0-1.0-1.5x dtracking error0.40.20-0.2-0.4T r a c k i n g e r r o r /r a d246810t /s(a) x x 1d (b)图1第1⽅案仿真结果210-1-2P o s i t i o n /r a d246810t /s(a) x x 1d (b)tracking error0.40.20-0.2-0.4T r a c k i n g e r r o r /r a d246810t /s图2第2⽅案仿真结果6结论本⽂针对永磁同步电动机的参数变化及负载转矩的不确定性,采⽤⾃适应模糊反步控制实现了永第10期于⾦鹏等:基于⾃适应模糊反步法的永磁同步电机位置跟踪控制1551磁同步电动机的⾮线性位置跟踪控制.仿真结果表明,所设计的⾮线性控制器可以保证永磁同步电动机伺服系统获得良好的跟踪效果,并且对参数不确定性及负载⼒矩扰动具有很好的鲁棒性.参考⽂献(References)[1]张涛,蒋静坪,张国宏.交流永磁同步电机伺服系统的线性化控制[J].中国电机⼯程学报,2001,21(6):40-43.(Zhang T,Jiang J P,Zhang G H.Feedback linearization of permanent magnet synchronous motor system[J]. Proceedings of the CSEE,2001,21(6):40-43.)[2]Karunadasa J P,Renfrew A C.Design and implementationof microprocessor based sliding mode controller for brushless servo motor[J].IEE Proceedings-B,1991, 138(6):345-363. 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[12]Wang L X,Mendel J M.Fuzzy basis functions,universalapproximation,and orthogonal least squares learning[J].IEEE Trans on Neural Networks,1992,3(5):807-814.(上接第1546页)[6]Florchinger P.Lyapunov-like techniques for stochasticstability[J].Siam J on Control and Optimization,1995, 33(4):1151-1169.[7]Krstic M,Deng H,Stabilization of uncertain nonlinearsystems[M].New York:Springer,1998.[8]Wu Z J,Xie X J,Zhang S Y.Adaptive backsteppingcontroller design using stochastic small-gain theorem[J].Automatica,2007,43(4):608-620.[9]段纳,解学军,张嗣瀛.⼀类⾼阶次随机⾮线性系统的状态反馈镇定[J].控制与决策,2008,23(1):60-64.(Duan N,Xie X J,Zhang S Y.State-feedback stabilization for a class of high-order stochastic nonlinear system[J].Control and Decision,2008,23(1):60-64.)[10]Li W Q,Xie X J.Inverse optimal stabilization forstochastic nonlinear systems whose linearizations are not stabilizable[J].Automatica,2009,45(2):498-503. 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F u r t h e r i n f o r m a t i o n a t w w w .v a c uub r a n d .c o m Self-optimizing vacuum for productivity and efficiencyThe VARIO® Chemistry-pumping units with adaptive vacuum controlVacuum applications in many laboratory and industrial processes benefit from electronical control by:■avoiding sample loss by foaming and boiling over■reducing process times for distillation and evaporation processes■improving reproducibility in drying, reaction and evaporation processes ■reducing operating time with continuous, automated optimization ■protecting the environment by capturing waste solvent vaporsVARIO ® controller provides fully automatic evaporation without parameter programming!VARIO ®-diaphragm pumps and chemistry pumping units optimize the vacuum automatically and accurately by adjusting the speed of the diaphragm pump. The CVC 3000 vacuum controller in the VARIO® pumping units detects the boiling pressure and responds automatically to provide the optimum vacuum conditions.■eliminates continuous oversight and manual readjust-ment, allowing you to focus on other research work ■avoids sample loss by eliminating bumping and foaming■waste vapor recovery rates near 100% keep lab airclean and protect the environment■ensuring of vapor pressures even incomplex mixtures reduces process times by as much as 30% compared with two-point vacuum controlOptimize laboratory processeswith VACUUBRAND VARIO ® technologyFully automatic processing by the adaptive VARIO® contolCompetitive unit in automatic mode - holds at first boiling point; evaporation stops because vacuum does not adapt to additional boiling pointsVACUUBRAND VARIO ®-Control - Complete distillation within shortest process time by adaptive boiling pressure-controlUp to 90% energy savings by VARIO® controlTwo-point control vs. VARIO® control■this reduces power consumption and energy costs byup to 90%■lower rotor speeds lead to fewer strokes per minuteand significantly extended service intervalsEvaporation Ethanol-Water 1:1Unlike some competitive pumping units, which detect the first boiling point and then hold the vacuum at that level, VACUUBRAND VARIO® control detects each boiling point and continuously adapts to optimize vacuum conditions even in complex mixtures!In a conventional two-point control with solenoid valve, the vacuum pump runs continuously at 100% speed, opening and closing the valve as needed to achieve pro-grammed vacuum levels. With the VACUUBRAND VARIO® control, the speed of the pump is adjusted automatically to the vacuum requirements of the process.VACUUBRAND offers the VARIO® chemistry diaphragm pump technology for a wide range of operations. Models with pumping speeds ranging from 2 m 3/h to nearly 20 m 3/h support applications ranging from individual laboratory applica-tions such as rotary evaporators, to multi-user lab vacuum networks, to replacement of rotary vane pumps in kilo labs and pilot plants. Depending on the pump version, the reachable ultimate vacuum is between 70 mbar and even down to 0.6 mbar. Select the right pumping unit for evaporation of your low- or high-boiling-point solvents at gentle temperatures.proPumping speed graph of VACUUBRAND´s VARIO® pumping unitsNew! VARIO Technology for a wider range of applications■automatically optimizing conditions ■without operator intervention ■and with reduced process timesAll while reducing emissions and saving energy.You focus on your research work......while the PC 3001 VARIO pro takes care of the evaporation!VACUUBRAND with SafetyAll of our VARIO® pumping units, and most of our other diaphragm pumps, as well, have no ignition sources in the internal, wetted area and are approved according to ATEX category 3. This means our pumps offer a high level of security in locations in which explosive mixtures might occur “infrequently“ in a neutral environment. In installations in hazardous areas characte-rized by the “occasional“ pumping of explosive mixtures, we continue to offer the special, ATEX-approved pumps. Thus, VACUUBRAND pro-ducts are also the safety leader in lab vacuum.The PC 3001 VARIO pro at a working pressure of 20 mbar provides:about 50% higher pumping speed than994291 - C h e m i s t r y p u m p i n g u n i t s E N 05/2009F u r t h e r i n f o r m a t i o n a t w w w .v a c u u b r a n d .c omT ec h n i c a ld a t a / o r de r i n g i nf o r m a t i o nTECHNICAL DATAVacuum controllerNumber of heads / stagesMax. pumping speedUltimate vacuum (abs.)Ultim. vac. (abs.) with gas ballast Max. back pressure (abs.)Inlet connectionOutlet connectionCoolant connectionMax. powerDegree of protectionDimensions (L x W x H), approx.Weight, approx.ORDERING INFORMATION200-230 V ~ 50-60 Hz 200-230 V ~ 50-60 Hz 200-230 V ~ 50-60 Hz 100-120 V ~ 50-60 Hz Versions, which include 230 V: ATEX: II 3G IIC T3 X, Internal Atm. only Pumping speed measured by ISO 21360* Country specific power cable, please order separately ** On request*** With NRTL certification for Canada and the USAm³/h mbar mbarbar kW mmkg PC 3003 VARIOCVC 30004 / 42.80.6 2 1.1Hose nozzle DN 10 mm Hose nozzle DN 10 mm2 x hose nozzle DN 6-8 mm 0.53 IP 40419 x 243 x 44420.6738400738401738402738403PC 3002 VARIOCVC 30002 / 22.87121.1Hose nozzle DN 10 mm Hose nozzle DN 10 mm 2 x hose nozzle DN 6-8 mm 0.53IP 40419 x 243 x 44417.4733500733501733502733503PC 3016 NT VARIOCVC 30008 / 119.3701001.1Small flange KF DN 25 Hose nozzle DN 10 mm 2 x hose nozzle DN 6-8 mm 0.53IP 40616 x 387 x 42029.7741800**741803PC 3004 VARIOCVC 30004 / 34.61.531.1Hose nozzle DN 10 mm Hose nozzle DN 10 mm2 x hose nozzle DN 6-8 mm 0.53IP 40419 x 243 x 44420.6737500737501737502737503PC 3010 NT VARIOCVC 30008 / 411.6 0.61.21.1Small flange KF DN 25 Hose nozzle DN 10 mm 2 x hose nozzle DN 6-8 mm 0.53IP 40616 x 387 x 42029.7744800744801***PC 3012 NT VARIOCVC 30008 / 312.91.531.1Small flange KF DN 25Hose nozzle DN 15 mm/10 mm 2 x hose nozzle DN 6-8 mm 0.53IP 40616 x 387 x 42029.7743800743801*743803PC 3001 VARIO proCVC 30004 / 32.0241.1Hose nozzle DN 6/10 mm Hose nozzle DN 10 mm 2 x hose nozzle DN 6-8 mm 0.16IP 20300 x 306 x 4007.7696700***696701***696702***696703***CEE CH,CN UKUS999184 - 02-1 / 2013The right VARIO®-Pump for your applicationRotary evaporators / reactorsThe PC 3001 VARIO pro is ideal for vacuum applications with high boiling solvents. The hysteresis-free vacuum control prevents superheating and foaming to protect valuable process samples. The controller enables automatic detection of vapor pressures and automatic adjustment of the vacuum level to the process requirements. The new ´pro´ version with improved pumping speed extends the range of use. Evacuation of larger vessels and process steps with high vapor volumes can be completed within shorter time. Programmed vacuum processes can be controlled by the integrated CVC 3000 controller or using an RS232C interface to your computer. The ´TE´ version of the PC 3001 VARIO pro uses a dry ice condenser to provide a cooling-water-free option for vapor capture if no cooling water connection is available or water conservation is critical. The PC 3001 VARIO pro with the Peltronic® emission condenser works without any cooling media.For exceptionally large amounts of vapor - like from parallel evaporators without condenser - the PC 3001 VARIO pro +IK with its condenser on the vacuum side is an excellent choice.Drying chambersVacuum drying chambers are used for drying very sensitive substances and when it is necessary to guarantee excellent residual drying. They generally need a very good ultimate vacuum depending upon the degree of drying, maximum acceptable temperature and the solvents used. At certain process parameters, there are large quantities of vapors that can only be handled with pump systems with a sufficiently large volume flow rate. Our product recommendations: PC 3003 VARIO or PC 3004 VARIO.Oil-free vacuum for kilo labsIn kilo labs and pilot plants, materials are produced in quantities of a few hundred gramsto several kilograms for pharmaceutical development, safety studies and early clinicaltrials for new drugs. Based on their extraordinary chemical resistance, our high perfor-mance chemistry pumping units PC 3016 VARIO, PC 3012 VARIO or PC 3010 VARIO areperfectly suited for these applications. The pumps operate without fluids such as water oroil, and thus reduce operating and maintenance costs. Variable-speed pumping systemsoffer unique control advantages in these applications, and are easily integrated intoprocess control via PC or programmable logic controllers.Operation in a local area network VACUU·LAN®VACUU·LAN® vacuum networks make it possible to supply high performance vacuum toseveral different applications from one vacuum pump (e.g., PC 3002 VARIO, PC 3003VARIO, PC 3004 VARIO). This is a money- and space-saving solution when a lot of users are working with vacuum in one laboratory and avoids the numerous drawbacks of a central (“house“) vacuum supply. For the vacuum outlets at workplaces, very versatile modules are available which can be easily upgraded. All of the components are available for new laboratory furnishings or for installation in existing or renovated laboratories. The modules are very resistant to chemicals and have built-in check valves to ensure that adjacent applications do not contaminate or interfere with one another.VACUUBRAND GMBH + CO KGAlfred-Zippe-Straße 4 · 97877 Wertheim · GermanyT +49 9342 808-0 · F +49 9342 808-5555*******************·Technical data are subject to change without notice。

E x t en dedF ee dbackC ontrolFun c t i o nExtended Feedback Control Function Flexible, Powerful, AdjustableThe challenge: ▪ Aim 1: Much greater control of fill levels in conjunction with statistical mean weight values to automatically ensure regulatory compliance ▪ Aim 2: Automatic correction of the target weight to bring it closer to the labelled weight to reduce product giveaway ▪ Aim 3: Taking full advantage of legal packaging regulation fill level limits to reduce product giveaway to an absolute minimum ▪ Aim 4: Much greater control of fill level correction speed to reduce scrap and get filling processes in tune faster The standard feedback control function minimises product weight errors and product giveaway through proactive feedback, keeping filler heads properly adjusted. The additional function "Extended Feedback Control” can substantially improve the filling process and save extra money while complying with Weights and Measure regulations. The "Extended Feedback Control Function” is an add-on to the existing feedback control programme and gives powerful new flexibility and adjustment capabilities to the filling process. The above statements i.e. aims are the base for this function. A good comparison for the difference between the standard feedback programme and the extended feedback control is the technical advances in music systems. The standard feedback programme can be compared to a radio with dials for just "Bass” and "Treble” adjustment whereas the extended feedback function can be compared to a stereo system with a graphic equaliser to fine tune the music for an excellent and perfect sound.Extension "Combination Statistics ” This extension combines the standard feedback programme with the checkweigher statistics function. This means that the statistic mean values are included in the feedback calculation. The combination of feedback and statistics ensure that at the end of the production run you will never have a too low "statistic mean value” which could lead to regulat ory sanctions. When the "statistic mean value” starts to drift from the target weight the feedback controller will automatically become activated. This will occur even if the weights of the products currently being weighed are correct. This extension regulates the filling process when the following events occur: 1. Actual filling level is correct and stable but the statistic mean value is lower than the target weight – correction signal sent to the filler → fill more! 2. Actual filling level is correct and stable but the statistic mean value is higher than the target weight – correction signal sent to the filler → fill less! 3. Actual filling level is below target (within T- limits) but the statistic mean value is still above the target weight – fill process under control → no adjustmentsThe main benefit of this combination is that you can set your target weight much closer to the nominal or labelled weight. This extension actively changes fill levels to ensure the mean value matches the target weight, which is normally just above the labelled weight, at the end of the complete production run. This not only ensures a better quality and more consistent product and compliance with Weights and Measures guidelines but it reduces dramatically over/under filling and unnecessary product giveaway. Constant mean weight value control also avoids manual adjustments of fill levels towards the end of a production run to fulfil net content laws. Extension "Optimal overfill ” This function permanently calculates the optimum mean value and target weight. The calculation is based on the checkweigher’s standard deviation value and normal weight distribution pattern. The calculation also takes into account that a certain percentage of the production (such as 2%) is allowed to fall below the T1 Limit. Once production begins the target weight is automatically adjusted to make use of the permissible range (e.g. max. 2% of products with a weight below T1). An automatic signal is sent to the filler to fill with the new target weight. The diagram below shows the initial settings at the start of production and how these settings change during production to reduce overfilling, bring the target weight closer to the labelled weight and make use of the legally acceptable percentage of products with a weight under the T1 limit.– 2 –ExtendedF ee dbackC ont rolFu nctio nExtension "2 Control Factors" This function allows you to determine two separate control factors for increasing and decreasing the fill volume. The possibility of setting different manipulated variables for different control actions allows you to choose your individual, preferred model. For example, allowing you to put a stronger emphasis on one of the two control actions. This function can be defined separately for every product preset (product setup memory). In model A an "overfill" is corrected much faster than an "underfill". In this case the focus is on reducing overfilling and product giveaway as quickly as possible. This can be used where underfilled products are not lost but can be re-used or recycled back into the process. In model B an "underfill" is corrected much faster than an "overfill". In this case the focus is on reducing underfilling as quickly as possible. This can be used where underfilled products are scrapped e.g. when processing frozen foods.Extension "Differential control"The standard control factor determines the value "by how much the filler is controlled". An additional (second) control factor serves as an "amplification factor" and allows you to strengthen the control factor after a measurement series. The amount the factor is actually strengthened depends on the saved values and the results of the preceding measurement series.The algorithm on which controlling is based allows the controller, in cases of extreme under or overfilling to get back to the target weight much more quickly.– 3 – E xtendedF ee dbackC ont rolFu nctio nThe correct setting of both factors allow for an optimal feedback control to the filler ensuring a reduction in rejected products where due to the product characteristics and filler process occasional extreme weight fluctuation may be experienced. Customer benefits: ⏹ Reduction of over and underfilling ⏹ Reduction of unnecessary product giveaway ⏹ Reduction of rejects and product scrap ⏹ Permanent control of mean weight values for a complete production run ⏹ Automatic adjustment of target weight nearer to labelled weight ⏹ Compliance with net content laws and regulations ⏹ Avoids manual adjustments of fill levels at the end of a production run ⏹ Higher and more consistent product qualityE x t e n d e dF e e d b a c k C o n t r o l F u n c t i o n Mettler-Toledo Garvens GmbH Kampstrasse 731180 GiesenGermanyTelephone +49 (0) 5121 933-0 Facsimile +49 (0) 5121 933-456 e-mail **************Subject to technical modifications © Mettler-Toledo Garvens GmbH Application Note 03 02/2016 /garvensFor more information。

Adaptive energy management of a plug-in hybrid electric vehicle based on driving pattern recognition and dynamicprogrammingShuo Zhang a ,Rui Xiong a ,b ,⇑aNational Engineering Laboratory for Electric Vehicles,School of Mechanical Engineering,Beijing Institute of Technology,No.5South Zhongguancun Street,Haidian District,Beijing 100081,China bCollaborative Innovation Center of Electric Vehicles in Beijing,Beijing Institute of Technology,No.5South Zhongguancun Street,Haidian District,Beijing 100081,Chinah i g h l i g h t sThe hierarchical control strategy has been proposed for the multiple energy sources. Three typical driving patterns have been classified with the fuzzy logic controller. A driving pattern recognition method was developed with the fuzzy logic controller. DP was used to develop suboptimal control strategies for different driving blocks. Adaptive energy management method for a plug-in HEV has been proposed and verified.a r t i c l e i n f o Article history:Received 24April 2015Received in revised form 26May 2015Accepted 1June 2015Available online 16June 2015Keywords:Plug-in hybrid electric vehicle Hybrid energy-storage system Multi-scaleEnergy managementDriving pattern recognition Dynamic programminga b s t r a c tTo achieve the optimal energy allocation for the engine-generator,battery and ultracapacitor of a plug-in hybrid electric vehicle,a novel adaptive energy management strategy has been proposed.Three efforts have been made.First,the hierarchical control strategy has been proposed for multiple energy sources from a multi-scale view.The upper level is for regulating the energy between the engine-generator and hybrid energy-storage system,while the lower level is for the battery and ultracapacitor.Second,a driving pattern recognition based adaptive energy management approach has been proposed.This approach uses a fuzzy logic controller to classify typical driving cycles into different driving patterns and to identify the real-time driving pattern.Dynamic programming has been employed to develop opti-mal control strategies for different driving blocks,and it is helpful for realizing the adaptive energy man-agement for real-time driving cycles.Third,to improve the real-time and robust performance of the energy management,the previous 100s duration of historical information has been determined to iden-tify a real-time driving pattern.Finally,an adaptive energy management strategy has been proposed.The simulation results indicate that the proposed energy management strategy has better fuel efficiency than the original and conventional dynamic programming-based control strategies.Ó2015Elsevier Ltd.All rights reserved.1.IntroductionEnergy shortages,environmental concerns over air pollution,and the prospect of the global warming support the need for fur-ther development of plug-in hybrid electric vehicles (HEVs).Plug-in HEVs have become more and more popular due to their excellent fuel economy and relatively low cost [1,2].However,pos-sessing both a highly specific energy density for long driving ranges and a highly specific power for deep and shallow dis-charge/charge cycles is difficult for current batteries [3].Because an ultracapacitor has a high power density and can be used as a power buffer during climbing,braking or acceleration,the combi-nation of lithium-ion batteries and ultracapacitors is an efficient solution to prolong the battery service life by optimizing its oper-ating range [4–7].1.1.Literature reviewA few topologies of a hybrid battery/ultracapacitor energy-storage system (HESS)have been proposed and can be roughly classified into four types from the control perspective./10.1016/j.apenergy.2015.06.0030306-2619/Ó2015Elsevier Ltd.All rights reserved.⇑Corresponding author at:National Engineering Laboratory for Electric Vehicles,School of Mechanical Engineering,Beijing Institute of Technology,No.5South Zhongguancun Street,Haidian District,Beijing 100081,China.Tel.:+86(10)68914070;fax:+86(10)68940589.E-mail address:rxiong@ (R.Xiong).They include directly connecting the battery and ultracapacitor in parallel[4],connecting the battery with a DC/DC converter in series before connecting with the ultracapacitor in parallel[5],connecting the ultracapacitor with a DC/DC converter in series before connect-ing with the battery in parallel[7À9],and connecting the battery and the ultracapacitor each with a DC/DC converter in series before they are connected in parallel[7].In addition to these types,Ali Emadi has proposed a new HESS topology in which the battery does not provide power unless its terminal voltage is higher than that of the ultracapacitor[8].However,the required voltage level of the ultracapacitor is twice as much as that of the battery,which is unsup-portable in some applications.Based on our previous research expe-rience on the systematical evaluation results for the four HESS topologies in Ref.[9],the second topology that the battery pack con-nects with a DC/DC converter in series before it is connected with the ultracapacitor pack in parallel has been selected for this study.This type has the potential to fully exert the dynamic performance of the ultracapacitor by avoiding the current/power impact of the bat-tery and to extend the calendar life of the HESS.To achieve optimal energy/power management for HEVs and plug-in HEVs,a number of strategies have been developed[10–12].The rule based strategy is the most direct and widely used method due to its easy implementation and high calculation effi-ciency[13–15].Jalil N et al.have proposed a rule-based strategy to determine the power split between the battery and engine for a ser-ies hybrid electric vehicle[15].To further improve the performance of the energy management system for hybrid electric vehicles,sev-eral optimal energy/power management methods have been pro-posed,such as methods based on a fuzzy logic approach[16]and an equivalent consumption minimization strategy[17].However, with the development of intelligent algorithms,multiple advanced algorithms such as neural network[18],particle swarm optimiza-tion[19],simulated annealing[20],model predictive control[21], and dynamic programming(DP)[22,23]have been widely employed to develop various advanced adaptive/online energy management systems and optimal strategies.With a prior knowledge of the driv-ing cycle,DP-based methods have the ability to locate the global optimal control strategy.However,the actual future driving cycles can hardly be known in advance.In this case,the DP-based strategies cannot be used for an online energy management.Few energy management methods have been conducted for more than two energy sources[13–28].Most publications have investigated control strategies for EVs and HEVs powered by the battery and engine or the battery and ultracapacitor[24–28]. Specifically,for a series plug-in HEV with HESS,the optimization allocation problem for electricity energy among the battery,ultra-capacitor and engine-generator has not been solved effectively.1.2.Motivation and innovationThe purpose of this study is to propose an adaptive energy man-agement approach via driving pattern recognition and dynamic pro-gramming and to improve the energy management efficiency for a plug-in HEV with a HESS.To avoid the adverse effects of the optimal result against unknown cycles,the driving pattern recognition(DPR) method has been employed to classify and train the typical driving patterns.With the DP algorithm,the micro-control strategies for dif-ferent classified driving patterns can be developed in a systematic ing the fuzzy control algorithm-based predictive approach, the current driving pattern can be recognized with a period of histor-ical driving information.To realize the optimal energy allocation between the engine-generator and HESS with less computational cost,a hierarchical control strategy has been proposed for three energy sources from a multi-scale view.The proposed energy man-agement strategy has been verified and evaluated by a combined driving cycle and Japanese10–15mode driving anization of the paperThis paper is organized as follows.Section2describes the con-figuration of the plug-in HEV and the original control strategy. Then,the classification of driving blocks,construction of DPR,sub-system modeling,DP formulation and energy management system are illustrated in Section3.The verification and evaluation of the proposed method are reported in Section4,and conclusions are drawn in Section5.2.Plug-in hybrid electric vehicle configuration2.1.Vehicle configurationThe structure of the researched target is illustrated in Fig.1. The electricity power of the plug-in HEV comes from two parts: the HESS and assistance power unit(APU).The APU consists of an80kW permanent magnetic generator and a 1.9L gasoline engine,and the rated power of the APU is75kW.Detailed mod-eling of the APU and HESS are introduced in Section3.2.The tar-get vehicle is an electric bus and its essential parameters are presented in Table1.2.2.Hierarchical energy management for the plug-in HEVThe energy management system of the plug-in HEV can be divided into two layers.The upper level is for controlling the energy between the APU and HESS,and the lower level is for con-trolling the energy between the battery and ultracapacitor.2.2.1.Upper level control strategyThe main objective of the energy management is to minimize the operation cost of the plug-in HEV.For optimizing the alloca-tion of energy/power between the HESS and APU,a systematic energy management strategy is necessary.The original control strategy of the researched plug-in HEV is a typical charge deplet-ing(CD)and charge sustaining(CS)method.Itfirst operates the plug-in HEV with the CD mode,which is similar to a pure electric vehicle,and then operates the plug-in HEV with the CS mode once its state-of-charge(SoC)level hit the lower threshold,which is similar to a traditional hybrid electric vehicle.The detailed original control rules in the CS model are identified by the required power of the plug-in HEV-P n and they are described by the following conditions.Condition I:P n<0.The HESS absorbs as much energy as possible,and the excess energy is consumed by the traditional mechanical braking system. It is noted that the APU is turned off in condition I.Condition II:P n P75kW.The output power of APUÀP APU will maintain to its rated power (75kW),and the insufficient power will be supported by the HESS.Condition III:06P n675kWIf the SoC of the battery pack(z b)is bigger than its lower thresh-old(z b,min),the HESS will provide the total required power and the APU will be in the off stage.If the SoC of the battery pack(z b)is smaller than its lower threshold(z b,min),the APU will work in the rated power condi-tion and the redundant power will be used to charge the HESS to its predetermined level.S.Zhang,R.Xiong/Applied Energy155(2015)68–78692.2.2.Lower level control strategyThe power management between the battery pack and ultraca-pacitor pack is implemented via a rule based control strategy with the following rules[28].Condition I:P HESS<0When the required power of HESS(P HESS)is negative,the ultra-capacitor pack will absorb as much braking energy as possible until its SoC is bigger than its upper threshold(z uc,max),and then the bat-tery is allowed to absorb the remaining energy.Condition II:P HESS P0If06P HESS<30kW,z b>0.201and z uc<0.85,then P b=30kW and P uc=P HESSÀP b.If06P HESS<30kW,z b>0.201and z uc P0.85,then P b=P HESS and P uc=0.If P HESS P30kW,z b>0.201and z uc P0.515,then P b=30kW and P uc=P HESSÀP b.If P HPESS P30kW,z b>0.201and z uc<0.515,then P b=P HESS and P uc=0.If P HESS P0kW,z b60.201and z uc P0.515,then P b=0and P uc=P HESS.If P HESS P0kW,z b60.201and z uc<0.515,then P b=0and P uc=0.where z b denotes the SoC of the battery pack,z uc denotes the SoC of the ultracapacitor pack,P b denotes the output power of the battery pack,and P uc denotes the output power of the ultracapac-itor pack.3.Decomposition of the drive cycles3.1.Driving blocks classificationThe traditional DPR method based power management approaches tend to use the existing unbroken driving cycles to classify the driving blocks and then develop the control strategies by recognizing a whole driving cycle[29–32].However,for a given driving cycle,these methods usually contain several types of driv-ing blocks that have been neglected in these methods.Fig.2illus-trates that different types of drive patterns may have similar driving blocks and that the same driving cycle may have different driving blocks.Thus,the control strategy developed by a whole driving cycle can hardly ensure the optimal vehicle performance. To overcome the drawback,a novel classification method that has the ability to classify the driving block into several groups has been proposed.The driving blocks from three typical drive cycles are plotted in Fig.2,which includes the Chinese Bus Driving Cycle(CBDC), ECEÀEUDC drive cycle and MANHATTAN drive cycle.For a deter-minate driving cycle,the number of description parameters may be as high as62[32].Too many parameters may unnecessarily bias the calculation.The average speed has been reported as the unique parameter to use in Ref.[33].This study considers the average and maximum speed of each block as its classification parameters.The calculation method for the average speed and maximum speed is displayed below:V ai¼Zv dt=tð1ÞV max i¼maxðv j;j¼1;2...kÞð2Þwhere V ai denotes the average speed of each driving block,i denotes the index of the driving blocks,and V maxi denotes the maximum speed of each driving block.The fuzzy logic controller is employed to classify the drive blocks and identify the driving types for the DPR process.The con-troller consists of four parts(as displayed in Fig.3),including fuzzi-fication,rule base,fuzzy reasoning and defuzzification.The fuzzification part is used to fuzzify the input values and these fuzzified values will be converted into the output fuzzy values through the fuzzy reasoning block based on the rule base part. Then,the output fuzzy variable will be defuzzified by theTable1Basic parameters of the plug-in HEV.Name Value UnitVehicle loaded mass M16,500kgEfficiency of the transmission system g00.9/Rolling resistance coefficient f0.011/Windward area A ar 6.6m2Air resistance coefficient C ar0.55/Gravitational acceleration g9.81m/s2Correction coefficient of rotating mass d 1.03/70S.Zhang,R.Xiong/Applied Energy155(2015)68–78defuzzification block.The details of the fuzzy logic controller oper-ation process are displayed below:(1)FuzzificationFuzzy sets represent the linguistic terms,and the linguistic terms of the input variables and output variable are set to Low ÀLevel (low speed driving pattern),Middle ÀLevel (medium speed driving pat-tern)and High ÀLevel (high speed driving pattern).It is worth noting that,for the low speed driving pattern,the maximum velocity is less than 25km/h,and the average velocity less than 15km/h.For the medium speed driving pattern,the maximum velocity is between 25km/h and 45km/h,and the average velocity is between 15km/h and 25km/h.For the high speed driving pattern,the maxi-mum velocity is greater than 45km/h,and the average velocity is greater than 25km/h.The input variables are fuzzified by member-ship functions as shown in Fig.4.Once the average speed and max-imum speed of a driving block are known,we can determine the memberships (Lower Àlevel l L (v ),Middle Àlevel l M (v )and High Àlevel l H (v ),where v denotes the input variables)through membership functions.After comparing these values,we can finally obtain the fuzzification results,which are the fuzzy sets.Rule baseFuzzificationOutput driving patternDrive block12i 8128 V ...V ...V max(,...)mn mn mn imn mn R R R R R R R R R R =⎧⎨=⎩S.Zhang,R.Xiong /Applied Energy 155(2015)68–7871(2)Rule baseThe rule base displayed in Table 2shows that the fuzzy logic is a typical type of the A +B ?C (if A and B,then C)mode,where A denotes the fuzzy sets of average speed,B denotes the fuzzy sets of maximum speed and C denotes the fuzzy sets of driving block pattern.The reasoning process is based on the Mamdani fuzzy theory [34].From each rule shown in Table 2,we can obtain a correspond-ing fuzzy relation matrix R i by the cross-product of A i and B i .The fuzzy relation matrix R can be obtained by the combination of the fuzzy relation matrix R i using the following equation:R ¼R 1V R 2...V R i ...V R 8R mn ¼max ðR 1mn ;R 2mn ...R imn :R 8mn Þð3Þwhere m and n (m =1,2,3and n =1,2,3)denote the index of matrix elements for R i and R .(3)Fuzzy reasoningWhen we obtain the fuzzification results of the input variables (A 1and B 1)and the fuzzy relation matrix R ,we can locate the driv-ing types using the following equation:C 1¼ðA 1ÂB 1Þ Rð4Þwhere C 1denotes the fuzzy set for the output variable.(4)DefuzzificationThe results obtained by Eq.(4)from a fuzzy set,which is not applicable under real conditions.Thus,we should convert the fuzzy set into a known driving pattern.The biggest subordinate principle is employed to locate the driving block pattern.According to this principle,the driving block pattern is located to the value whose membership is the biggest one in the domain of discourse.Fig.5shows the classification results.From Fig.5we can observe that most of the driving blocks have similar profiles in the rearranged drive cycles.Three drive cycles will be used for the power manage-ment design during the following DP process.3.2.Modeling for subsystemsThe correspondingly optimal control strategy can be developed through analyzing the DP optimization results under different types of driving conditions.By combining these strategies together with the proposed DPR process,a suboptimal solution for the energy management of the plug-in HEV can be achieved.Before the implementation of the DP formulation process,we should first build the subsystem models.Considering that the DP process relies on the state equations of the plug-in HEV powertrain system,if the total order number of the system is too high,the computational cost is usually unacceptable.In this way,simplified backward sim-ulation models for the HESS,APU and vehicle are developed.It is noting that the parameters of the battery pack,ultracapacitor pack and DC/DC converter in the HESS were determined by the Ref.[9].The models are described as follows.(1)APU modelAs an independent power unit in the series powertrain,the engine and generator are mechanically decoupled from the drive-line.The APU operates according to the maximum efficiency line.The optimal fuel rate line of the APU is derived from the APU effi-ciency map from a combination of the efficiency map between the engine and generator.The optimal fuel rate line of the APU system is shown in Fig.6(a).In this study,we neglect the APU transience influence and calculate the fuel consumption of the engine by its static operating points.Once the output power of APU is deter-mined,we can obtain the fuel consumption using the following equation:_m f ¼f ðP APU Þð5Þwhere _mf denotes fuel consumption and f ðP APU Þdescribes the map-ping function between the output power of APU and engine fuel rate according to the combined optimal fuel rate line presented in Fig.6(a).Fig.6(b)shows the fuel consumption when the APU output is 1kJ of energy under different output power conditions.From Fig.6(b)we can observe that the efficiency of the APU will increase with increasing output power,and when the output power reaches 75kW,the efficiency is at its highest.Thus,as the rated power and maximum power of APU,75kW is the best operation point of the APU.(2)Ultracapacitor model The dynamic property of the ultracapacitor is recognized as a series connection of a resistance R c (0.0756X )and an idealTable 2Rule base for the driving pattern recognition.V a ÀLowV a ÀMiddle V a ÀHigh V max ÀLow Low Middle –V max ÀMiddle Low Middle High V max ÀHighMiddleMiddleHigh72S.Zhang,R.Xiong /Applied Energy 155(2015)68–78capacitor (maximum voltage is 576V).The operation behavior of the ultracapacitor is illustrated by the following equation:U ct ¼U co ÀR c i c ð6Þwhere U ct is terminal voltage of ultracapacitor,U co denotes the ideal capacitor voltage and i c denotes the output current.(3)Battery modelTo execute the optimization and analyze the dynamic features of the battery,we need a ‘‘discrete-time cell dynamic model’’that relates the SoC to its voltage.Based on our research experience in battery control and state estimation [2,35],a classical lumped parameters battery model,the Thevenin model,has been selected for this study.Its electrical behavior can be expressed as the following:_U D ¼À1D D U D þ1D i L U t ¼U oc ÀU D Ài L R i(ð7Þwhere U oc denotes the open circuit voltage (OCV)of a battery,R i denotes the series resistance,and R D and C D denote the diffusion resistance and diffusion capacitance,respectively.The parameter i L denotes the load current (positive indicates discharging and neg-ative indicates charging),U D denotes the diffusion voltage and U t denotes terminal voltage.It is worth noting that the lithium-ion battery cell with graphite anodes and nickel–manganese–cobalt oxide (NMC)cathodes is used in this study,and its upper and lower cutoff voltages are 4.2V and 3.0V,respectively.Each cell has a nominal capacity of 79A h and nominal voltage of 3.7V.It is noted that the battery pack consists of 135lithium-ion battery cells con-nected in series.Thus,the nominal capacity and voltage of the bat-tery pack are 79A h and 499.5V,respectively.The total energy of the battery pack is 39kW h according to the energy requirement of the target vehicle.The parameters of the battery model have been obtained by the parameter identification method based on the recursive least squares filter described in Ref.[35].(4)DC/DC converter modelTo analyze the dynamic behavior of the HESS,we first need a model for the DC/DC converter.Table 3shows an efficiency map n (i DC ,P DC )to describe the operating behavior of the DC/DC con-verter,where i DC and P DC denote the output current and output power of the DC/DC converter,respectively.The current points contain four levels:i DC =10A,i DC =50A,i DC =100A,and i DC P 150A.The power points contain five levels:P DC =10kW;P DC =20kW;P DC =30kW;P DC =40kW;and P DC P 50kW.The rated power of the DC/DC converter is 30kW.(5)Vehicle and transmission modelIn this study we only consider the vehicle’s longitudinal dynam-ics,namely,the vehicle is modeled as a point-mass.The required power (P n )of the plug-in HEV can be calculated from Eq.(8)[36].Its transmission is modeled as a fixed efficiency g as shown in Eq.(8).P n ¼u a g Mgf cos ðb Þ3600þMg sin ðb Þ3600þC ar A ar 76140u 2a þd M 3600d u ad tð8Þwhere u a denotes the vehicle velocity and b represents the grade of the road.3.3.Formulation of the DP algorithmBased on the above models,the DP algorithm can be used to locate the optimal power distribution ratio between the APU and HESS.According to Bellman’s optimization theory,a numerical-based DP approach is adopted and the state equation of the battery model and ultracapacitor model can be generally expressed by the following equation:x ðk þ1Þ¼f ðx ðk Þ;u ðk ÞÞð9Þwhere x (k )denotes the state vector of system and u (k )denotes con-trol variable (power increment P iAPU ).The parameter x (k )can be cal-culated by the following equation:x ðk Þ¼P APU z b z uc U D ½ ð10ÞIt is obvious that we can reduce the state order by removing the output power of the APU from the state equation and selecting the output power as the control variable,but this reduction will lead to drastic fluctuations in the output power of the APU from the lowest working point directly to the highest working point;it is not reasonable.To reduce the dimensions of the optimization problem and improve the control efficiency for the multi-power system of the plug-in HEV,the energy management of the HESS employs the rule-based strategy,which has been illustrated in Section 2.2;this strategy is helpful for reducing the order of the state equation and calculation burden.Then,the control variable has been simplified to the power increment of the APU (P iAPU )and once the output power of the APU is provided then the output power of HESS will be determined according to the required power of the plug-in HEV.The detailed state equations of the APU,battery and ultracapac-itor are described by the following equation:P APU ðk þ1Þ¼P APU ðk ÞþP iAPU ðk Þð11ÞU D ðk þ1Þz b ðk þ1Þ¼exp ðÀD t =R D C D Þ001U D ðk Þz b ðk Þþð1Àexp ðÀD t =R D C D ÞÞR DÀ1=3600Q bi L ðk Þð12Þz uc ðk þ1Þ¼z uc ðk ÞÂQ c Ài cQ cð13Þwhere Q b and Q c denote the nominal capacity of the battery packand ultracapacitor pack,respectively,i L and i C denote the output current of the battery pack and the ultracapacitor pack respectively,and D t denotes the calculation step,which herein is set to1s .The optimization target is to locate the optimal control variable P iAPU to minimize a cost function (minimum usage costs),as dis-played below:J ¼X N À1k ¼0L ðx ðk Þ;u ðk ÞÞ¼X N À1k ¼0½L fuel ðx ðk Þ;u ðk ÞÞþL e ðx ðk Þ;u ðk ÞÞ L fuel ðx ðk Þ;u ðk ÞÞ¼_m ðk ÞM fuel L e ðx ðk Þ;u ðk ÞÞ¼i L ðk ÞU t ðk ÞM e8>>>><>>>>:ð14Þwhere N denotes the duration of the driving cycle,L denotes the instantaneous cost which represents usage costs,L fuel and L e denote the fuel and electric cost,respectively,and M fuel and M e denote the current fuel and electric price,respectively.It is noted that,M fuel and M e are set to 8.9908RMB per liter and 0.799RMB per KWH,respectively (according to the data on Dec.62014,in Beijing).During the optimization process,the following inequalityTable 3Efficiency map of the DC/DC converter [9].n (i DC ,P DC )10kW 20kW 30kW 40kW P 50kW 10A 92%95%97%95%94%50A 91%93%96%93%92%100A 88%91%95%92%91%P 150A82%89%92%91%90%S.Zhang,R.Xiong /Applied Energy 155(2015)68–7873constraints are necessary to ensure safe and reasonable operation of the APU and HPS:z b ;min 6z b ðk Þ6z b ;max z uc ;min 6z uc ðk Þ6z uc ;max j zuc ;end Àz uc ;start j 60:5%i L ;min 6i L ðk Þ6i L ;max i c ;min 6i c ðk Þ6i c ;max U t ;min 6U t ðk Þ6U t ;max8>>>>>>>><>>>>>>>>:ð15Þwhere z b,min and z b,max denote the lower and upper bounds of thebattery SoC,U t,min and U t,max denote the lower and upper con-strains of the battery terminal voltage,i L,min and i L max denote the lower and upper constrains of the battery current,and i c,min and i c,max denote the bounds of the ultracapacitor current.The param-eters z uc,start and z uc,end denote the start and end values of the SoC of the ultracapacitor pack during the optimization process.It is worth noting that less than 0.5%of the difference between the start and end SoC of the ultracapacitor pack indicates the energy consump-tion of ultracapacitor pack can be approximated to zero.In this study,z b,min and z b,max are set to 0.2and 1,respectively,U t,min and U t,max are set to be 405V and 567V,respectively,i L,min and i L,max are set to À158A (À2C)and 158A (2C),respectively,and i c,min and i c,max are set to À500A and 500A,respectively.According to the dynamic optimization theory of Bellman,we first need to solve the problem from the last stage and then we extend the problem to solve for the last two stages and last three stages until all of the stages are included.Under this condition the optimization problem has been decomposed into a sequence of minimization problems as shown below.Step N À1:J ÃN À1ðx ðN À1ÞÞ¼min u ðN À1Þ½L ðx ðN À1Þ;u ðN À1ÞÞþG ðx ðN ÞÞð16ÞStep k ,for 06k <N À1:J Ãk ðx ðk ÞÞ¼min u ðk Þ½L ðx ðk Þ;u ðk ÞÞþJ Ãk þ1ðx ðk þ1ÞÞð17Þwhere J k *(x (k ))denotes the optimal value function at state x (k )start-ing from k th time stage to the last stage.The operation of the opti-mization process is subject to constraints presented in Eq.(15).Because the APU and HESS are nonlinear systems,the DP optimiza-tion process has been implemented with some approximations.Quantization and interpolation are used to solve Eq.(17)numeri-cally.At each step,the function J k (x (k ))is only calculated at the grid points of the state variables.The values of J k *(x (k ))in Eq.(17)and G (x (N ))in Eq.(16)will be determined through linear interpolation when the next state does not fall on a quantized value.3.4.Power management design frameworkThe detailed development process of the adaptive energy man-agement for the plug-in HEV with the DPR and DP is illustrated in Fig.7.It mainly consists of four parts:driving cycle classification,system modeling,DP processing and DPR process.The detailed operation for each part has been described in the above sections.First,three typical drive cycles are used to train the representa-tive driving blocks with the fuzzy logic algorithm based on the driving cycle classification method.The driving cycle classification process is used to rearrange the driving blocks into several types of new cycles.Its classification is implemented with the average speed and maximum speed.Driving pattern recognitionOriginal driving cycleReal driving cycle Classified driving blocksFuzzy logic based classification module Fuzzy logic based DPR74S.Zhang,R.Xiong /Applied Energy 155(2015)68–78。

自动控制专业英语词汇（一）acceleration transducer 加速度传感器acceptance testing 验收测试accessibility 可及性accumulated error 累积误差AC-DC-AC frequency converter 交-直-交变频器AC (alternating current) electric drive 交流电子传动active attitude stabilization 主动姿态稳定actuator 驱动器，执行机构adaline 线性适应元adaptation layer 适应层adaptive telemeter system 适应遥测系统adjoint operator 伴随算子admissible error 容许误差aggregation matrix 集结矩阵AHP (analytic hierarchy process) 层次分析法amplifying element 放大环节analog-digital conversion 模数转换annunciator 信号器antenna pointing control 天线指向控制anti-integral windup 抗积分饱卷aperiodic decomposition 非周期分解a posteriori estimate 后验估计approximate reasoning 近似推理a priori estimate 先验估计articulated robot 关节型机器人assignment problem 配置问题，分配问题associative memory model 联想记忆模型associatron 联想机asymptotic stability 渐进稳定性attained pose drift 实际位姿漂移attitude acquisition 姿态捕获AOCS (attritude and orbit control system) 姿态轨道控制系统attitude angular velocity 姿态角速度attitude disturbance 姿态扰动attitude maneuver 姿态机动attractor 吸引子augment ability 可扩充性augmented system 增广系统automatic manual station 自动-手动操作器automaton 自动机autonomous system 自治系统backlash characteristics 间隙特性base coordinate system 基座坐标系Bayes classifier 贝叶斯分类器bearing alignment 方位对准bellows pressure gauge 波纹管压力表benefit-cost analysis 收益成本分析bilinear system 双线性系统biocybernetics 生物控制论biological feedback system 生物反馈系统black box testing approach 黑箱测试法blind search 盲目搜索block diagonalization 块对角化Boltzman machine 玻耳兹曼机bottom-up development 自下而上开发boundary value analysis 边界值分析brainstorming method 头脑风暴法breadth-first search 广度优先搜索butterfly valve 蝶阀CAE (computer aided engineering) 计算机辅助工程CAM (computer aided manufacturing) 计算机辅助制造Camflex valve 偏心旋转阀canonical state variable 规范化状态变量capacitive displacement transducer 电容式位移传感器capsule pressure gauge 膜盒压力表CARD 计算机辅助研究开发Cartesian robot 直角坐标型机器人cascade compensation 串联补偿catastrophe theory 突变论centrality 集中性chained aggregation 链式集结chaos 混沌characteristic locus 特征轨迹chemical propulsion 化学推进calrity 清晰性classical information pattern 经典信息模式classifier 分类器clinical control system 临床控制系统closed loop pole 闭环极点closed loop transfer function 闭环传递函数cluster analysis 聚类分析coarse-fine control 粗-精控制cobweb model 蛛网模型coefficient matrix 系数矩阵cognitive science 认知科学cognitron 认知机coherent system 单调关联系统combination decision 组合决策combinatorial explosion 组合爆炸combined pressure and vacuum gauge 压力真空表command pose 指令位姿companion matrix 相伴矩阵compartmental model 房室模型compatibility 相容性，兼容性compensating network 补偿网络compensation 补偿，矫正compliance 柔顺，顺应composite control 组合控制computable general equilibrium model 可计算一般均衡模型conditionally instability 条件不稳定性configuration 组态connectionism 连接机制connectivity 连接性conservative system 守恒系统consistency 一致性constraint condition 约束条件consumption function 消费函数context-free grammar 上下文无关语法continuous discrete event hybrid system simulation 连续离散事件混合系统仿真continuous duty 连续工作制control accuracy 控制精度control cabinet 控制柜controllability index 可控指数controllable canonical form 可控规范型[control] plant 控制对象,被控对象controlling instrument 控制仪表control moment gyro 控制力矩陀螺control panel 控制屏，控制盘control synchro 控制[式]自整角机control system synthesis 控制系统综合control time horizon 控制时程cooperative game 合作对策coordinability condition 可协调条件coordination strategy 协调策略coordinator 协调器corner frequency 转折频率costate variable 共态变量cost-effectiveness analysis 费用效益分析coupling of orbit and attitude 轨道和姿态耦合critical damping 临界阻尼critical stability 临界稳定性cross-over frequency 穿越频率，交越频率current source inverter 电流[源]型逆变器cut-off frequency 截止频率cybernetics 控制论cyclic remote control 循环遥控cylindrical robot 圆柱坐标型机器人damped oscillation 阻尼振荡damper 阻尼器damping ratio 阻尼比data acquisition 数据采集data encryption 数据加密data preprocessing 数据预处理data processor 数据处理器DC generator-motor set drive 直流发电机-电动机组传动D controller 微分控制器decentrality 分散性decentralized stochastic control 分散随机控制decision space 决策空间decision support system 决策支持系统decomposition-aggregation approach 分解集结法decoupling parameter 解耦参数deductive-inductive hybrid modeling method 演绎及归纳混合建模法delayed telemetry 延时遥测derivation tree 导出树derivative feedback 微分反馈describing function 描述函数desired value 希望值despinner 消旋体destination 目的站detector 检出器deterministic automaton 确定性自动机deviation 偏差deviation alarm 偏差报警器DFD 数据流图diagnostic model 诊断模型diagonally dominant matrix 对角主导矩阵diaphragm pressure gauge 膜片压力表difference equation model 差分方程模型differential dynamical system 微分动力学系统differential game 微分对策differential pressure level meter 差压液位计differential pressure transmitter 差压变送器differential transformer displacement transducer 差动变压器式位移传感器differentiation element 微分环节digital filer 数字滤波器digital signal processing 数字信号处理digitization 数字化digitizer 数字化仪dimension transducer 尺度传感器direct coordination 直接协调disaggregation 解裂discoordination 失协调discrete event dynamic system 离散事件动态系统discrete system simulation language 离散系统仿真语言discriminant function 判别函数displacement vibration amplitude transducer 位移振幅传感器dissipative structure 耗散结构distributed parameter control system 分布参数控制系统distrubance 扰动disturbance compensation 扰动补偿diversity 多样性divisibility 可分性domain knowledge 领域知识dominant pole 主导极点dose-response model 剂量反应模型dual modulation telemetering system 双重调制遥测系统dual principle 对偶原理dual spin stabilization 双自旋稳定duty ratio 负载比dynamic braking 能耗制动dynamic characteristics 动态特性dynamic deviation 动态偏差dynamic error coefficient 动态误差系数dynamic exactness 动它吻合性dynamic input-output model 动态投入产出模型econometric model 计量经济模型economic cybernetics 经济控制论economic effectiveness 经济效益economic evaluation 经济评价economic index 经济指数economic indicator 经济指标eddy current thickness meter 电涡流厚度计effectiveness 有效性effectiveness theory 效益理论elasticity of demand 需求弹性electric actuator 电动执行机构electric conductance levelmeter 电导液位计electric drive control gear 电动传动控制设备electric hydraulic converter 电-液转换器electric pneumatic converter 电-气转换器electrohydraulic servo vale 电液伺服阀electromagnetic flow transducer 电磁流量传感器electronic batching scale 电子配料秤electronic belt conveyor scale 电子皮带秤electronic hopper scale 电子料斗秤elevation 仰角emergency stop 异常停止empirical distribution 经验分布endogenous variable 内生变量equilibrium growth 均衡增长equilibrium point 平衡点equivalence partitioning 等价类划分ergonomics 工效学error 误差error-correction parsing 纠错剖析estimate 估计量estimation theory 估计理论evaluation technique 评价技术event chain 事件链evolutionary system 进化系统exogenous variable 外生变量expected characteristics 希望特性external disturbance 外扰fact base 事实failure diagnosis 故障诊断fast mode 快变模态feasibility study 可行性研究feasible coordination 可行协调feasible region 可行域feature detection 特征检测feature extraction 特征抽取feedback compensation 反馈补偿feedforward path 前馈通路field bus 现场总线finite automaton 有限自动机FIP (factory information protocol) 工厂信息协议first order predicate logic 一阶谓词逻辑fixed sequence manipulator 固定顺序机械手fixed set point control 定值控制FMS (flexible manufacturing system) 柔性制造系统flow sensor/transducer 流量传感器flow transmitter 流量变送器fluctuation 涨落forced oscillation 强迫振荡formal language theory 形式语言理论formal neuron 形式神经元forward path 正向通路forward reasoning 正向推理fractal 分形体，分维体frequency converter 变频器frequency domain model reduction method 频域模型降阶法frequency response 频域响应full order observer 全阶观测器functional decomposition 功能分解FES (functional electrical stimulation) 功能电刺激functional simularity 功能相似fuzzy logic 模糊逻辑game tree 对策树gate valve 闸阀general equilibrium theory 一般均衡理论generalized least squares estimation 广义最小二乘估计generation function 生成函数geomagnetic torque 地磁力矩geometric similarity 几何相似gimbaled wheel 框架轮global asymptotic stability 全局渐进稳定性global optimum 全局最优globe valve 球形阀goal coordination method 目标协调法grammatical inference 文法推断graphic search 图搜索gravity gradient torque 重力梯度力矩group technology 成组技术guidance system 制导系统gyro drift rate 陀螺漂移率gyrostat 陀螺体Hall displacement transducer 霍尔式位移传感器hardware-in-the-loop simulation 半实物仿真harmonious deviation 和谐偏差harmonious strategy 和谐策略heuristic inference 启发式推理hidden oscillation 隐蔽振荡hierarchical chart 层次结构图hierarchical planning 递阶规划hierarchical control 递阶控制homeostasis 内稳态homomorphic model 同态系统horizontal decomposition 横向分解hormonal control 内分泌控制hydraulic step motor 液压步进马达hypercycle theory 超循环理论I controller 积分控制器identifiability 可辨识性IDSS (intelligent decision support system) 智能决策支持系统image recognition 图像识别impulse 冲量impulse function 冲击函数，脉冲函数inching 点动incompatibility principle 不相容原理incremental motion control 增量运动控制index of merit 品质因数inductive force transducer 电感式位移传感器inductive modeling method 归纳建模法industrial automation 工业自动化inertial attitude sensor 惯性姿态敏感器inertial coordinate system 惯性坐标系inertial wheel 惯性轮inference engine 推理机infinite dimensional system 无穷维系统information acquisition 信息采集infrared gas analyzer 红外线气体分析器inherent nonlinearity 固有非线性inherent regulation 固有调节initial deviation 初始偏差initiator 发起站injection attitude 入轨姿势input-output model 投入产出模型instability 不稳定性instruction level language 指令级语言integral of absolute value of error criterion 绝对误差积分准则integral of squared error criterion 平方误差积分准则integral performance criterion 积分性能准则integration instrument 积算仪器integrity 整体性intelligent terminal 智能终端interacted system 互联系统，关联系统interactive prediction approach 互联预估法，关联预估法interconnection 互联intermittent duty 断续工作制internal disturbance 内扰ISM (interpretive structure modeling) 解释结构建模法invariant embedding principle 不变嵌入原理inventory theory 库伦论inverse Nyquist diagram 逆奈奎斯特图inverter 逆变器investment decision 投资决策isomorphic model 同构模型iterative coordination 迭代协调jet propulsion 喷气推进job-lot control 分批控制joint 关节Kalman-Bucy filer 卡尔曼-布西滤波器knowledge accomodation 知识顺应knowledge acquisition 知识获取knowledge assimilation 知识同化KBMS (knowledge base management system) 知识库管理系统knowledge representation 知识表达ladder diagram 梯形图lag-lead compensation 滞后超前补偿Lagrange duality 拉格朗日对偶性Laplace transform 拉普拉斯变换large scale system 大系统lateral inhibition network 侧抑制网络least cost input 最小成本投入least squares criterion 最小二乘准则level switch 物位开关libration damping 天平动阻尼limit cycle 极限环linearization technique 线性化方法linear motion electric drive 直线运动电气传动linear motion valve 直行程阀linear programming 线性规划LQR (linear quadratic regulator problem) 线性二次调节器问题load cell 称重传感器local asymptotic stability 局部渐近稳定性local optimum 局部最优log magnitude-phase diagram 对数幅相图long term memory 长期记忆lumped parameter model 集总参数模型Lyapunov theorem of asymptotic stability 李雅普诺夫渐近稳定性定理自动控制专业英语词汇（二）macro-economic system 宏观经济系统magnetic dumping 磁卸载magnetoelastic weighing cell 磁致弹性称重传感器magnitude-frequency characteristic 幅频特性magnitude margin 幅值裕度magnitude scale factor 幅值比例尺manipulator 机械手man-machine coordination 人机协调manual station 手动操作器MAP (manufacturing automation protocol) 制造自动化协议marginal effectiveness 边际效益Mason's gain formula 梅森增益公式master station 主站matching criterion 匹配准则maximum likelihood estimation 最大似然估计maximum overshoot 最大超调量maximum principle 极大值原理mean-square error criterion 均方误差准则mechanism model 机理模型meta-knowledge 元知识metallurgical automation 冶金自动化minimal realization 最小实现minimum phase system 最小相位系统minimum variance estimation 最小方差估计minor loop 副回路missile-target relative movement simulator 弹体-目标相对运动仿真器modal aggregation 模态集结modal transformation 模态变换MB (model base) 模型库model confidence 模型置信度model fidelity 模型逼真度model reference adaptive control system 模型参考适应控制系统model verification 模型验证modularization 模块化MEC (most economic control) 最经济控制motion space 可动空间MTBF (mean time between failures) 平均故障间隔时间MTTF (mean time to failures) 平均无故障时间multi-attributive utility function 多属性效用函数multicriteria 多重判据multilevel hierarchical structure 多级递阶结构multiloop control 多回路控制multi-objective decision 多目标决策multistate logic 多态逻辑multistratum hierarchical control 多段递阶控制multivariable control system 多变量控制系统myoelectric control 肌电控制Nash optimality 纳什最优性natural language generation 自然语言生成nearest-neighbor 最近邻necessity measure 必然性侧度negative feedback 负反馈neural assembly 神经集合neural network computer 神经网络计算机Nichols chart 尼科尔斯图noetic science 思维科学noncoherent system 非单调关联系统noncooperative game 非合作博弈nonequilibrium state 非平衡态nonlinear element 非线性环节nonmonotonic logic 非单调逻辑nonparametric training 非参数训练nonreversible electric drive 不可逆电气传动nonsingular perturbation 非奇异摄动non-stationary random process 非平稳随机过程nuclear radiation levelmeter 核辐射物位计nutation sensor 章动敏感器Nyquist stability criterion 奈奎斯特稳定判据objective function 目标函数observability index 可观测指数observable canonical form 可观测规范型on-line assistance 在线帮助on-off control 通断控制open loop pole 开环极点operational research model 运筹学模型optic fiber tachometer 光纤式转速表optimal trajectory 最优轨迹optimization technique 最优化技术orbital rendezvous 轨道交会orbit gyrocompass 轨道陀螺罗盘orbit perturbation 轨道摄动order parameter 序参数orientation control 定向控制originator 始发站oscillating period 振荡周期output prediction method 输出预估法oval wheel flowmeter 椭圆齿轮流量计overall design 总体设计overdamping 过阻尼overlapping decomposition 交叠分解Pade approximation 帕德近似Pareto optimality 帕雷托最优性passive attitude stabilization 被动姿态稳定path repeatability 路径可重复性pattern primitive 模式基元PR (pattern recognition) 模式识别P control 比例控制器peak time 峰值时间penalty function method 罚函数法perceptron 感知器periodic duty 周期工作制perturbation theory 摄动理论pessimistic value 悲观值phase locus 相轨迹phase trajectory 相轨迹phase lead 相位超前photoelectric tachometric transducer 光电式转速传感器phrase-structure grammar 短句结构文法physical symbol system 物理符号系统piezoelectric force transducer 压电式力传感器playback robot 示教再现式机器人PLC (programmable logic controller) 可编程序逻辑控制器plug braking 反接制动plug valve 旋塞阀pneumatic actuator 气动执行机构point-to-point control 点位控制polar robot 极坐标型机器人pole assignment 极点配置pole-zero cancellation 零极点相消polynomial input 多项式输入portfolio theory 投资搭配理论pose overshoot 位姿过调量position measuring instrument 位置测量仪posentiometric displacement transducer 电位器式位移传感器positive feedback 正反馈power system automation 电力系统自动化predicate logic 谓词逻辑pressure gauge with electric contact 电接点压力表pressure transmitter 压力变送器price coordination 价格协调primal coordination 主协调primary frequency zone 主频区PCA (principal component analysis) 主成分分析法principle of turnpike 大道原理priority 优先级process-oriented simulation 面向过程的仿真production budget 生产预算production rule 产生式规则profit forecast 利润预测PERT (program evaluation and review technique) 计划评审技术program set station 程序设定操作器proportional control 比例控制proportional plus derivative controller 比例微分控制器protocol engineering 协议工程prototype 原型pseudo random sequence 伪随机序列pseudo-rate-increment control 伪速率增量控制pulse duration 脉冲持续时间pulse frequency modulation control system 脉冲调频控制系统pulse width modulation control system 脉冲调宽控制系统PWM inverter 脉宽调制逆变器pushdown automaton 下推自动机QC (quality control) 质量管理quadratic performance index 二次型性能指标qualitative physical model 定性物理模型quantized noise 量化噪声quasilinear characteristics 准线性特性queuing theory 排队论radio frequency sensor 射频敏感器ramp function 斜坡函数random disturbance 随机扰动random process 随机过程rate integrating gyro 速率积分陀螺ratio station 比值操作器reachability 可达性reaction wheel control 反作用轮控制realizability 可实现性,能实现性real time telemetry 实时遥测receptive field 感受野rectangular robot 直角坐标型机器人rectifier 整流器recursive estimation 递推估计reduced order observer 降阶观测器redundant information 冗余信息reentry control 再入控制regenerative braking 回馈制动，再生制动regional planning model 区域规划模型regulating device 调节装载regulation 调节relational algebra 关系代数relay characteristic 继电器特性remote manipulator 遥控操作器remote regulating 遥调remote set point adjuster 远程设定点调整器rendezvous and docking 交会和对接reproducibility 再现性resistance thermometer sensor 热电阻resolution principle 归结原理resource allocation 资源分配response curve 响应曲线return difference matrix 回差矩阵return ratio matrix 回比矩阵reverberation 回响reversible electric drive 可逆电气传动revolute robot 关节型机器人revolution speed transducer 转速传感器rewriting rule 重写规则rigid spacecraft dynamics 刚性航天动力学risk decision 风险分析robotics 机器人学robot programming language 机器人编程语言robust control 鲁棒控制robustness 鲁棒性roll gap measuring instrument 辊缝测量仪root locus 根轨迹roots flowmeter 腰轮流量计rotameter 浮子流量计，转子流量计rotary eccentric plug valve 偏心旋转阀rotary motion valve 角行程阀rotating transformer 旋转变压器Routh approximation method 劳思近似判据routing problem 路径问题sampled-data control system 采样控制系统sampling control system 采样控制系统saturation characteristics 饱和特性scalar Lyapunov function 标量李雅普诺夫函数SCARA (selective compliance assembly robot arm) 平面关节型机器人scenario analysis method 情景分析法scene analysis 物景分析s-domain s域self-operated controller 自力式控制器self-organizing system 自组织系统self-reproducing system 自繁殖系统self-tuning control 自校正控制semantic network 语义网络semi-physical simulation 半实物仿真sensing element 敏感元件sensitivity analysis 灵敏度分析sensory control 感觉控制sequential decomposition 顺序分解sequential least squares estimation 序贯最小二乘估计servo control 伺服控制，随动控制servomotor 伺服马达settling time 过渡时间sextant 六分仪short term planning 短期计划short time horizon coordination 短时程协调signal detection and estimation 信号检测和估计signal reconstruction 信号重构similarity 相似性simulated interrupt 仿真中断simulation block diagram 仿真框图simulation experiment 仿真实验simulation velocity 仿真速度simulator 仿真器single axle table 单轴转台single degree of freedom gyro 单自由度陀螺single level process 单级过程single value nonlinearity 单值非线性singular attractor 奇异吸引子singular perturbation 奇异摄动sink 汇点slaved system 受役系统slower-than-real-time simulation 欠实时仿真slow subsystem 慢变子系统socio-cybernetics 社会控制论socioeconomic system 社会经济系统software psychology 软件心理学solar array pointing control 太阳帆板指向控制solenoid valve 电磁阀source 源点specific impulse 比冲speed control system 调速系统spin axis 自旋轴spinner 自旋体stability criterion 稳定性判据stability limit 稳定极限stabilization 镇定，稳定Stackelberg decision theory 施塔克尔贝格决策理论state equation model 状态方程模型state space description 状态空间描述static characteristics curve 静态特性曲线station accuracy 定点精度stationary random process 平稳随机过程statistical analysis 统计分析statistic pattern recognition 统计模式识别steady state deviation 稳态偏差steady state error coefficient 稳态误差系数step-by-step control 步进控制step function 阶跃函数stepwise refinement 逐步精化stochastic finite automaton 随机有限自动机strain gauge load cell 应变式称重传感器strategic function 策略函数strongly coupled system 强耦合系统subjective probability 主观频率suboptimality 次优性supervised training 监督学习supervisory computer control system 计算机监控系统sustained oscillation 自持振荡swirlmeter 旋进流量计switching point 切换点symbolic processing 符号处理synaptic plasticity 突触可塑性synergetics 协同学syntactic analysis 句法分析system assessment 系统评价systematology 系统学system homomorphism 系统同态system isomorphism 系统同构system engineering 系统工程tachometer 转速表target flow transmitter 靶式流量变送器task cycle 作业周期teaching programming 示教编程telemechanics 远动学telemetering system of frequency division type 频分遥测系统telemetry 遥测teleological system 目的系统teleology 目的论temperature transducer 温度传感器template base 模版库tensiometer 张力计texture 纹理theorem proving 定理证明therapy model 治疗模型thermocouple 热电偶thermometer 温度计thickness meter 厚度计three-axis attitude stabilization 三轴姿态稳定three state controller 三位控制器thrust vector control system 推力矢量控制系统thruster 推力器time constant 时间常数time-invariant system 定常系统，非时变系统time schedule controller 时序控制器time-sharing control 分时控制time-varying parameter 时变参数top-down testing 自上而下测试topological structure 拓扑结构TQC (total quality control) 全面质量管理tracking error 跟踪误差trade-off analysis 权衡分析transfer function matrix 传递函数矩阵transformation grammar 转换文法transient deviation 瞬态偏差transient process 过渡过程transition diagram 转移图transmissible pressure gauge 电远传压力表transmitter 变送器trend analysis 趋势分析triple modulation telemetering system 三重调制遥测系统turbine flowmeter 涡轮流量计Turing machine 图灵机two-time scale system 双时标系统ultrasonic levelmeter 超声物位计unadjustable speed electric drive 非调速电气传动unbiased estimation 无偏估计underdamping 欠阻尼uniformly asymptotic stability 一致渐近稳定性uninterrupted duty 不间断工作制，长期工作制unit circle 单位圆unit testing 单元测试unsupervised learing 非监督学习upper level problem 上级问题urban planning 城市规划utility function 效用函数value engineering 价值工程variable gain 可变增益，可变放大系数variable structure control system 变结构控制vector Lyapunov function 向量李雅普诺夫函数velocity error coefficient 速度误差系数velocity transducer 速度传感器vertical decomposition 纵向分解vibrating wire force transducer 振弦式力传感器vibrometer 振动计viscous damping 粘性阻尼voltage source inverter 电压源型逆变器vortex precession flowmeter 旋进流量计vortex shedding flowmeter 涡街流量计WB (way base) 方法库weighing cell 称重传感器weighting factor 权因子weighting method 加权法Whittaker-Shannon sampling theorem 惠特克-香农采样定理Wiener filtering 维纳滤波work station for computer aided design 计算机辅助设计工作站w-plane w平面zero-based budget 零基预算zero-input response 零输入响应zero-state response 零状态响应zero sum game model 零和对策模型z-transform z变换。

Adaptive neural tracking control for stochastic nonlinear strict-feedback systems with unknown inputsaturationHuanqing Wang a ,c ,Bing Chen a ,⇑,Xiaoping Liu b ,Kefu Liu b ,Chong Lin aaInstitute of Complexity Science,Qingdao University,Qingdao,266071Shandong,PR China bFaculty of Engineering,Lakehead University,Orillia,ON P7A 5E1,Canada cSchool of Mathematics and Physics,Bohai University,Jinzhou,121000Liaoning,PR Chinaa r t i c l e i n f o Article history:Received 11January 2013Received in revised form 4June 2013Accepted 22September 2013Available online 2October 2013Keywords:Adaptive neural tracking control Stochastic nonlinear system Input saturationBackstepping techniquea b s t r a c tIn this paper,the problem of adaptive neural tracking control is considered for a class of single-input/single-output (SISO)strict-feedback stochastic nonlinear systems with input saturation.To deal with the non-smooth input saturation nonlinearity,a smooth nonaffine function of the control input signal is used to approximate the input saturation function.Classical adaptive technique and backstepping are used for control synthesis.Based on the mean-value theorem,a novel adaptive neural control scheme is systematically derived without requiring the prior knowledge of bound of input saturation.It is shown that under the action of the proposed adaptive controller all the signals of the closed-loop system remain bounded in probability and the tracking error converges to a small neighborhood around the origin in the sense of mean quartic value.Two simulation examples are pro-vided to demonstrate the effectiveness of the presented results.Ó2013Elsevier Inc.All rights reserved.1.IntroductionIt is well known that stochastic disturbance,which is usually a source of instability of control systems,often exists in practical systems.Therefore,the control design of nonlinear stochastic systems has attracted increasing attention in recent years [9,10,16,27,29,30,36–38,49–54].Many control design approaches for deterministic nonlinear systems have been suc-cessfully extended to stochastic nonlinear systems.Especially,backstepping technique [18]has been a popular tool for con-trol design of stochastic nonlinear systems,see, e.g.,[9,10,16,27,29,30,49–52]and the reference therein.In [30],the quadratic Lyapunov function is used to solve the stabilization problem for stochastic nonlinear strict-feedback systems based on a risk-sensitive cost criterion,and the proposed controller guarantees globally asymptotic stability in probability.In [9,10],a quartic Lyapunov function is applied for control design and stability analysis of stochastic nonlinear strict-feedback and output-feedback pared with the quadratic Lyapunov function,the quartic Lyapunov function can be used to easily deal with the high-order Hessian term.Since then,the quartic Lyapunov function has been widely applied for con-trol design of stochastic nonlinear systems [16,29,49–52].However,the aforementioned control schemes maybe invalid to control stochastic systems with unknown nonlinear function,because they require that the nonlinear dynamics models are known precisely or the unknown parameters appear linearly with respect to known nonlinear functions.During the past decades,many approximation-based adaptive neural (or fuzzy)control approaches have been developed to control uncertain lower-triangular nonlinear systems,and lots of significant results have been reported,for example,see [2–5,12–14,19,22,23,25,26,28,35,39–42,44,46,55–58]for deterministic nonlinear systems and [8,21,33,43,47]for stochastic 0020-0255/$-see front matter Ó2013Elsevier Inc.All rights reserved./10.1016/j.ins.2013.09.043⇑Corresponding author.Tel.:+86053285953607.E-mail address:chenbing1958@ (B.Chen).nonlinear systems.In these proposed control schemes,radial basis function (RBF)neural networks (or fuzzy logic systems)are used to approximate uncertain smooth nonlinear functions,and then adaptive backstepping technique is applied to de-sign controllers.For the deterministic systems,Ge et al.[12–14]develop several adaptive neural control schemes for SISO nonlinear systems and multi-input and multi-output (MIMO)nonlinear systems.In [57,58],the problem of adaptive neural tracking control is considered for MIMO nonlinear systems with dead-zone.Then,for stochastic systems,Psillakis and Alex-andridis [33]proposes an adaptive neural network control scheme to solve the problem of output tracking control for uncer-tain stochastic nonlinear strict-feedback systems with unknown covariance noise.Alternatively,in [47],a fuzzy-based adaptive control scheme is presented for a class of uncertain strict-feedback stochastic nonlinear systems with unknown vir-tual control gain function.The proposed controller guarantees that all the signals in the closed-loop systems are semi-glob-ally uniformly bounded in probability.Recently,in [8,21,24,43],several approximation-based adaptive control approaches are proposed for some classes of stochastic nonlinear strict-feedback time-delay (or delay-free)systems.In many practical systems,input saturation is one of the most important non-smooth nonlinearities.It often severely lim-its the system performance,gives rise to undesirable inaccuracy or leads to instability [32].Therefore,the phenomenon of input saturation has to be considered when the controller is designed in practical industrial process control field.So far,many significant results on control design of the systems with input saturation have been obtained,for example,see [6,7,11,48,59].In [59],a globally stable adaptive control approach is presented for minimum phase SISO systems with input saturation.Chen et al.[6]proposes a robust adaptive neural control for a class of MIMO nonlinear systems with input non-linearities.By introducing auxiliary design systems to analyze the effect of input constraints,in [7],an adaptive tracking con-trol is proposed for a class of uncertain nonlinear systems with non-symmetric input constraints,and the derived controller guarantees that the closed-loop system is semi-globally uniformly ultimately bounded stability.Wen et al.[48]considers the problem of adaptive control for a class of uncertain nonlinear systems in the presence of input saturation and external dis-turbance,in which two new schemes are developed to compensate for the effects of the saturation nonlinearity and distur-bances.Though the aforementioned results take input saturation nonlinearity into account,the effect of stochastic disturbance is ignored.Note that stochastic disturbance and input constraint could be existed in many practical systems.Motivated by the above observations,this paper considers the problem of adaptive neural tracking control for the case of nonlinear strict-feedback systems with stochastic disturbance and input saturation simultaneously.The proposed adaptive neural control scheme guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error eventually con-verges to a small neighborhood around the origin in the sense of mean quartic pared with the existing results,the main idea of control design in this paper is that a smooth non-affine function of the control input signal is firstly used to approximate the saturation function,and furthermore,the mean-value theorem is used to transform the non-affine function into affine form,i.e.,g ðv Þ¼g v l v .Then,the classical adaptive technique and backstepping are used to design controller.The proposed design approach does not require the prior knowledge of the bound of input saturation.In addition,the number of adaptive parameters just depends on the order of the considered systems.So,it is reduced considerably.In this way,the computational burden is significantly alleviated.This paper is organized as follows.The preliminaries and problem formulation are given in Section 2.A novel adaptive neural control scheme is presented in Section 3.Section 4gives two simulation examples to illustrate the effectiveness of our results,and Section 5concludes the work.2.Preliminaries and problem formulationThe following notations are used throughout this paper.R denotes the set of all real numbers;R n indicates the real n-dimensional space.For a given vector or matrix X ,X T denotes its transpose;Tr{X }is its trace when X is a square matrix;and k X k denotes the Euclidean norm of a vector X .C i denotes the set of all functions with continuous i th partial derivative.Consider the following strict-feedback stochastic nonlinear system given by:dx i ¼ðg i ðx i Þx i þ1þf i ð x i Þþd i ðt ;x ÞÞdt þw T i ð x i Þdw ;16i 6n À1;dx n ¼ðg n ð x n Þu ðv Þþf n ð x n Þþd n ðt ;x ÞÞdt þw Tn ð x n Þdw ;y ¼x 1;8><>:ð1Þwhere x i ¼½x 1;x 2;...;x i T 2R i ,x =[x 1,x 2,...,x n ]T 2R n and y 2R are the state variables and the system output,respectively;w denotes an r-dimensional standard Brownian motion defined on the complete probability space (X ,F ,P )with X being a sam-ple space,F being a r -field,and P being a probability measure;f i (Á),g i (Á):R i ?R ,w i (Á):R i ?R r ,(i =1,2,...,n )stand for the unknown smooth nonlinear functions with f i (0)=0and w i (0)=0(16i 6n ),d i (Á),i =1,2,...,n are the external disturbance uncertainties of the system.v is the control signal to be designed,and u (v )denotes the plant input subject to saturation non-linearity described byu ðv Þ¼sat ðv Þ¼sign ðv Þu max ;j v j P u max ;v ;j v j <u max ;&ð2Þwhere u max is a unknown parameter of input saturation.H.Wang et al./Information Sciences 269(2014)300–315301Remark 1.There exist many practical systems which are described by strict-feedback form,such as One-Link Robot system,Pendulum System With Motor,Single-Link Manipulator system [55],and Brusselator model [45].Meanwhile,stochastic disturbance and input saturation are inevitable in practical process.Therefore,the aforementioned systems can be governed by nonlinear differential equations of the form (1).The control objective is to design an adaptive neural controller for system (1)such that the system output y follows the specified desired trajectory y d and all the signals in the closed-loop systems remain bounded in probability.From (2),it can be seen that there exists a sharp corner when j v j =u max .So backstepping technique cannot be directly applied to construct control input signal.To solve this problem,the method proposed in [48]will be implemented.By this method,a smooth function is used to approximate the saturation function and defined asg ðv Þ¼u max Ãtanh ðv =u max Þ¼u max Ãe v =u max Àe Àv =u maxv max v max:ð3ÞThen,sat (v )in (2)can be expressed in the following form:sat ðv Þ¼g ðv Þþd ðv Þ;ð4Þwhere d (v )=sat (v )Àg (v )is a bounded function and its bound can be obtained asj d ðv Þj ¼j sat ðv ÞÀg ðv Þj 6u max ð1Àtanh ð1ÞÞ¼D :ð5ÞFig.1shows the saturation nonlinearity in (2)and its approximation function in (3).According to the mean-value theorem [1],there exists a constant l with 0<l <1,such thatg ðv Þ¼g ðv 0Þþg v l ðv Àv 0Þ;ð6Þwhere g v l ¼@g ðv Þv j v ¼v l¼4ðe =u max þe À=u max Þj v ¼v l ,v l =l v +(1Àl )v 0.By choosingv 0=0,(6)can be written asg ðv Þ¼g v l v ;ð7ÞSubstituting (4)into (1)and using (7)givesdx i ¼ðg i ðx i Þx i þ1þf i ð x i Þþd i ðt ;x ÞÞdt þw T i ð x i Þdw ;16i 6n À1;dx n ¼ðg n ð x n Þðg v l v þd ðv ÞÞþf n ð x n Þþd n ðt ;x ÞÞdt þw T n ð x n Þdw ;y ¼x 1:8><>:ð8ÞTo facilitate control system design,the following assumptions and lemmas are presented and will be used in the subsequent developments.Assumption 1([3,14]).For 16i 6n ,the function g i ðx i Þis unknown,but the sign of g i ð x i Þdoes not change,and there exist unknown constants b m and b M ,such that0<b m 6j g i ð x i Þj 6b M <1;8 x i 2R i :ð9ÞApparently,(9)implies that g i ðx i Þis strictly either positive or negative.Without loss of generality,it is further assumed that 0<b m 6g i ð x i Þ6b M ;8x i 2R i :ð10ÞAssumption 2[45].For 16i 6n ,thereexistunknownsmoothpositivefunctionsh i ð x i Þsuchthat8ðt ;x Þ2R þÂX ;j d i ðt ;x Þj 6h i ðx i Þ.302H.Wang et al./Information Sciences 269(2014)300–315Assumption 3[3].The desired trajectory y d (t )and its n th order time derivatives are continuous and bounded.To introduce some useful conceptions and lemmas,consider the following stochastic system:dx ¼f ðx Þdt þh ðx Þdw ;ð11Þwhere x and w are defined in (1),and f (Á)and h (Á)are locally Lipschitz functions in x and satisfy f (0)=0and h (0)=0.Definition 1.For any given V (x )2C 2,associated with the stochastic differential Eq.(11),define the differential operator L as follows:LV ¼@V @x f þ12Tr h T@2V @x 2h ();ð12Þwhere Tr (A )is the trace of A .Remark 2.As stated in [29],the term 1Tr h T @2Vh n ois called It ^o correction term or high-order Hessian term,in which the second-order differential @2V2makes the controller design much more difficult than that of the deterministic system.Definition 2[17].The solution process {x (t ),t P 0}of stochastic system (11)is said to be bounded in probability,if lim c ?1sup 06t <1P{k x (t )k >c }=0,where P{B }denotes the probability of event B .Lemma 1[33].Consider the stochastic system (11).If there exists a positive definite,radially unbounded,twice continuously dif-ferentiable Lyapunov function V :R n !R ,and constants a 0>0,b 0P 0such thatLV ðx Þ6Àa 0V ðx Þþb 0;then (i)the system has a unique solution almost surely and (ii)the system is bounded in probability.Lemma 2(Young’s inequality [9]).For "(x,y)2R 2,the following inequality holds:xy 6e ppj x j p þ1q eq j y j q ;where e >0,p >1,q >1,and (p À1)(q À1)=1.Lemma 3[31].For any variable g 2R and constant>0,the following inequality holds.06j g j Àg tanhg6d ;d ¼0:2785:ð13ÞIn this note,the following RBF neural networks will be used to approximate any continuous function f (Z ):R n ?R ,f nn ðZ Þ¼W T S ðZ Þ;ð14Þwhere Z 2X Z &R q is the input vector with q being the neural networks input dimension,weight vector W =[w 1,w 2,...,w l ]-T2R l ,l >1is the neural networks node number,and S (Z )=[s 1(Z ),s 2(Z ),...,s l (Z )]T means the basis function vector with s i (Z )being chosen as the commonly used Gaussian function of the forms i ðZ Þ¼exp ÀðZ Àl i ÞT ðZ Àl i Þr 2"#;i ¼1;2;...;l ;ð15Þwhere l i =[l i 1,l i 2,...,l iq ]T is the center of the receptive field and r is the width of the Gaussian function.In [34],it has been indicated that with sufficiently large node number l ,the RBF neural networks (14)can approximate any continuous function f (Z )over a compact set X Z &R q to arbitrary any accuracy e >0asf ðZ Þ¼W ÃTS ðZ Þþd ðZ Þ;8z 2X z 2R q ;ð16Þwhere W ⁄is the ideal constant weight vector and defined asW Ã:¼arg min W 2lsup Z 2X Zj f ðZ ÞÀW T S ðZ Þj ();and d (Z )denotes the approximation error and satisfies j d (Z )j 6e .H.Wang et al./Information Sciences 269(2014)300–315303Lemma 4[20].Consider the Gaussian RBF networks (14)and (15).Let q :¼12min i –j kl i Àl j k ,then an upper bound of k S(Z)k istaken ask S ðZ Þk 6X 1k ¼03q ðk þ2Þq À1e À2q 2k 2=r 2:¼s :ð17ÞIt has been shown in [44]that the constant s in Lemma 3is a limited value and is independent of the variable Z and the dimension of neural weights l .3.Adaptive neural control designIn this section,a backstepping-based design procedure will be proposed to construct the adaptive neural tracking control-ler for the original systems (1)with input saturation nonlinearity (2).The design procedure contains n steps and involves the following coordinate transformation:z 1¼x 1Ày d ;z i ¼x i Àa i À1;i ¼2;...;n ;ð18Þwhere a i is a virtual control signal to be designed for the corresponding i -subsystem based on an appropriate Lyapunov func-tion V i .During the design procedure,the virtual control signal and adaptive law will be constructed in the following form:a i ðZ i Þ¼Àk i z i À^h i k S i ðZ i Þk tanhz 3i k S i ðZ i Þk i;ð19Þ_^h i ¼Àc i ^h i þk i z 3i k S i ðZ i Þk tanh z 3i k S i ðZ i Þk a i;ð20Þwhere 16i 6n ,k i ,a i ,c i and k i are positive design contants,S i (Z i )is the RBF neural network basis function vector with Z 1¼½x 1;y d ;_y d T 2X Z 1&R 3;Z i ¼ x T i ; ^h T i À1; y ði ÞT d h i T 2X Z i &R 2i þ2ði ¼2;...;n Þ; ^h i ¼½^h 1;^h 2;...;^h i T . yði Þd denotes the vector composed of y d and up to its i th order time derivative,^h i is the estimation of an unknown constant h i which will be given at the i th step,Specially,a n denotes the actual control input v .Remark 3.It is easy to prove from (20)that if initial condition ^h i ð0ÞP 0,then ^h i ðt ÞP 0for all t P 0.Note that ^h i is an estimation of h i ,and the initial condition of (20)can be given by designer.So,it is reasonable to choose ^h i ð0ÞP 0.Thisproperty will be used in each step of control design.In the following,for simplicity,the time variable t and the state vector x i will be omitted from the corresponding functions and denote S i (Z i )by S i .Step 1:Since z 1=x 1Ày d ,the first subsystem of (1)givesdz 1¼ðg 1x 2þf 1þd 1À_y d Þdt þw T 1dw :ð21ÞConsider Lyapunov function candidate asV 1¼1z 41þb m 1~h 21;ð22Þwhere ~h 1¼h 1À^h 1is the parameter error.It can be verified easily from (12)along (21)and using the completion of squares thatLV 16z 31g 1x 2þf 1þd 1À_y d þ34l À21z 1k w 1k 4þ34l 21Àb m k 1~h 1_^h 1;ð23Þwhere l 1is a design constant.By means of Assumption 3,the following inequality holds:z 31d 16j z 1j 3h 1ðx 1Þ612g211z 61h 21ðx 1Þþ12g 211:ð24ÞSubstituting (24)into (23)yieldsLV 16z 31ðg 1x 2þ f 1ðZ 1ÞÞÀ3z 41À3g 1z 41þ3l 21þ1g 211Àb m 1~h 1_^h 1;ð25Þwhere f 1ðZ 1Þ¼f 1À_y d þ12g 211z 31h 21ðx 1Þþ34l À21z 1k w 1k 4þ34z 1þ34g 1z 1.Since the smooth functions f 1,g 1,h 1and w 1are unknown, f 1ðZ 1Þcannot be directly used to construct virtual control signal a 1.Thus,an RBF neural network W T 1S 1ðZ 1Þis employed toapproximate the function f 1ðZ 1Þsuch that,for any given e 1>0,f 1ðZ 1Þ¼W T 1S 1ðZ 1Þþd 1ðZ 1Þ;j d 1ðZ 1Þj 6e 1ð26Þ304H.Wang et al./Information Sciences 269(2014)300–315with d 1(Z 1)being the approximation error.Then,according to Lemma 3,one hasz 31 f 1ðZ 1Þ¼z 31W T1S 1þz 31d 16j z 31jk W 1kk S 1kþ34z 41þ14e 416z 31b m h 1k S 1k tanh z 31k S 1k a 1þd b m h 1a 1þ34z 41þ14e 41;ð27Þwhere the unknown constant h 1¼k W 1k m.Substituting (26)into (25)and using (27)givesLV 16z 31g 1z 2þz 31g 1a 1þz 31b m h 1k S 1k tanhz 31k S 1k 1þd b m h 1a 1þ1e 41À3g 1z 41þ3l 21þ1g 211Àb m 1~h 1_^h 1;ð28Þwhere z 2=x 2Àa 1.At the present stage,constructing the virtual control signal a 1asa 1¼Àk 1z 1À^h 1k S 1k tanhz 31k S 1k a 1;ð29Þthen using (10),we havez 31g 1a 16Àk 1b m z 41Àz 31b m ^h 1k S 1k tanhz 31k S 1k a 1:ð30ÞFrom (30),rewrite (28)asLV 16Àk 1b m z 41þz 31g 1z 2À3g 1z 41þd b m h 1a 1þ1e 41þ3l 21þ1g 211þb m 1~h 1k 1z 31k S 1k tanh z 31k S 1k 1 À_^h 1:ð31ÞBy choosing adaptive law _^h 1in (20)with i =1,it followsLV 16Àk 1b m z 41þz 31g 1z 2þd b m h 1a 1þ14e 41þ34l 21þ12g 211þb m c1k 1~h 1^h 1:ð32ÞFurthermore,applying Young’s inequality yieldsz 31g 1z 263g 1z 41þ1g 1z 42;ð33Þb m c 1k 1~h 1^h 1¼Àb m c 1k 1~h 21þb m c 1k 1~h 1h 16Àb m c 12k 1~h 21þb m c 12k 1h 21:ð34ÞUsing (33)and (34),we can further haveLV 16Àk 1b m z 41Àb mc 12k 1~h 21þd b m h 1a 1þ14e 41þ34l 21þ12g 211þb m c 12k 1h 21þ14g 1z 426Àc 1z 41Àb m c 12k 1~h 21þq 1þ14g 1z 42;ð35Þwhere c 1¼k 1b m ;q 1¼d b m h 1a 1þb m c 11h 21þ1e 41þ3l 21þ1g 211.The term 1g 1z 42will be dealt with in the next step.Step 2:From z 2=x 2Àa 1and It ^oformula,we have dz 2¼ðg 2x 3þf 2þd 2À‘a 1Þdt þw 2À@a 1@x 1w 1Tdw ;ð36Þwhere‘a 1¼@a 1@x 1ðg 1x 2þf 1þd 1ÞþN 1ð37ÞwithN 1¼X 1j ¼0@a 1@y ðj Þdy ðj þ1Þdþ@a 1@^h 1_^h 1þ12@2a 1@x 21w T1w 1:ð38ÞChoose the Lyapunov function asV 2¼V 1þ14z 42þb m 2k 2~h 22:ð39ÞFurthermore,by (12)it can be verified thatLV 2¼LV 1þz 32ðg 2x 3þf 2þd 2À‘a 1Þþ3z 22w 2À@a 11w 1 T w 2À@a 11w 1Àb m 2~h 2_^h 2:ð40ÞBy substituting (31)and (37)into (40)and using the completion squares to the term next to the last one in (40),one hasH.Wang et al./Information Sciences 269(2014)300–315305LV26Àc1z41Àb m c12k1~h21þq1þ14g1z42þz32g2x3þf2þd2À@a1@x1ðg1x2þf1þd1ÞÀN1þ34lÀ22z2k w2À@a1@x1w1k4þ34l22Àb mk2~h2_^h2;ð41Þwhere l2is a positive design ing the similar way to(24)yieldsÀz32@a1@x1d16j z32j@a1@x1h1612g21z62@a1@x12h21þ12g221;ð42Þz3 2d2612g222z62h22þ12g222:ð43ÞWith the help of(42)and(43),(41)can be written asLV26Àc1z41Àb m c11~h21þq1þz32g2x3þ f2ðZ2ÞÀÁÀ3z42À3g2z42þ3l22þ1X2j¼1g22jÀb m2~h2_^h2;ð44Þwheref 2ðZ2Þ¼f2À@a1@x1ðg1x2þf1Þþ14g1z2ÀN1þ3z24l2k w2À@a1@x1w1k4þ12g21z32@a1@x12h21þ12g22z32h22þ34z2þ34g2z2:ð45ÞNote that f2ðZ2Þis an unknown smooth function.Therefore,an RBF neural network W T2S2ðZ2Þis used to model the unknownf2ðZ2Þsuch thatf 2ðZ2Þ¼W T2S2ðZ2Þþd2ðZ2Þ;ð46Þwhere the approximate error d2(Z2)satisfies j d2(Z2)j6e2with e2being a given positive constant.Similar to(27),the following inequality holds.z3 2 f2ðZ2Þ6z32b m h2k S2k tanhz32k S2ka2þd b m h2a2þ34z42þ14e42;ð47Þwhere the unknown constant h2¼k W2kb m.Substituting(46)into(44)and using the inequality(47),we haveLV26Àc1z41Àb m c11~h21þq1þd b m h2a2þ1e42þ3l22þ1X2j¼1g22jþz32g2z3þz32g2a2þz32b m h2k S2k tanhz32k S2k2À34g2z42Àb mk2~h2_^h2;ð48Þwhere z3=x3Àa2.Then,take a2in(19)and^h2in(20)into account with i=2,the following inequalities can be obtained.z3 2g2a26Àk2b m z42Àz32b m^h2k S2k tanhz32k S2ka2;ð49Þz3 2g2z3634g2z42þ14g2z43:ð50ÞBy using the above inequalities,we can rewrite(48)asLV26ÀX2j¼1c j z4jÀb m c12k1~h21þq1þd b m h2a2þ14e42þ34l22þ12X2j¼1g22jþb m c2k2~h2^h2þ14g2z436ÀX2j¼1c j z4jÀX2j¼1b mc jj~h2jþX2j¼1qjþ1g2z43;ð51Þwhere c j¼k j b m;q j¼d b m h j a jþb m c jj h2jþ1e4jþ3l2jþ1P jk¼1g2jk;j¼1;2,and the inequality~h2^h26À1~h22þ1h22has been used.Step i(36i6nÀ1):By using(18)and It^o formula,one hasdz i¼ðg i x iþ1þf iþd iÀ‘a iÀ1Þdtþw iÀX iÀ1j¼1@a iÀ1@x jwj!Tdw;ð52Þwhere‘a iÀ1¼X iÀ1j¼1@a iÀ1jðg j x jþ1þf jþd jÞþN iÀ1ð53Þ306H.Wang et al./Information Sciences269(2014)300–315with N iÀ1¼P iÀ1j¼1@a iÀ1@^h j_^hjþP iÀ1j¼0@a iÀ1@yðjÞdyðjþ1Þdþ12P iÀ1p;q¼1@2a iÀ1@x p@x qw Tpwq.Consider Lyapunov function asV i¼V iÀ1þ1z4iþb mi~h2i:ð54ÞIt follows immediately from(12)thatLV i¼LV iÀ1þz3i ðg i x iþ1þf iþd iÀ‘a iÀ1Þþ32z2iwiÀX iÀ1j¼1@a iÀ1@x jwj!TwiÀX iÀ1j¼1@a iÀ1@x jwj!Àb mk i~hi_^hi;ð55Þwhere the term LV iÀ1can be obtained by a straightforward calculation as former steps.LV iÀ16ÀX iÀ1j¼1c j z4jÀX iÀ1j¼1b mc jj~h2jþX iÀ1j¼1qjþ1giÀ1z4i;ð56Þwhere c j¼k j b m;q j¼d b m h j a jþb m c jj h2jþ1e4jþ3l2jþ1P jk¼1g2jk;j¼1;2;...;iÀ1.By using the completion of squares,the following inequality holds:3 2z2iwiÀX iÀ1j¼1@a iÀ1@x jwj2634l2iþ34lÀ2iz4iwiÀX iÀ1j¼1@a iÀ1@x jwj4;ð57Þwhere l i is a positive design parameter.Next,by following a same line used in the procedures from(42)and(43),we haveÀz3iX iÀ1j¼1@a iÀ1@x jd j6X iÀ1j¼1j z i j3j@a iÀ1@x jj h j6X iÀ1j¼112g2ijz6i@a iÀ1@x j2h2jþX iÀ1j¼112g2ij;ð58Þz3 i d i612g2iiz6ih2iþ12g2ii:ð59ÞFurther,substituting(53),(56)and(57)into(55)and using the formulas(58),(59)and(55)can be rewritten asLV i6ÀX iÀ1j¼1c j z4jÀX iÀ1j¼1b mc jj~h2jþX iÀ1j¼1qjþz3iðg i x iþ1þ f iðZ iÞÞÀ3z4iÀ3giz4iþ3l2iþ1X ij¼1g2ijÀb mi~hi_^hi;ð60Þwhere f iðZ iÞis defined asf i ðZ iÞ¼f iÀX iÀ1j¼1@a iÀ1@x jðg j x jþ1þf jÞÀN iÀ1þ34lÀ2iz i k w iÀX iÀ1j¼1@a iÀ1@x jwjk4þX iÀ1j¼112g ijz3i@a iÀ1@x j2h2jþ12g iiz3ih2iþ14giÀ1z i þ34z iþ34giz ið61ÞCurrently,by employing a neural networks W TiS iðZ iÞto approximate the unknown smooth function f iðZ iÞand constructing the virtual control law a i and adaptive law_^h i defined respectively in(19)and(20),and then repeating the similar procedure from(27)–(35)in Step1,the following result is true.LV i6ÀX ij¼1c j z4jÀX ij¼1b mc j2k j~h2jþX ij¼1qjþ14giz4iþ1;ð62Þwhere c j¼k j b m;q j¼d b m h j a jþb m c j2k j h2jþ14e4jþ34l2jþ12P jk¼1g2jk;j¼1;2; (i)Step n:This is thefinal step,and the actual control input v will be constructed.By(18)and It^o formula,we havedz n¼ðg nðg vl vþdðvÞÞþf nþd nÀ‘a nÀ1ÞdtþwnÀX nÀ1j¼1@a nÀ1jwj!Tdw;where‘a nÀ1is given in(53)with i=n.Choose the following Lyapunov function candidate:V n¼V nÀ1þ14z4nþg2k n~h2n;H.Wang et al./Information Sciences269(2014)300–315307。

自动化专业英语常用词汇acceleration transducer 加速度传感器accumulatederror 累积误差AC-DC-AC frequency converter 交 -直 -交变频器AC (alternating current)electric drive 交流电子传动active attitudestabilization 主动姿态稳定adjointoperator 伴随算子admissibleerror 容许误差amplifyingelement 放大环节analog-digital conversion 模数转换operationalamplifiers 运算放大器aperiodic decomposition 非周期分解approximate reasoning 近似推理a prioriestimate 先验估计articulatedrobot 关节型机器人asymptoticstability 渐进稳定性attained posedrift 实际位姿漂移attitudeacquisition 姿态捕获AOCS ( attitude and orbit control system) 姿态轨道控制系统attitude angular velocity 姿态角速度attitude disturbance 姿态扰动automatic manual station 自动 -手动操作器automaton 自动机base coordinate system 基座坐标系bellows pressure gauge 波纹管压力表gauge 测量仪器black box testingapproach 黑箱测试法bottom-up development 自下而上开发boundary value analysis 边界值分析brainstorming method 头脑风暴法CAE (computer aided engineering) 计算机辅助工程CAM (computer aided manufacturing) 计算机辅助制造capacitive displacement transducer 电容式位移传感器capacity 电容displacement 位移capsule pressure gauge 膜盒压力表rectangular coordinatesystem 直角坐标系cascade compensation 串联补偿using series or parallel capacitors 用串联或者并联的电容chaos 混沌calrity 清晰性classical informationpattern 经典信息模式classifier 分类器clinical control system 临床控制系统closed loop pole 闭环极点open loop 开环closed loop transfer function 闭环传递函数combined pressure and vacuum gauge 压力真空表command pose 指令位姿companion matrix 相伴矩阵compatibility 相容性，兼容性compensating network 补偿网络Energy is conserved in all of its forms 能量是守恒的compensation 补偿，矫正conditionally instability 条件不稳定性configuration 组态connectivity 连接性conservative system 守恒系统consistency 一致性constraint condition 约束条件control accuracy 控制精度Gyroscope 陀螺仪control panel 控制屏，控制盘control system synthesis 控制系统综合corner frequency 转折频率coupling of orbit and attitude 轨道和姿态耦合critical damping 临界阻尼Damper 阻尼器临界 criticalcritical stability 临界稳定性cross-overfrequency 穿越频率，交越频率cut-off frequency 截止频率cybernetics 控制论cyclic remotecontrol 循环遥控cycle 循环 cyclic cylindrical robot 圆柱坐标型机器人damped oscillation 阻尼振荡oscillation 振荡；振动；摆动damper 阻尼器damping ratio 阻尼比ratio 比data acquisition 数据采集data preprocessing 数据预处理data processor 数据处理器D controller 微分控制器微分控制： Differentialcontrol积分控制： integralcontrol 比例控制： proportional controldescribing function 描述函数desired value 希望值真值： truthvalues 参考值： reference valuedestination 目的站detector 检出器deviation 偏差deviation alarm 偏差报警器differential dynamicalsystem 微differential pressure level meter差压液位计 meter=gauge仪表differen tial差别的 微分的differential pressure transmitter 差压变送器differential transformer displacement transducerdifferentiation element 微分环节差动变压器式位移传感器digital filer 数字滤波器 fil ter滤波器digital signal processing数字信号处理dimension transducer 尺度传感器discrete system simulation language 离散系统仿真语言discrete 离散的 不连续的displacement vibration amplitude transducer 位移振幅传感器 幅度： amplitude distrubance 扰动disturbance compensation 扰动补偿diversit y 多样性 divisibi lity 可分性domain knowledge 领域知识dominant pole 主导极点 零点 zero 调制： modulation ； modulate 解调： demodulation countermodulatio n duty ratio 负载 比 dynamic characteristics 动态特性 dynamic deviation 动态偏差dynamic error coefficient 动态误差系数 dynamic input-output model 动态投入产出模型Index 指数eddy current thickness meter 电涡流厚度计 meter 翻译成计 gauge 翻译成表 electric conductance level meter 电导液位计 electromagnetic flow transducer 电磁流量传感器electronic batching scale 电子配料秤 scale 秤electronic belt conveyor scale 电子皮带秤 electronic hopper scale 电子料斗秤elevation 仰角depression 俯角equilibrium point 平衡点error 误差estimate 估计量estimation theory 估计理论expected characteristics 希望特性failure diagnosis 故障诊断feasibility study 可行性研究feasible 可行的feasible region 可行域feature detection 特征检测feature extraction 特征抽取feedback compensation 反馈补偿Feed forward path 前馈通路前馈： feed forward 反馈 feedbackFMS ( flexible manufacturing system) 柔性制造系统柔性： flexible 刚性： rigiditybending deflection 弯曲挠度deflect 偏向偏离flow sensor/transducer流量传感器flow transmitter 流量变送器forward path 正向通路frequency converter 变频器frequency domain model reduction me thod 频域模型降阶法频域frequency response 频域响应functional decomposition 功能分解FES (functional electrical stimulation ) 功能电刺激stimulate 刺激functional simularity 功能相似fuzzy logic 模糊逻辑generalized least squares estimation 广义最小二乘估计geometric similarity 几何相似global optimum 全局最优goal coordinationmethod 目标协调法graphic search 图搜索guidance system 制导系统gyro drift rate 陀螺漂移率gyrostat 陀螺体Hall displacement transducer 霍尔式位移传感器horizontaldecomposition 横向分解hydraulic step motor 液压步进马达Icontroller 积分控制器integral 积分identifiability 可辨识性imagerecognition 图像识别impulse 冲量impulsefunction 冲击函数，脉冲函数index of merit 品质因数index 指数inductive force transducer 电感式位移传感器感应的inductive电感：inductanceindustrial automation 工业自动化inertial attitude sensor 惯性姿态敏感器inertial coordinate system 惯性坐标系information acquisition 信息采集infrared gas analyzer 红外线气体分析器infrared 红外线红外线的ultraviolet ray 紫外线的visible light可见光inherent nonlinearity 固有非线性inherent regulation 固有调节initial deviation 初始偏差input-output model 投入产出模型instability 不稳定性integrity 整体性intelligent terminal 智能终端internal disturbance 内扰invariant embedding principle 不变嵌入原理inverse Nyquist diagram 逆奈奎斯特图investment decision 投资决策joint 关节knowledge acquisition 知识获取knowledge assimilation 知识同化knowledge representation 知识表达lag-lead compensation滞后超前补偿Laplacetransform 拉普拉斯变换large scale system 大系统least squares criterion 最小二乘准则criterion 准则linearizationtechnique 线性化方法linear motion electricdrive 直线运动电气传动linear motionvalve 直行程阀linearprogramming 线性规划load cell 称重传感器local optimum 局部最优local 局部log magnitude-phase diagram对数幅相图magnitude大小的程度amplitude 振幅long term memory 长期记忆Lyapunov theorem of asymptotic stability 李雅普诺夫渐近稳定性定理magnetoelastic weighing cell 磁致弹性称重传感器magnitude-frequency characteristic 幅频特性magnitude margin幅值裕度margin边缘magnitude scalefactor幅值比例尺manipulator机械手man-machine coordination人机协调MAP (manufacturing automation protocol) 制造自动化协议protocol 协议marginal effectiveness 边际效益Mason‘‘ s gain formula 梅森增益公式matchingcriterion匹配准则maximum likelihood estimation 最大似然估计maximum overshoot 最大超调量maximum principle 极大值原理mean-square error criterion 均方误差准则minimal realization 最小实现minimum phase system 最小相位系统minimum variance estimation 最小方差估计model reference adaptive control system 模型参考适应控制系统 model verification 模型验证modularization 模块化mean 平均MTBF (mean time between failures) 平均故障间隔时间 MTTF (mean time to failures) 平均无故障时间multiloop control 多回路控制multi-objective decision 多目标决策Nash optimality 纳什最优性nearest-neighbor 最近邻necessity measure 必然性侧度negative feedback 负反馈neural assembly 神经集合neural network computer 神经网络计算机Nichols chart 尼科尔斯图Nyquist stability criterion 奈奎斯特稳定判据objective function 目标函数on-line assistance 在线帮助on-off control 通断控制optic fiber tachometer 光纤式转速表optimal trajectory 最优轨迹optimization technique 最优化技术order parameter 序参数orientation control 定向控制oscillating period 振荡周期周期：period cycleoutput prediction method 输出预估法oval wheel flowmeter 椭圆齿轮流量计Over damping 过阻尼underdamping 欠阻尼PR (pattern recognition) 模式识别P control 比例控制器peak time 峰值时间penalty function method 罚函数法perceptron 感知器phase lead 相位超前phase lag相位滞后Photoelectri c光电tachometric transducer光电式转速传感器piezoelectric force transducer压电式力传感器PLC (programmable logic controller) 可编程序逻辑控制器plug braking 反接制动pole assignment 极点配置pole-zero cancellation零极点相消polynomial input 多项式输入portfolio theory 投资搭配理论pose overshoot位姿过调量position measuring instrument 位置测量仪posentiometric displacement transducer 电位器式位移传感器positive feedback 正反馈power system automation 电力系统自动化pressure transmitter 压力变送器primary frequency zone 主频区priority 优先级process-oriented simulation 面向过程的仿真proportional control 比例控制proportional plus derivative controller 比例微分控制器pulse duration 脉冲持续时间pulse frequency modulation control system 脉冲调频控制系统： frequency modulation 频率调制调频pulse width modulation control system 脉冲调宽控制系统PWM inverter 脉宽调制逆变器QC (qualitycontrol) 质量管理quantized noise 量化噪声ramp function 斜坡函数randomdisturbance 随机扰动random process 随机过程rate integratinggyro 速率积分陀螺real time telemetry 实时遥测receptive field 感受野rectangular robot 直角坐标型机器人redundantinformation 冗余信息regional planningmodel 区域规划模型regulatingdevice 调节装载regulation 调节relationalalgebra 关系代数remoteregulating 遥调reproducibility 再现性resistance thermometer sensor 热电阻 电阻温度计传感器response curve 响应曲线return difference matrix 回差矩阵 return ratio matrix回比矩阵revolute robot 关节型机器人revolution speed transducer 转速传感器 rewriting rule重写规则rigid spacecraft dynamics 刚性航天动力学 dynamics 动力学robotics 机器人学robot programming language 机器人编程语言 robust control 鲁棒控制 robustness 鲁棒性 root locus 根轨迹 roots flowmeter腰轮流量计rotameter 浮子流量计，转子流量计sampled-data control system 采样控制系统sampling control system 采样控制系统saturation characteristics 饱和特性 scalar Lyapunov function 标量李雅普诺夫函数s-domain s 域self-operated controller 自力式控制器 self-organizing system 自组织系统self-reproducing system 自繁殖系统self-tuning control 自校正控制sensing element 敏感元件 sensitivity analysis 灵敏度 分析sensory control 感觉控制 sequential decomposition顺序分解sequential least squares estimation 序贯最小二乘估计 servo control 伺服控制，随动控制servomotor settling time伺服马达过渡时间 sextan t六分仪short term planning短期计划short time horizon coordinationsignal detection and estimation短时程协调信号检测和估计signal reconstruction 信号重构similarity 相似性simulated interrupt 仿真中断simulation block diagram 仿真框图simulation experiment 仿真实验simulation velocity 仿真速度simulator 仿真器single axle table 单轴转台single degree of freedom gyro 单自由度陀螺翻译顺序呵呵spin axis 自旋轴spinner 自旋体stability criterion 稳定性判据stabilitylimit 稳定极限stabilization 镇定，稳定state equation model 状态方程模型state space description 状态空间描述static characteristicscurve 静态特性曲线station accuracy 定点精度stationary randomprocess 平稳随机过程statistical analysis 统计分析statistic patternrecognition 统计模式识别steady state deviation稳态偏差顺序翻译即可steady state error coefficient稳态误差系数step-by-step control步进控制step function 阶跃函数strain gauge load cell 应变式称重传感器subjective probability 主观频率supervisory computer control system 计算机监控系统sustained oscillation 自持振荡swirlmeter 旋进流量计switching point 切换点systematology 系统学system homomorphism 系统同态system isomorphism 系统同构system engineering 系统工程tachometer 转速表target flow transmitter 靶式流量变送器task cycle 作业周期temperature transducer 温度传感器tensiometer 张力计texture 纹理theorem proving 定理证明therapy model 治疗模型thermocouple 热电偶thermometer 温度计thickness meter 厚度计three-axis attitude stabilization 三轴姿态稳定three state controller 三位控制器thrust vector control system 推力矢量控制系统推力器thrustertime constant 时间常数time-invariant system 定常系统，非时变系统invariant不变的时序控制器time schedulecontrollertime-sharing control 分时控制time-varying parameter 时变参数top-down testing 自上而下测试全面质量管理TQC (total qualitycontrol)tracking error 跟踪误差trade-off analysis 权衡分析transfer function matrix传递函数矩阵transformation grammar 转换文法transient deviation 瞬态偏差短暂的瞬间的transient process过渡过程transition diagram 转移图transmissible pressure gauge 电远传压力表transmitter 变送器trend analysis 趋势分析triple modulation telemetering system 三重调制遥测系统turbine flowmeter 涡轮流量计Turing machine 图灵机two-time scale system 双时标系统ultrasonic levelmeter 超声物位计unadjustable speed electric drive 非调速电气传动unbiased estimation 无偏估计underdamping 欠阻尼uniformly asymptotic stability 一致渐近稳定性uninterrupted duty 不间断工作制，长期工作制unit circle 单位圆unit testing 单元测试unsupervised learing 非监督学习upper level problem 上级问题urban planning 城市规划value engineering 价值工程variable gain 可变增益，可变放大系数variable structure control system 变结构控制function 函数vector Lyapunov function 向量李雅普诺夫函数velocity error coefficient 速度误差系数velocity transducer 速度传感器 vertical decomposition纵向分解vibrating wire force transducer 振弦式力传感器vibrometer 振动计vibrationVibrate 振动viscousdamping 粘性阻尼voltage source inverter 电压源型逆变器vortex precessionflowmeter 旋进流量计vortex sheddingflowmeter 涡街流量计WB (way base) 方法库weighing cell 称重传感器weightingfactor 权因子weightingmethod 加权法Whittaker-Shannon sampling theorem 惠特克 -香农采样定理Wiener filtering维纳滤波w- plane w 平面zero-based budget 零基预算zero-input response零输入响应zero-state response零状态响应z-transform z 变换《信号与系统》专业术语中英文对照表第1章绪论信号（ signal）系统（ system）电压（ voltage）电流（ current）信息（ information）电路（ circuit ）网络（ network）确定性信号（ determinate signal）随机信号（ random signal）一维信号（ one–dimensional signal）多维信号（ multi –dimensional signal）连续时间信号（ continuous time signal）离散时间信号（ discrete time signal）取样信号（ sampling signal）数字信号（ digital signal）周期信号（ periodic signal）非周期信号（ nonperiodic（aperiodic） signal）能量（ energy）功率（ power）能量信号（ energy signal）功率信号（ power signal）平均功率（ average power）平均能量（ average energy）指数信号（ exponential signal）时间常数（ time constant）正弦信号（ sine signal）余弦信号（ cosine signal）振幅（ amplitude）角频率（ angular frequency）初相位（ initial phase）周期（ period）频率（ frequency）欧拉公式（ Euler ’s formula）复指数信号（ complex exponential signal）复频率（ complex frequency）实部（ real part）虚部（ imaginary part）抽样函数Sa(t)（sampling（Sa） function）偶函数（ even function）奇异函数（ singularity function ）奇异信号（ singularity signal）单位斜变信号（ unit ramp signal）斜率（ slope）单位阶跃信号（ unit step signal）符号函数（ signum function）单位冲激信号（ unit impulse signal）广义函数（ generalized function）取样特性（ sampling property）冲激偶信号（ impulse doublet signal）奇函数（ odd function）偶分量（even component）偶数even 奇数odd 奇分量（odd component）正交函数（ orthogonal function）正交函数集（ set of orthogonal function）数学模型（ mathematics model）电压源（ voltage source）基尔霍夫电压定律（ Kirchhoff ’s voltage law（KVL ））电流源（ current source）连续时间系统（ continuous time system）离散时间系统（ discrete time system）微分方程（ differential function）差分方程（ difference function）线性系统（ linear system）非线性系统（ nonlinear system）时变系统（ time–varying system）时不变系统（ time–invariant system）集总参数系统（ lumped–parameter system）分布参数系统（ distributed–parameter system）偏微分方程（ partial differential function ）因果系统（ causal system）非因果系统（ noncausal system）因果信号（ causal signal）叠加性（ superposition property）均匀性（ homogeneity）积分（ integral）输入–输出描述法（ input–output analysis）状态变量描述法（ state variable analysis）单输入单输出系统（ single–input and single–output system）状态方程（ state equation）输出方程（ output equation）多输入多输出系统（ multi –input and multi–output system）时域分析法（ time domain method）变换域分析法（ transform domain method）卷积（ convolution）傅里叶变换（ Fourier transform）拉普拉斯变换（ Laplace transform）第 2 章连续时间系统的时域分析齐次解（ homogeneous solution）特解（ particular solution）特征方程（ characteristic function）特征根（ characteristic root）固有（自由）解（ natural solution）强迫解（ forced solution）起始条件（ original condition）初始条件（ initial condition）自由响应（ natural response）强迫响应（ forced response）零输入响应（ zero-input response）零状态响应（ zero-state response）冲激响应（ impulse response）阶跃响应（ step response）卷积积分（ convolution integral）交换律（ exchange law）分配律（ distribute law）结合律（ combine law）第3 章傅里叶变换频谱（ frequency spectrum）频域（ frequency domain）三角形式的傅里叶级数（trigonomitric Fourier series）指数形式的傅里叶级数（exponential Fourier series）傅里叶系数（ Fourier coefficient）直流分量（ direct component）基波分量（ fundamental component）component分量n 次谐波分量（ nth harmonic component）复振幅（ complex amplitude）频谱图（ spectrum plot（diagram））幅度谱（ amplitude spectrum）相位谱（ phase spectrum）包络（ envelop）离散性（ discrete property）谐波性（ harmonic property）收敛性（ convergence property）奇谐函数（ odd harmonic function）吉伯斯现象（ Gibbs phenomenon）周期矩形脉冲信号（ periodic rectangular pulse signal）直角的周期锯齿脉冲信号（ periodic sawtooth pulse signal）周期三角脉冲信号（ periodic triangular pulse signal）三角的周期半波余弦信号（ periodic half–cosine signal）周期全波余弦信号（ periodic full –cosine signal）傅里叶逆变换（inverse Fourier transform）inverse 相反的频谱密度函数（ spectrum density function）单边指数信号（ single–sided exponential signal）双边指数信号（ two–sided exponential signal）对称矩形脉冲信号（ symmetry rectangular pulse signal）线性（ linearity ）对称性（ symmetry）对偶性（ duality）位移特性（ shifting）时移特性（ time–shifting）频移特性（ frequency–shifting ）调制定理（ modulation theorem）调制（ modulation）解调（ demodulation）变频（ frequency conversion）尺度变换特性（ scaling）微分与积分特性（ differentiation and integration）时域微分特性（ differentiation in the time domain）时域积分特性（ integration in the time domain）频域微分特性（ differentiation in the frequency domain）频域积分特性（ integration in the frequency domain）卷积定理（ convolution theorem）时域卷积定理（ convolution theorem in the time domain）频域卷积定理（ convolution theorem in the frequency domain）取样信号（ sampling signal）矩形脉冲取样（ rectangular pulse sampling）自然取样（ nature sampling）冲激取样（ impulse sampling）理想取样（ ideal sampling）取样定理（ sampling theorem）调制信号（ modulation signal）载波信号（ carrier signal）已调制信号（ modulated signal）模拟调制（ analog modulation）数字调制（ digital modulation）连续波调制（ continuous wave modulation）脉冲调制（ pulse modulation）幅度调制（ amplitude modulation）频率调制（ frequency modulation）相位调制（ phase modulation）角度调制（ angle modulation）频分多路复用（ frequency–division multiplex （FDM ））时分多路复用（ time–division multiplex （TDM ））相干（同步）解调（ synchronous detection）本地载波（ local carrier）载波系统函数（ system function）网络函数（ network function）频响特性（ frequency response）幅频特性（ amplitude frequency response）幅频响应相频特性（ phase frequency response）无失真传输（ distortionless transmission）理想低通滤波器（ideal low–pass filter）截止频率（ cutoff frequency）正弦积分（ sine integral）上升时间（ rise time）窗函数（ window function ）理想带通滤波器（ ideal band–pass filter）太直译了第 4 章拉普拉斯变换代数方程（ algebraic equation）双边拉普拉斯变换（ two-sided Laplace transform）双边拉普拉斯逆变换（ inverse two-sided Laplace transform）单边拉普拉斯变换（ single-sided Laplace transform）拉普拉斯逆变换（ inverse Laplace transform）收敛域（ region of convergence（ ROC））延时特性（ time delay）s 域平移特性（ shifting in the s-domain）s域微分特性（ differentiation in the s-domain）s 域积分特性（ integration in the s-domain）初值定理（ initial-value theorem）终值定理（ expiration-value）复频域卷积定理（ convolution theorem in the complex frequency domain）部分分式展开法（ partial fraction expansion）留数法（ residue method）第 5 章策动点函数（ driving function ）转移函数（ transfer function）极点（ pole）零点（ zero）零极点图（ zero-pole plot）暂态响应（ transient response）稳态响应（ stable response）稳定系统（ stable system）一阶系统（ first order system）高通滤波网络（ high-pass filter）低通滤波网络（ low-pass filter）二阶系统（ second order system）最小相位系统（ minimum-phase system）高通（ high-pass）带通（ band-pass）带阻（ band-stop）有源（ active）无源（ passive）模拟（ analog）数字（ digital）通带（ pass-band）阻带（ stop-band）佩利－维纳准则（ Paley-Winner criterion）最佳逼近（ optimum approximation）过渡带（ transition-band）通带公差带（ tolerance band）巴特沃兹滤波器（ Butterworth filter ）切比雪夫滤波器（ Chebyshew filter）方框图（ block diagram）信号流图（ signal flow graph）节点（ node）支路（ branch）输入节点（ source node）输出节点（ sink node）混合节点（ mix node）通路（ path）开通路（ open path）闭通路（ close path）环路（ loop）自环路（ self-loop）环路增益（ loop gain）不接触环路（ disconnect loop）前向通路（ forward path）前向通路增益（ forward path gain）梅森公式（ Mason formula）劳斯准则（ Routh criterion）第 6 章数字系统（ digital system）数字信号处理（ digital signal processing）差分方程（ difference equation）单位样值响应（ unit sample response）卷积和（ convolution sum）Z 变换（ Z transform）序列（ sequence）样值（ sample）单位样值信号（ unit sample signal）单位阶跃序列（ unit step sequence）矩形序列(rectangular sequence)单边实指数序列（ single sided real exponential sequence）单边正弦序列（ single sided exponential sequence）斜边序列（ ramp sequence）复指数序列（ complex exponential sequence）线性时不变离散系统（ linear time-invariant discrete-time system）常系数线性差分方程（ linear constant-coefficient difference equation）后向差分方程（ backward difference equation）前向差分方程（ forward difference equation）海诺塔（ Tower of Hanoi）菲波纳西（ Fibonacci）冲激函数串（ impulse train）第7 章数字滤波器（ digital filter ）单边 Z 变换（ single-sided Z transform）双边 Z 变换 (two-sided (bilateral) Z transform)幂级数（ power series）收敛（ convergence）有界序列（ limitary-amplitude sequence）正项级数（ positive series）有限长序列（ limitary-duration sequence）右边序列（ right-sided sequence）左边序列（ left-sided sequence）双边序列（ two-sided sequence）Z逆变换（ inverse Z transform）围线积分法（ contour integral method）幂级数展开法（ power series expansion）z域微分（ differentiation in the z-domain）序列指数加权（ multiplication by an exponential sequence）z域卷积定理（ z-domain convolution theorem）帕斯瓦尔定理（ Parseval theorem）传输函数（ transfer function）序列的傅里叶变换（ discrete-time Fourier transform：DTFT）序列的傅里叶逆变换（ inverse discrete-time Fourier transform：IDTFT ）幅度响应（ magnitude response）相位响应（ phase response）量化（ quantization）编码（ coding）模数变换（ A/D 变换： analog-to-digital conversion）数模变换（ D/A 变换： digital-to- analog conversion）第8 章端口分析法（ port analysis）状态变量（ state variable）无记忆系统（ memoryless system）有记忆系统（ memory system）矢量矩阵（ vector-matrix ）常量矩阵（ constant matrix ）输入矢量（input vector）输出矢量（ output vector）直接法（ direct method）间接法（ indirect method）状态转移矩阵（ state transition matrix）系统函数矩阵（ system function matrix）冲激响应矩阵（ impulse response matrix）光学专业词汇大全Accelaration 加速度Myopia-near-sighted 近视Sensitivity to Light 感光灵敏度boost 推进lag behind 落后于Hyperopic-far-sighted 远视visual sensation 视觉ar Pattern 条状图形approximate 近似adjacent 邻近的normal 法线Color Difference 色差V Signal Processing 电视信号处理back and forth 前后vibrant 震动quantum leap 量子越迁derive from 起源自inhibit 抑制 ,约束stride 大幅前进obstruction 障碍物substance 物质实质主旨residue 杂质criteria 标准parameter 参数parallax 视差凸面镜convex mirror凹面镜concave mirror分光镜 spectroscope入射角angle of incidence 出射角emergent angle平面镜plane mirror放大率角度放大率 angularmagnification放大率：magnification折射refraction反射reflect干涉 interfere衍射diffraction干涉条纹interference fringe衍射图像diffraction fringe 衍射条纹偏振polarize polarization透射 transmission透射光transmission light光强度 ] light intensity电磁波electromagnetic wave振动杨氏干涉夫琅和费衍射焦距brewster Angle 布鲁斯特角quarter Waveplates 四分之一波片ripple 波纹capacitor 电容器vertical 垂直的horizontal 水平的airy disk 艾里斑exit pupil 出[ 射光 ]瞳Entrance pupil 入瞳optical path difference 光称差radius of curvature 曲率半径spherical mirror 球面镜reflected beam 反射束YI= or your information 供参考phase difference 相差interferometer 干涉仪ye lens 物镜 /目镜spherical 球的field information 场信息standard Lens 标准透镜refracting Surface 折射面principal plane 主平面vertex 顶点 ,最高点fuzzy 失真 ,模糊light source 光源wavelength 波长angle 角度spectrum 光谱diffraction grating 衍射光栅sphere 半球的DE= ens data editor Surface radius of curvature 表面曲率半径surface thickness 表面厚度semi-diameter 半径focal length 焦距field of view 视场stop 光阑refractive 折射reflective 反射机械专业英语词汇（大全）金属切削metal cutting机床machine tool tool 机床金属工艺学technology of metals刀具 cutter摩擦 friction传动 drive/transmission轴shaft弹性 elasticity频率特性frequency characteristic误差 error响应 response定位 allocation动力学dynamic运动学kinematic静力学static分析力学analyse mechanics 力学拉伸 pulling压缩 hitting compress剪切 shear扭转 twist弯曲应力bending stress强度 intensity几何形状geometricalUltrasonic 超声波精度 precision交流电路AC circuit机械加工余量machining allowance变形力deforming force变形 deformation应力 stress硬度 rigidity热处理heat treatment电路 circuit半导体元件semiconductor element反馈 feedback发生器generator直流电源DC electrical source门电路 gate circuit逻辑代数logic algebra磨削grinding螺钉 screw铣削 mill铣刀 milling cutter功率 power装配 assembling流体动力学fluid dynamics流体力学fluid mechanics加工 machining稳定性 stability介质 medium强度 intensity载荷 load应力 stress可靠性 reliability精加工 finish machining粗加工 rough machining腐蚀 rust氧化 oxidation磨损 wear耐用度durability随机信号random signal离散信号discrete signal超声传感器ultrasonic sensor摄像头CCD cameraLead rail 导轨合成纤维synthetic fibre电化学腐蚀electrochemical corrosion车架 automotive chassis悬架 suspension转向器redirector变速器speed changer车间 workshop工程技术人员engineer数学模型mathematical model标准件standard component零件图part drawing装配图assembly drawing刚度 rigidity内力 internal force位移 displacement截面 section疲劳极限fatigue limit断裂 fracture 破裂塑性变形plastic distortionelastic deformation 弹性变形脆性材料brittleness material刚度准则rigidity criterion齿轮gearGrain 磨粒转折频率corner frequency =break frequencyConvolution Convolution integral Convolution property Convolution sum 卷积卷积积分卷积性质卷积和Correlation function Critically damped systems Crosss-correlation functions Cutoff frequencies 相关函数临界阻尼系统互相关函数截至频率transistor diode semiconduct or nn晶体管二极管n半导体resistor n 电阻器capacitor n 电容器alternating adj 交互的amplifier n 扩音器，放大器integrated circuit 集成电路linear time invariant systems 线性时不变系统voltage n 电压，伏特数Condenser= capacitor n 电容器dielectric electromagnetic adj 电磁的adj 非传导性的deflection n 偏斜；偏转；偏差linear device 线性器件the insulation resistance 绝缘电阻anode n 阳极，正极cathode n 阴极breakdown n 故障；崩溃terminal n 终点站；终端，接线端emitter n 发射器collect v 收集，集聚，集中insulator n 绝缘体，绝热器oscilloscope n 示波镜；示波器gain n 增益，放大倍数forward biased 正向偏置reverse biased 反向偏置P-N junction PN 结MOS（ metal-oxide semiconductor ）金属氧化物半导体enhancement and exhausted 增强型和耗尽型integrated circuits 集成电路analog n 模拟digital adj 数字的，数位的horizontal adj, 水平的，地平线的vertical adj 垂直的，顶点的amplitude n 振幅，广阔，丰富multimeter n 万用表frequency n 频率，周率the cathode-ray tube 阴极射线管dual-trace oscilloscope 双踪示波器signal generating device 信号发生器peak-to-peak output voltage 输出电压峰峰值sine wave 正弦波triangle wave 三角波square wave 方波amplifier 放大器，扩音器oscillator n 振荡器feedback n 反馈，回应phase n 相，阶段，状态filter n 滤波器，过滤器rectifier n 整流器；纠正者band-stop filter 带阻滤波器band-pass filter 带通滤波器decimal adj 十进制的，小数的hexadecimal adj/n 十六进制的binary adj 二进制的；二元的octaladj八进制的n绝缘体；电解质domain n 域；领域code n 代码，密码，编码 v 编码 the Fourier transform 傅里叶变换 Fast Fourier Transform 快速傅里叶变换 microcontro ller n 微处理器；微控制器 assembly language instrucions n 汇编语言指令 chip n 芯片，碎片modular adj 模块化的；模数的 sensor n 传感器plugvt 堵，塞，插上 n 塞子，插头，插销coaxial adj 同轴的，共轴的fiber n 光纤 relay contact 继电接触器 ArtificialIntelligence 人工智能 Perceptive Systems 感知系统 neural network 神经网络 fuzzy logic 模糊逻辑intelligent agent 智能代理 electromagn etic adj 电磁的coaxial adj 同轴的，共轴的 microwav e n 微波charge v 充电，使充电 insulato r n 绝缘体，绝缘物 nonconducti ve adj 非导体的，绝缘的 simulati on n 仿真；模拟 prototyp e n 原型 array n 排队，编队 vector n 向量，矢量inverse adj 倒转的，反转的 n 反面；相反 v倒转 high-performance 高精确性，高性能 two-dimensional 二维的；缺乏深度的 three-dimensional 三维的；立体的；真实的。