基于AMESim的自适应电液控制系统仿真

Force control for hydraulic load simulator using self-tuning grey predictor –fuzzy PIDDinh Quang Truong 1,Kyoung Kwan Ahn *School of Mechanical and Automotive Engineering,University of Ulsan,San 29,Muger 2dong,Nam-gu,Ulsan 680-764,Republic of Koreaa r t i c l e i n f o Article history:Received 14September 2007Accepted 29July 2008Keywords:HydraulicLoad simulator FuzzyPID controller Grey predictora b s t r a c tHydraulic systems play an important role in modern industry for the reason that hydraulic actuator sys-tems have many advantages over other technologies with electric motors,as they possess high durability and the ability to produce large forces at high speeds.Therefore,the hydraulic actuator has a wide range of application fields such as hydraulic punching,riveting,pressing machines,and molding technology,where controlled forces or pressures with high accuracy and fast response are the most significant demands.Consequently,many hybrid actuator models have been developed for studying how to control forces or pressures with best results.This paper presents a kind of hydraulic load simulator for conducting performance and stability testing related to the force control problem of hydraulic hybrid systems.In the dynamic loading process,pertur-bation decreases control performance such as stability,frequency response,and loading sensitivity decreasing or bad.In order to improve the control quality of the loading system while eliminating or reducing the disturbance,a grey prediction model combined with a fuzzy PID controller is suggested.Fur-thermore,fuzzy controllers and a tuning algorithm are used to change the grey step size in order to improve the control quality.The grey prediction compensator can improve the system settle time and overshoot problems.Simulations and experiments on the hydraulic load simulator are carried out to eval-uate the effectiveness of the proposed control method when applied to hydraulic systems with various external disturbances encountered in real working conditions.Ó2008Elsevier Ltd.All rights reserved.1.IntroductionIn recent years,hydraulic systems have been widely used in modern industries because of their durability,high power,control-lability,accuracy and reliability.However,most previous hydraulic actuators contain a hydraulically controlled valve that utilizes an open loop control,thus significant energy is transferred into heat due to throttle losses at the control valves.To save energy,the use of load-sensing technology for hydraulic actuators in closed loop control systems is necessary.Energy consumption and the le-vel of noise have become important factors to evaluate the perfor-mance of machines and equipment.In order to overcome these weak points in conventional hydraulic systems and satisfy new de-mands,many alternative concepts regarding new hybrid actuators have presented.Engineers at Moog,Inc.(East Aurora,NY)have developed a hybrid actuation system known as the PowerShift which shifts from high-speed electric to high-force hydraulic,thuscreating a sleeker,cleaner,more energy efficient way to produce high forces.The advantages of hybrid actuator were proved by Rahmfeld and Ivantysynova [1].These authors developed a precise mathematical model describing the losses of energy in the hybrid actuator including servo pump losses,cylinder losses,and pressure losses in hydraulic lines.In addition,a comparison between the conventional hydraulic system and the hybrid actuator in the load-sensing system was also presented.Because of its efficiency,the hybrid actuator has a wide range of applications where force or pressure control with high accuracy and fast response are exceedingly necessary.Contrary to the simplicity of hybrid actua-tors,the control problem is very complicated because of the non-linearity and large uncertainties in hydraulic systems due to unstableness of some hydraulic parameters such as bulk modulus,compressibility of oil or viscosity of oil [2].In the literature,several kinds of load simulator systems have been presented.Su and Wang [3]presented a new kind of elec-tro-hydraulic load simulator with high precision.This model adopts synchronous structure and electronic control compensa-tions to compensate for the surplus torque.The experiment results demonstrated how to eliminate or reduce the disturbance torque and improve the control performances of a loading system.Li [4]carried out a thorough analysis and research on torque load0957-4158/$-see front matter Ó2008Elsevier Ltd.All rights reserved.doi:10.1016/j.mechatronics.2008.07.007*Corresponding author.Tel.:+82522592282;fax:+82522591680.E-mail address:kkahn@ulsan.ac.kr (K.K.Ahn).1Present address:Graduate School of Mechanical and Automotive Engineering,University of Ulsan.Mechatronics 19(2009)233–246Contents lists available at ScienceDirectMechatronicsj o ur na l h om e pa ge :w w w.e ls e v ie r.c o m/lo c at e/me c h at r on icssimulator using electro-hydraulic servo control.A control law that consists of compensation to disturbance,internal loop PID control and generalized proportion–integral control is applied to this mod-el to forward the error to improve the control performance and de-crease the extraneous torque effectively.In dynamic loading process,there exist some unknown distur-bances which decrease the control performances such as the stabil-ity,frequency response and loading sensitivity.To eliminate or reduce the disturbance on a large scale,which is essential to im-prove force control performance,several force control strategies have been proposed[5–7].Conventional proportional–integral–derivative(PID)controllers are commonly used in industry due to their simplicity,clear functionality and ease of implementation. Meanwhile,fuzzy control,an intelligent control method imitating the logical thinking of humans and being independent on accurate mathematical model of the controlled object,can overcome some shortcomings of the traditional PID.However,fuzzy control is a nonlinear method and the output of the controller has a static error as noted by Guo et al.[8].For these reasons,fuzzy PID control which combines the traditional PID control and the fuzzy control algorithm is a good solution.Fuzzy PID technique has been applied to solve many engineering problems such as position control of sli-der crank mechanisms[9],position control of a shape memory al-loy actuator[10]and speed control for high performance brushless servo drives[11].However,the design of fuzzy rules depends largely on the expe-rience of experts or input–output data.There is no systematic method to design and examine the number of rules,input space partitions and membership functions[12].Hence,another control technique is needed to combine with the fuzzy PID to overcome this weakness[13–16].And predictive control analysis is also a solution.As a result,the objective of this paper is to introduce a new hydraulic load simulator model which contains a new hybrid actuator and a disturbance generator using a self-tuning grey pre-dictor based fuzzy PID controller to develop force control strategy. The concept of‘‘grey systems”wasfirst proposed by Deng[17].The grey theory is distinguished by its ability to deal with systems that have partially unknown parameters.The grey prediction technique has been successfully employed to solve many engineering prob-lems including robot position control,fluid engineering control and manufacturing systems[18–20].A fuzzy PID controller with a grey predictor whose step size is changed by fuzzy controllers and a self-tuning algorithm is pre-sented in this paper.In order to verify the overall control system, a co-simulation between AMESim[21,22]and Simulink[23]is cho-sen and experiments are carried out.Simulation and experimental results show the effectiveness of the proposed control method to reach the control target of the new hybrid actuator.The remainder of this paper is organized as follows:In Section 2,the comparison between the proposed and the conventional sys-tems is shown.In Section3,the model of the new hydraulic hybrid load simulator system is described and Section4presents the pro-cedure of designing the force controller.Section5shows the sim-ulation and experimental results of the load simulator force control.Conclusions are presented in Section6.parison between the new hybrid actuator and conventional hydraulic systemEnergy consumption is one of the most important factors to be considering in designing most of hydraulic systems.Consequently, new hybrid actuator presented in this paper offers a solution to these challenges.In this section,simulations were carried out to compare the energy consumption between the proposed system and the conventional hydraulic system.Two hydraulic circuits rep-resenting two systems were built in the simulation AMESim soft-ware,version4.3(Imagine S.A.,2005).AMESim corresponds to Advanced Modeling Environment Simulation software,which al-lows the simulation of actuator dynamics including electrical mo-tor,hydraulic systems through using several libraries.In the AMESim code,each physical component of the system is repre-sented by an appropriate icon,and is associated to one or more parameter models(called sub-models).Developing a model of the actuator requires the knowledge of several parameters includ-ing electrical and mechanical factors,hydraulic characteristics,and physical dimensions of the actuator.The schematic diagrams of both systems are shown in Figs.1and2.In the simulations,the desired performance is force control by using PID controllers.The working environment is a spring.The ra-tio of signal from force sensor and the spring deformation is the spring stiffness.The signal from the force sensor connected to a load M and a spring represents the feedback signal.The control in-puts for the conventional and the proposed hydraulic circuits are electric signals for the solenoid and AC servo driver,respectively. The pressure transducers and theflow meters are also connected to the hydraulic systems to verify the energy consumptions.All ini-tial conditions and the PID controllers’parameters for the simula-tions are shown in Table1.Fig.3shows the step responses of the systems.From thisfigure, the force response of the proposed hydraulic system is faster than the conventional system when the initial conditions are the same. In both hydraulic systems,the PID coefficients were tuned to ob-tain the best force control performance.Consequently,these values were used for all simulations.To prove the effectiveness of the new hybrid actuator,simula-tions with the input references as a multi-step signal,sine wave were also performed.Figs.4and5show the results.From all sim-ulations,the energy consumptions were calculated to verify the energy saving in each case using following equation:Energy savingð%Þ¼E convÀE newconvÂ100%ð1Þwhere E conv and E new are energy consumption of the conventional hydraulic system and the new hybrid actuator,respectively,taken from the simulation outputs as shown in Figs.1and2ðE¼R tPðtÞQðtÞd tÞ.By applying Eq.(1),the energy saving in the two cases in which the reference inputs were multi-step signal and sine wave were 42.72%and46.33%,respectively.Fig.1.Schematic diagram of conventional hydraulic system.234 D.Q.Truong,K.K.Ahn/Mechatronics19(2009)233–246From the simulation results,when compared with the conven-tional hydraulic system,the energy saving features of the new hy-brid actuator are clearly proven.3.Experimental apparatusThe schematic diagram of the new hydraulic load simulator is shown in Fig.6.The system hardware consists of a new hybrid actuator,a computer included PCI-bus multi-function cards and another hydraulic circuit for simulating noise in the working envi-ronment of the hydraulic systems.In this model,the new hybrid actuator is an intelligent hydrau-lic system composed of an AC servo motor (SGMGH-30PCA21),pis-ton pump,reservoir and hydraulic control circuit.Operation at the speed which meets the machine requirements (flow rate and pres-sure)will reduce power losses,and provide energy savings.The pressure oil line from the pump without a control valve minimizes pressure losses and substantially reduces heat generation within the hydraulic fluid.Regarding the operation of the hybrid actuator,the bidirectional rotational pump is used and driven by the AC ser-vo motor so that the pump can supply pressured oil in both direc-tions.The pump is well equipped as a hydraulic driving force.With the servo driver,the digital control parameter facilitates the oper-ation and maintenance of the system.In addition,to prove the effectiveness of the presented control method when the system operates under real conditions,another hydraulic circuit to generate a disturbance is installed in the load simulator.This part created disturbance which was in a combina-tion of band-limited white noises and a sine wave noise.A PC with compatible PCI cards was used to supply the noise signal for the AC servo motor (FMA-KN55),through a hydraulic control circuit and piston.The connection between the load simulator part and the distur-bance generator part is a load cell (YG38-T5),which is used for obtaining the feedback force signal and a compression spring with a 519kN/m stiffness.The deviation between the reference signal and sensor signal is measured on the PC,and the control signal is sent from the PC to the servo driver to drive the AC servo motor (SGMGH-30PCA21)using PCI cards,and consequently forming a feedback control loop.The setting parameters for the load simula-tor system are shown in Table 2.Fig.2.Schematic diagram of new hybrid actuator.Table 1Setting parameters for AMESim –hybrid actuator models Parameters ValueMeaningModel parametersM (kg)1000Loadk (kN/m)519Environment stiffness Sensor gain (1/N)3Force sensor signalCylinder para.(mm)63Â35Â150Piston diameter ÂRod diameter ÂLength of stroke Relief pressure (bar)175Relief valve cracking pressure Solenoid valve (4way 3position)24Power supply (V DC)110Maximum flow rate (l/min)AC servo motor 200Power supply (V AC)2.9Power (kW)Pump2500Speed (rev/min)10Displacement (cc/rev)Controller parametersK p 0.38and 1For new hybrid actuator and conventional hydraulic systemK i 0.003K d0.051D.Q.Truong,K.K.Ahn /Mechatronics 19(2009)233–246235A PC(AMD Athlon1.9GHz)included two PCI-bus data acquisi-tion and control cards(Advantech cards,PCI1711and PCI1720)is used to receive,process the feedback signals and generate the out-put signals to control the motors.The control algorithm is built within Simulink environment combined with Real-time Windows Target Toolbox of Matlab.Fig.7displays the experimental apparatus.236 D.Q.Truong,K.K.Ahn/Mechatronics19(2009)233–2464.Force controller design 4.1.Force control analysisHydraulic hybrid systems are complex and contain nonlineari-ties,which make the modeling and design of a feed-back controller challenging.The nonlinearities are mainly caused by flow–pressure characteristics,orifice area openings,variations of fluid volume un-der compression and in part,cavitation and friction.Beside the nonlinearities,hydraulic systems contain a large number of model uncertainties.The uncertainties can originate from fluctuation in supply pump pressure,variation of hydraulic parameters such as bulk modulus,and external environmental working condition.Therefore,force control in hydraulic actuators is a difficult prob-lem.In these systems,the speed of the AC servo motor is controlled in order to adjust supply pressure and flow rate of the hydraulic pump.Hence,the performance of the hybrid actuator depends on the control task of the AC servo motor.It is known that,the PID controller is the most widely used in modern industry due to its simple control structure and easy to de-sign.But the conventional PID controllers do not yield reasonable performance over a wide range of operating conditions because of the fixed gains used.Then the PID parameters need to be ad-justed by a fuzzy set automatically.However,the design of fuzzy rules depends largely on the experience of experts or input–output data.Hence,another controller,such as prediction analysis,is needed in addition to the fuzzy PID for systems with nonlinearity and uncertainties as the load simulator system.Meanwhile,the grey prediction technique has the ability to deal with the systems that have partially unknown parameters.The prediction technique has been successfully employed to solve many engineering problems,including robot position control,fluidFig.6.Schematic diagram of hydraulic load simulator.Table 2Setting parameters for the hydraulic load simulator system System parametersPartsMeaningLoad simulatorDisturbance generation AC Servo Motor200200Power supply (V AC)2.9 2.2Power (kW)18.626.18Rate torque (Nm)Pump25002000Speed (rev/min)1510Pump displacement (cc/rev)Cylinder parameters 63Â35Â15055Â35Â100Piston diameter ÂRod diameter ÂLength of stroke (mm)2121Maximum pressure (Mpa)Spring –k (kN/m)519Environment stiffnessRelief Pressure (bar)175Relief valve cracking pressure Working liquid –oil 0.87Specific gravity 1.5Â109Bulk modulus (Pa)Load cell5Capacity (tonf)D.Q.Truong,K.K.Ahn /Mechatronics 19(2009)233–246237engineering control,and manufacturing systems [18–20].Thus,this paper presents a self-tuning grey predictor based fuzzy PID controller for the load simulator system.A self-tuning fuzzy PID controller with a grey predictor is a powerful combination for the system to improve the control performance with fast response,minimal overshoot,and greater stability.Furthermore,to improve the control quality,adopt and stabilize systems rapidly and effec-tively,the grey step size is tuned by other fuzzy sets and a tuning algorithm.The overall structure of the proposed controller is shown in Fig.8.To control force of the hybrid system,a conventional PID con-troller is combined with fuzzy laws.The control signal can be ex-pressed in the time domain as:u ðt Þ¼K p e ðt ÞþK iZte ðt Þd t þK dde ðt Þð2Þwhere e (t )is the error between the desired force set point and the output,de (t )is the derivation of error,u (t )is the control signal used to control the AC servo motor velocity,K p is the proportional gain,K i is the integral gain,and K d is the derivative gain.The PID parame-ters are tuned by the fuzzy inferences,which provide a nonlinear mapping from the error and derivation of error to the PID parame-ters.These parameters are changed within the initial parameter boundaries.4.2.Self-tuning fuzzy PID controller designGenerally,fuzzy rules are dependent on the control purpose and the control type.From Eq.(2),three coefficients K p ,K i and K d aretuned by using the fuzzy tuner.Then,the three fuzzy-PID sub-con-trollers are combined to form the overall fuzzy-PID controller.In this research,the designed rules are based on the characteristic of the hydraulic load simulator such as slow response,nonlinearity,large uncertainties existing in the hydraulic systems,disturbances,and properties of the PID controller.Consequently,the fuzzy rea-soning results of the outputs are gained by aggregation of the input fuzzy sets and the designed fuzzy rules,where a MAX–MIN aggre-gation method is used.The detailed fuzzy-PID scheme applied to hydraulic load simulator is shown in Fig.9.From the fuzzy structure,there are two inputs to the controller:the absolute value of error j e (t )j and the absolute value of the derivative of error j de (t )j .The ranges of these inputs are from 0to 1,which are obtained from the absolute values of the system er-ror and its derivative through the chosen gains.For each input variable,four membership functions are used.Here,‘‘Z”,‘‘S”,‘‘M”and ‘‘B”are ‘‘Zero”,‘‘Small”,‘‘Medium”and ‘‘Big”,respectively.Details of the fuzzy inputs’membership func-tions are shown in Fig.10.There are three outputs of the fuzzy set:kp ,ki and kd .The ranges of the outputs are from 0to 1.The membership functions for each output are set as each input (Fig.10).Then these output values are substituted into the following equations to compute the coefficients K p K i and K d in Eq.(2)kp ¼K p ÀK p min p max pmin ki ¼K i ÀKi minimaxi minkd ¼K d ÀK d min dmax d min8>>><>>>:ð3ÞFig.7.Photograph of experimentalapparatus.Fig.8.Structure of proposed control algorithm.238 D.Q.Truong,K.K.Ahn /Mechatronics 19(2009)233–246The ranges of K p ,K i and K d are [K pmin ,K pmax ],[K imin ,K imax ],and [K dmin ,K dmax ],ing the above fuzzy sets of the input and output variables,fuzzy rules are composed as follows:Rule i th:If e(t)is A i and d e (t )is B i then kp is C i ,ki is D i and kd is E i ,i =1,2,...,n ,where n is the number of fuzzy rules;A i ,B i ,C i ,D i and E i are the i th fuzzy sets of the input and output variables used in the fuzzy controller,respectively.In this paper,the ‘‘centroid”method is used for defuzzification to obtain kp ,ki and kd ,which are sent to the PID controller and using Eqs.(2)and (3)to control the AC servo motor of the hybrid actuator.As a result,the rule sets are established and shown in the surfaces in Fig.11.4.3.Grey predictionThe grey predictor can predict the future outputs of the system with high accuracy without knowing the mathematical model of the real system.In grey prediction theory,GM ðn ;m Þdenotes a grey model,where n ,m are the order of the difference equation and the number of variables.The purpose of the grey predictor is to con-duct an accumulated generating operation on an original sequence.The resultant series is used to establish a difference equation to calculate coefficients via a least-square method.The accumulated generating series of the prediction model are then obtained.The value can be returned to estimate the future system output in the time-domain by means of inverse accumulated generating operation.GM(1,1)(Grey Model First Order One Variable),the most popular grey model,is used for prediction purposes in this research.4.3.1.Grey predictor –GM(1,1)The prediction procedure is as follows:Step 1:At least four output data points are needed to approxi-mate a system.For a nonnegative time series,n raw data is collected:y ð0Þ¼f y ð0Þð1Þ;y ð0Þð2Þ;...;y ð0Þðn Þg ð4ÞStep 2:Use the accumulated generating operation (AGO)toobtain y (1)from y (0):y ð1Þðk Þ¼X k i ¼1y ð0Þði Þ;k ¼1;2;...;n ð5ÞStep 3:Apply a consecutive neighbor generation z (1)from y (1)bythe following mean generating operation (MGO):(k =2,3,...,n )z ð1Þðk Þ¼0:5y ð1Þðk Þþ0:5y ð1Þðk À1Þð6ÞStep 4:Establish grey differential equation of GM(1,1):y ð0Þðk Þþaz ð1Þðk Þ¼bð7ÞIn which,parameter ½a ;b can be obtained by using the least-square method as follows:^a¼a b¼ðB T B ÞÀ1B T Yð8ÞwhereB ¼Àz ð1Þð2Þ1Àz ð1Þð3Þ1......Àz ð1Þðn Þ1266664377775;Y ¼y ð0Þð2Þy ð0Þð3Þ...y ð0Þðn Þ266664377775ð9ÞStep 5:Set up the prediction model GM(1,1)as:^y ð1Þðk þ1Þ¼y ð1Þð1ÞÀb ae Àak þb að10Þ^y ð0Þðk þ1Þ¼^y ð1Þðk þ1ÞÀ^y ð1Þðk Þð11ÞStep 6:Calculate the predictive output at time sequence (n+p)thstep,^yð0Þðn þp Þ:^y ð1Þðn þp Þ¼y ð1Þð1ÞÀbeÀa ðn þp À1Þþb ð12Þ^y ð0Þðn þp Þ¼^y ð1Þðn þp ÞÀ^y ð1Þðn þp À1Þð13Þwhere p is the step size of the grey prediction.4.3.2.Fuzzy predictor stepIn the control strategy,the control purpose is to design a con-troller for the hydraulic load simulator to control force with fast re-sponse and high accuracy.As a result,considering the settling time process of the system,the greater the operating time,the nearer the system response reaches the control target when compared with the current status.For designing the load simulator controller,a fixed step size grey predictor is considered fiing a small step will speed up the system response,but it can cause large overshoot or oscilla-tion.Otherwise,a large step will reduce the overshoot butincreaseFig.9.Fuzzy-PID inferenceblock.Fig.10.Fuzzy-PID –membership functions for e (t ),de (t ),kp ,ki and kd .D.Q.Truong,K.K.Ahn /Mechatronics 19(2009)233–246239the rise time.Hence,the step should be self-adjusting.In this paper,a fuzzy controller used to generate the step size of the f pre-dictor is proposed.The configuration of the fuzzy step size is shown in Fig.12.There are two fuzzy inputs,error e(t)and deriva-tion of error de(t),and one output is the step size p fuzzy of the grey predictor.The membership functions of these fuzzy sets are shown in Fig.13.The‘‘centroid”method is used for defuzzification in order to obtain the value p fuzzy.As a result,the rule sets are estab-lished and shown in the surface in Fig.14.4.3.3.Self-tuning predictor stepA parameter c was considered as an evaluation coefficient.This factor is substituted in the learning algorithm to define the current predictor step size based on the last step(p tÀ1)and the given step p fuzzy by the fuzzy predictor step part.Therefore,it is capable of evaluating whether the status of the current predictive state is appropriate for the control target or not.In order to obtain the above coefficient,a fuzzy set of two inputs and one output is con-structed.The membership functions of the inputs[error e(t)and derivation of error de(t))]and output[assess factor c(t)]are as shown in Fig.15.The fuzzy set is described in Fig.16.The factor c(t)obtained from the fuzzy inference is then applied in the following algorithm:pðtÞ¼cðtÞpðtÀ1Þþð1ÀcðtÞÞp fuzzyð14ÞThe predictor step size p(t) p is sent to the grey predictor to calculate the predictive output at time sequence(n+p)th step by using Eq.(13):^yð0ÞðnþpÞ¼^yð1ÞðnþpÞÀ^yð1ÞðnþpÀ1Þ5.Simulation and experiment results5.1.Simulation results5.1.1.Load simulator modelIn our simulation setup,the simulation software AmeSim is used to model the hydraulic system.Fig.17shows theAMESimFig.11.3D rule view of fuzzy-PID tuners:(a)kp tuner;(b)ki tuner;(c)kdtuner.Fig.12.Structure of the fuzzy predictor step–inference block.240 D.Q.Truong,K.K.Ahn/Mechatronics19(2009)233–246model of the load simulator,in a topology similar to that of Fig.6.AmeSim generates C-files for the actuator model and creates a DLL file for the model.The DLL is then used in the simulation mod-el via Simulink by associating with an S-function block.5.1.2.Overall control system modelIn the next section,the co-simulation between Simulink and other simulation tools are mentioned.MATLAB/Simulink is chosen as a common shell for building the simulation model due to its ability to support and interface seamlessly with the different DLLs provided from other tools.The DLL can be included in the Simulink environment in the form of an S-function [21].All individual blocks of the simulation model are validated against real test data.Fig.18shows the system with the controller built in Simulink.5.1.3.Simulation resultsIn this section,by using the above developed co-simulation platform,the states of the hydraulic system solved in AMESim are fed into the Simulink controller.The control signals from the controller are then fed back into the AMESim hydraulic model and the new states are solved.The setting parameters for the hy-brid system model are obtained from the real components as shown in Table 3.The simulations were done with a 0.01second sampling rate,to check the system responses.The comparison of the conventional PID,the fuzzy PID,and the fixed step grey predictor –fuzzy PID and the self-tuning step grey predictor –fuzzy PID controllers for the load simulator model were performed.First,the same PID’s coefficients were used for both control models.Fig.19shows the simulation step responses of the system in cases of using different controllers.The parameter values set for the conventional PID (K p =0.38,K i =0.003and K d =0.051)were derived from experiments with the real model.The control performance of system using the fuzzy PID was better than that using the conventional PID.However,when using the self-tuning step grey predictor –fuzzy PID,the control quality was the best not only with regard to the rising time but also over-shoot,settling time,and steady error.Next,to prove the effectiveness of the proposed controller,a disturbance scheme was included in the control diagram asshownFig.13.Membership functions of fuzzy predictorstep.Fig.14.Fuzzy predictor step controller –3D ruleview.Fig.15.Fuzzy evaluation factor –membershipfunctions.Fig.16.Fuzzy evaluation factor –3D rule view.D.Q.Truong,K.K.Ahn /Mechatronics 19(2009)233–246241。