Application of adaptive Grey predictor based
algorithm to boiler drum level control
Yu Nanhua *,Ma Wentong,Su Ming
Key Laboratory for Power Machinery and Engineering of Ministry of Education,Shanghai Jiao Tong University,
Shanghai 200030,PR China
Received 4February 2005;received in revised form 3September 2005;accepted 22March 2006
Available online 22May 2006
Abstract
To improve the boiler drum level control system of a power plant,the three challenging issues encountered include (1)e?ect of ‘‘false water level’’,(2)controller parameter mismatches due to variant working conditions and (3)signal noise caused by uncertainties of drum level.In this paper,based on analyses of the drum level signal,an adaptive derivative action is presented to monitor steam ?ow,and thus,the e?ect of ‘‘false water level’’is weakened.The uncertainties of parameter mismatches and noise are predicted by developing a Grey predictor based algorithm (GPBA).In order to resolve the three problems and further control performance,an adaptive technique is combined with the GPBA to develop an adaptive Grey predictor based method.Finally,concrete simulations give that the proposed method has obvious supe-riority over conventional methods.
ó2006Elsevier Ltd.All rights reserved.
Keywords:Drum level;False water level;PID control;Grey predictor;Median ?lter
1.Introduction
Since many of emergency shutdowns are caused by poor drum level control in power plants,stable drum level control is critical to economic operation of any power plant steam generator system.Generally,there are uncertain disturbances for the water level process [1].These disturbances o?er us an interesting challenge for better control performance [2,3].
The PI controller,a sub-class of generic proportional–integral–derivative (PID)controllers,is widely used in drum level regulation.PID controllers can handle most problems except under certain operation conditions such as the e?ects of ‘‘false water level’’[10]and wave action (wild oscillation of water surface).Many methods aiming at the above problems are readily found in the open literature.Adaptive optimal control (AOC)is an important approach for dealing with nonlinearity problem [4],similar to other approaches such as model
0196-8904/$-see front matter ó2006Elsevier Ltd.All rights reserved.doi:10.1016/j.enconman.2006.03.035
*
Corresponding author.Tel.:+862164477748;fax:+862164078095.E-mail address:ynhzy2@https://www.doczj.com/doc/f29217780.html, (N.
Yu).
3000N.Yu et al./Energy Conversion and Management47(2006)2999–3007
predictive control(MPC)[5],fuzzy control(FC)[6]and robust control[7]that are implemented successfully in thermal power plants.In most cases,the e?ect of‘‘false water level’’is of interest to researchers,however,it is noted that wave action is often ignored because of an insu?cient assumption that multiple sensor measure-ment can eliminate the errors originating from water surface waves.In addition,the severe oscillation of sen-sor readings forces us to try to avoid the derivative(D)action of the PID controller,whereas the D action represents a signi?cant prediction ability to improve control.Moreover,the drum level shows nonlinear dynamics under varying operation condition.Therefore,‘‘parameter mismatch’’of the PID controller should be a consideration for us.
In this paper,we denote the drum level signal’s errors caused by wave action as noise and develop an adap-tive Grey predictor based method to deal with the discussed problems including(1)the e?ect of‘‘false water level’’,(2)parameter mismatches and(3)noise.This paper is organized as follows:Section2focuses on the problem descriptions;in Section3,the proposed approach is illustrated;and comparisons and conclusions are presented in Sections4and5,respectively.
2.Problem descriptions
Our work is speci?cally motivated by an ongoing research project associated with a boiler of the power plant in Qingdao of China.A cascade three element drum level control system is applied in the boiler(see Fig.1).The master controller of part A in Fig.1is designed with a?xed parameter PI algorithm,and the sub-master controller of part B is realized by a?xed parameter P algorithm.Note that part B is used to deal with the disturbances from steam?ow and feedwater,and part A is the key control part to a?ect control per-formance.With this control system serving the boiler,a set of?eld data is collected and shown in Fig.2(sam-pling period is1s).As indicated by the A in Fig.2,the known nonlinear e?ect of‘‘false water level’’is described as a reverse shift of the drum level when the steam?ow rises abruptly.Given that the D action
is employed in part A or B,to a certain extent,such e?ect would make the controller respond excessively. Therefore,one task in this project is to deal with D action properly.
When under stable operation conditions,drum level can be approximated by the transfer function G1 between feedwater and drum level and the transfer function G2between steam?ow and drum level.These two functions are given by
G1?HesT
WesT
?
e1
s
à
e1s
1tT w s
?
e1
se1tT w sT
e1T
G2?HesT
DesT
?
K s
1tT s
à
e2
s
e2T
where T w,T s represent time constants,e1,e2denote response speeds,and K s is a constant.A PID controller parameter is tuned to match the stable operation condition.If a boiler operates under a varying operation condition,the?xed parameters of the PID controller would not match the dynamics of the drum level.Param-eters mismatches corrupt control performance and may even lead to severe incidents,so this issue is another consideration for us.
Based on several datasets,we analyze the measurement device and the inner condition of the drum and?nd that noise originates from the water surface wave in the drum,and an important behavior of the noise is its low frequency.Fig.3presents a set of raw data from a relatively steady operating condition.If we employ the widely used median?lter to the data of Fig.3,with10steps as the online memory sizes,then for comparison, the result is shown in Fig.4.Fig.4shows that the median?lter only eliminates the high frequency noise while the higher weight low frequency noise still remains.This means that the noise e?ects should be reduced or eliminated by more e?ective methods.
N.Yu et al./Energy Conversion and Management47(2006)2999–30073001
3002N.Yu et al./Energy Conversion and Management47(2006)2999–3007
3.Adaptive GPBA based control
The Grey predictor based algorithm(GPBA)was proposed by Cheng in1986[8].Many approaches of Grey prediction controllers have been developed in recent years[8–11].In this paper,the physical character-istics of the GPBA in the signals are found to be able to describe the uncertainties of parameter mismatches and noise at varying operation points.Therefore,the GPBA is exploited by us.
3.1.Analyses of signal components
Fig.5is a schematic diagram of back feed drum level signal?ow associated with the control system in Fig.1.To begin,we analyze the components of the measured drum level signal l under a certain operation point as follows:
l?l matl mitl die3Twhere l ma denotes the ideal component that matches the controller parameter,l mi represents the error compo-nent from parameter mismatches and l di is the noise component.It is observed that all the components of sig-nal l are sent into the master controller.Only l ma matches the controller parameter because of the uncertainty of the others.Therefore,the conventional controller parameter needs to be optimized by developing corre-sponding techniques for l mi and l di.
The GPBA method can predict system state variables and determine corresponding control strategies for the future[10].If we employ the GPBA for the master controller of the cascade three element feedwater con-trol system,then both l mi and l di can be predicted and separated.This scheme is illustrated in Fig.6.
3.2.GPBA algorithm
The drum level system can be regarded as a Grey system because of its uncertainty.With regard to the GPBA,the Grey system can be described as follows:
_x?AxetTtbuetTtbDex;tTe4TDex;tT?V1x1tV2x2tááátV n x ntfetTe5Twhere x,u and V i(i=1,2,...,n)are state and input vectors and constants;D denotes the uncertain compo-nent of x and is associated with x;f represents the independent noise component of D.For the drum boiler,x and u can be regarded as drum level(or other variables in the drum)and feedwater controller output,and thus,D characterizes the drum level’s uncertainty including(1)l mi,described by x of a certain length of time and(2)l di,independent of x,due to its randomness characteristics.
Suppose x(0)is an original data sequence and its data length is N(N P n+1),which is denoted as xe0T?exe0Te1T;xe0Te2T;...;xe0TeNTTe6TThen,D(0),xe0Tiei?1;2;...;NTand f(0)can be expressed as follows:
De0T?eDe1T;De2T;...;DeNTTe7Txe0Ti?exe0Tie1T;xe0Tie2T;...;xe0TieNTTe8Tfe0T?exe0Te1T;fe0Te2T;...;fe0TeNTTe9Twhere D(i)is immeasurable and can be calculated by
Dex;kT?1
e_xetTàAxetTàbuetTTe10T
According to Grey theory,the accumulated generating operation(AGO)on x(0)is the?rst step in devel-oping the Grey model.The AGO can weaken the e?ect of a disturbance.The?rst order AGO is denoted by xe1TekT?AGOáxe0T?
X k
m?1
xe0TemT;k?1;2;...;ne11TBased on Eqs.(7)–(9),the?rst order AGO sequences of D(x,t),f(t)and x i can be denoted by De1T?eDe1Te1T;De1Te2T;...;De1TeNTTe12Txe1Ti?exe1Tie1T;xe1Tie2T;...;xe1TieNTTe13Tfe1T?exe1Te1T;fe1Te2T;...;fe1TeNTTe14Twhere
fe1TejT?jáfej?1;2...;NTe15TAccording to the AGO algorithm,there exists a corresponding function to Eq.(5)as follows:
De1T?V1xe1T
1tV2xe1T
2
tááátV n xe1T
n
tfetTe1Te16T
Then,the parameter V i(i=1,2,...n)can be approximated by
b V T?eB T BTà1B T De1Te17Twhere
B?
xe1T
1
e2Táááxe1T
n
e2T1
xe1T
1
e3Táááxe1T
n
e3T2
.........
xe1T
1
eNTáááxe1T
n
eNTNà1
2
66
66
64
3
77
77
75e18T
b V T represents the estimated value of V i and f and is given by
b V T?eb V1;b V2;...;b V n;^fTTe19TApparently,with Eq.(19),the uncertainties of the drum level signal can be determined[9].Speci?cally,we can use a white noise signal to approximate^f.
https://www.doczj.com/doc/f29217780.html,pensation control for uncertainties
When the PID algorithm serves the controller online,whose output is calculated by
uekTT?k p eekTTtk i
X k
i?1eeiTTTtk d
eekTTàeeekà1TTT
T
e20T
N.Yu et al./Energy Conversion and Management47(2006)2999–30073003
where R,T and kT is the drum level set,sampling period and current sampling time,respectively,with e(kT)=R(kT)àl(kT).
According to Eq.(4),it is necessary to add compensation control to the PID control as follows: u0etT?uetTtu cetTe21Twhere
u c?à
X n
i?1b V i x it^f
"#
e22TBased on the conventional cascade three element control system,the GPBA based control model is developed as described in Eqs.(19)and(22).
3.4.Adaptive GPBA based control
Naturally,a self-tuning technique is a critical consideration in this work because it is undesirable to imple-ment a?xed parameter PID controller to serve the dynamic process of drum level.The adaptive technique is developed to adapt the GPBA based control to the dynamic operating condition of the drum,and the corre-sponding content is given by
(1)Standard PID:The standard PID with constant parameters is expressed as Eq.(20).
(2)Adaptive GPBA based PID:Fig.7illustrates the key idea of the adaptive technique.
Given that the current sampling time is kT and f kT represents the current steam?ow,we create a factor marked by b,which is de?ned by
b?j f kTàfekà1TT j
j D f max j
e23T
where|D f max|is the possible maximum value of the steam?ow interval(can be estimated by historical data). From Eq.(23),we know that06b61and b has an identical trend with the‘‘false water level’’.Therefore,we can create a variable to represent the D action of the PID.This variable K0
d
is given by
K0
d
?e1àbTáK de24TThis new‘‘D action’’is di?erent from the standard form in that it rises or falls according to the steam?ow variation,and thus,the e?ect of‘‘false water level’’is weakened,but the prediction ability of the PID is strengthened.
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4.Simulations
In this section,we perform simulations to validate our method.The diagram of the proposed GPBA based control system is illustrated in Fig.8,and a simulation model(for a410t/h boiler)is developed as follows:
G1?
0:018
13:5s2ts
;G2?
1:92
13:3st1
à
0:042
s
e25T
The sampling period T is0.5s and the set R is10.For the PID controller of part A,the parameters are given by K p1=4.2,K i=0.02and K d=6.25.For part B,the parameters are given by K p2=1.2,K w=0.21and K s=0.21.For the GPBA,we choose drum level x1and drum pressure x2as state variables,and the white noise variances in Eq.(22)are set as40and5,respectively.To further perform our validation,the conven-tional method shown in Fig.1simulated for comparison in which the parameters of the PI controller in part A are denoted as K p3=4.14,K i3=0.02and the parameters of the P controller of part B are K p4=1.14,N=4. The other parameters concerned are de?ned as above.
Firstly,we simulate a case of dynamic varying steam?ow to valuate our method.If we withdraw the adap-tive technique?rst,i.e.give the D parameter of the PID a constant value,and add a white noise to the steady steam?ow(the variance of the noise is60),then the simulation results are given in Fig.9.Observation of Fig.9gives that the GPBA based PID method satis?es us,although the uncertainty of the steam?ow is sig-ni?cant.When compared with the traditional method,the proposed GPBA method has better robustness to steam?ow disturbances.Secondly,we give di?erent values to the D parameter of the PID to continue the above case.The results are shown in Fig.10,and two conclusions can be drawn therefrom as follows:
(1)properly increasing the D parameter of the PID will improve the control performance obviously,
(2)overly high values of the D parameter of the PID reduce the control performance.
N.Yu et al./Energy Conversion and Management47(2006)2999–30073005
Therefore,there exists a proper value for the D parameter of the PID,and as such,tuning of the D action helps to improve control.
Finally,we simulate abrupt changes of the drum level dynamics to evaluate the complete adaptive GPBA based PID.The process is given in Table 1and the upper part of Fig.11.The simulation results are shown in the lower part of Fig.11.From Fig.11,it is observed that while the drum level dynamics su?ers abrupt changes,the traditional method fails to stabilize the drum level because of the ‘‘parameter mismatches’’,how-ever,the adaptive GPBA based method achieves satisfactory results.The proposed method has excellent robustness for steam ?ow,but the traditional one has severe oscillation e?ects.This can be explained because
Table 1
The tuning of parameters for simulation Time (s)Steam ?ow (t/h)G 1
G 2
t =000:01813:5s 2ts 1:9213:3s t1à
0:042
s t =50600:0151:35à
0:031
t =100à100:01410:2s 2ts 1:4710:9s t1à
0:051
s t =150800:0111:31à
0:026
t =200
20
0:0159:6s 2ts
1:5010:5s t1à
0:042
s
3006N.Yu et al./Energy Conversion and Management 47(2006)2999–3007
N.Yu et al./Energy Conversion and Management47(2006)2999–30073007 the adaptive D action technique has more?exibility than the traditional one.As such,the adaptive tuning of the D action helps to restrain the e?ect of the false water level and accelerate system balance.Additionally, di?erent model parameters make the traditional controller fail to follow the operating condition points(see 100–150s),but our method exhibits proper adaptation to it because the error from the parameter mismatches have been compensated by using the GPBA.
Above all,the adaptive GPBA based PID method has better performance,which is attributed to the GPBA algorithm and the adaptive technique for the D action.
5.Conclusions
To improve boiler drum level control performance in a power plant,current problems can be ascribed to three issues including(1)e?ect of‘‘false water level’’,(2)controller parameter mismatches and(3)signal noise. Several methodologies are proposed to deal with them,and the speci?c contents are listed as follows: (1)Based on the analyses on the principle of false water level,proper derivative action of the PID helps to
provide process stability and enhance system robustness.As such,the adaptive derivative action tech-nique is developed by monitoring the steam?ow variation.
(2)Because parameter mismatches corrupt controller response,some analyses are conducted,and the con-
clusions show the resulting errors should be considered.Besides,the noise component of the sensor read-ing holds a considerable proportion due to the surface wave of the drum water.
(3)The Grey predictor has apparent advantages in its estimation of both correlated uncertainties and inde-
pendent uncertainties.Hence,the Grey predictor is developed to predict the uncertainties of two issues, parameter mismatches and noise.
Finally,several sets of simulations show that the proposed methods help to improve the control system’s robustness.Speci?cally,this method has been employed in an important research project of China. Acknowledgement
This work was funded by a research grant from the National Natural Science Foundation of China (5997022)(NSFC).
References
[1]Wang Wei,Li Han-xiong,Zhang Jing Tao.Intelligence-based hybrid control for power plant boiler.IEEE Trans Control Syst
Technol2002;10(2):280–5.
[2]Rafael A,Ebasco https://www.doczj.com/doc/f29217780.html,bined-cycle plants can challenge feed water control.Power Eng1994;98(3):43–4.
[3]Parthasarathy Sanjay,Parlos Alexander,Atiya Amir.Neuro-predictive process control using on-line controller adaptation.IEEE
Trans Control Syst Technol2001;9(5):741–55.
[4]Nomura M,Sato Y.Adaptive optimal control of steam temperatures for thermal power plants.IEEE Trans Power Electron
1989;4(1):25–33.
[5]Ben-Abdennour A,Lee KY,Edwards RM.Multivariable robust control of a power plant deaerator.IEEE Trans Energy Conver
1993;8(1):123–9.
[6]Van Landingham HF,Tripathi ND.Knowledge-based adaptive fuzzy control of drum level in a boiler system.In:Southcon/96.
Conference Record,1996.p.454–9.
[7]Tan W,Marquez HJ,Chen T.Multivariable robust controller design for a boiler system.IEEE Trans Control Syst Technol
2002;10(5):735–42.
[8]Zhang Guangli,Fu Ying,Yang Ruqing.Fuzzy grey prediction force control scheme based on outer force control loop.Chin J Mech
Eng2004;40(12):177–81.
[9]Wang DF,Han P,Han W,Liu HJ.Typical Grey prediction control methods and simulation studies.In:Proceedings of the second
international conference on machine learning and cybernetics,Xi’an,November2003,vol.1.p.513–8.
[10]Shieh Ming-Yuan.Design of an integrated Grey-fuzzy PID controller and its application to pion-minimum phase systems,SICE
2002.In:Proceedings of the41st SICE annual conference,August2002,vol.5(1).p.2776–81.
[11]Li Chien-Ying,Huang Tsong-Liang.Optimal design of the Grey prediction PID controller for power system stabilizers by
evolutionary programming.In:Networking,sensing and control,2004IEEE international conference,vol.2,2004.p.1370–5.