In this study, auto tuning of PID control gains in hot strip looper controller is made based on RNN model. Neuro emulator is employed to model the characteristics of looper
dynamics. Combining neuro emulator and RNN model, auto tuning system of PID control gains is constructed. As the inputs to RNN, plural evaluation functions which reflect individual preference of human experts. Further, Self learning mechamism is embeded to RNN model which enables adaptation to the change in rolling chracteristics. Through numerical experiments, the effect of the proposed method is ascertained

Abe, Yoshihiro

Imai, Jun

Konishi, Masami

Nishi, Tatsushi

Okayama University Scientific Achievement Repository

Yoshihiro Abe ∗Dept. of Electrical and Electronic EngineeringOkayama University3-1-1, Tsushima-Naka Okayama, 700-8530　　　　Masami KonishiDept. of Electrical and Electronic EngineeringDivision of Industrial Innovation ScienceThe Graduate School of Natural Science andTechnologyOkayama University3-1-1, Tsushima-Naka Okayama, 700-8530Jun ImaiDept. of Electrical and Electronic EngineeringDivision of Industrial Innovation ScienceThe Graduate School of Natural Science andTechnologyOkayama University3-1-1, Tsushima-Naka Okayama, 700-8530Tatsushi NishiDept. of Electrical and Electronic EngineeringDivision of Industrial Innovation ScienceThe Graduate School of Natural Science andTechnologyOkayama University3-1-1, Tsushima-Naka Okayama, 700-8530In this study, auto tuning of PID control gains in hot strip looper controller is madebased on RNN model. Neuro emulator is employed to model the characteristics of looperdynamics. Combining neuro emulator and RNN model, auto tuning system of PID controlgains is constructed. As the inputs to RNN, plural evaluation functions which reflect indi-vidual preference of human experts. Further, Self learning mechamism is embeded to RNNmodel which enables adaptation to the change in rolling chracteristics. Through numericalexperiments, the eﬀect of the proposed method is ascertained.1 IntroductionIn these years, plant control systems are being highlyautomated. But both the performances of plant andcontroller change with the passage of time, so it is nec-essary to tune them. This is why human experts inter-vene and tune the control system to improve the totalplant performances. In this paper, it is targeted espe-cially to tune looper control gains in the threading ofhot strip mills. In hot strip mills, the looper height con-trol system is set up between stands. By use of them,the rolling operation are kept to be stable. It is usualthat the looper control system is governed by PID con-∗y-abe@cntr.elec.okayama-u.ac.jptroller. Usually PID gains are determined by gain tableaccording to a variety of strip thickness and hardness,but the optimal gain also varies with time due to thedeterioration of plant characteristics. Now, it is oftenthe cases that the skillful operators tune these gains.It is necessary to tune the PID gains appropriately inorder to stabilize the looper’s behavior. In the past,the looper control in the steady state has been widelybuilt up as the control technique [1]. Contrary to this,in threading condition of the looper ’s behavior tendsto be unstable, and then human expert never fail tointervene and stabilize the looper ’s behavior by tun-ing PID gains and interposing manipulated variable oflooper height control system. In general, it is diﬃcultRNN Based Auto-tuning of PID Control Gains in Hot StripLooper ControllerMemoirs of the Faculty of Engineering, Okayama University, Vol.40, pp.16-22, January, 2006(Received December 14, 2005)This work is subjected to copyright.All rights are reserved by this author/authors.16to automatize human’s action because of flexibility anddiversity of his human operations not only in hot striprolling but also in other objects. In this paper, we tryto automatize tuning of PID gains by human. That is,the method of using recurrent neural networks (RNN)[2][3][4] is proposed. Because human can memorize thepast tuning results whether old or new, human’s tun-ing action depends on past tuning experiences. RNN isa simple mechanism generating its outputs dependingon the past data. Firstly, neuro emulation is studied toemulate a dynamic behavior of hot strip rolling. Theobtained neuro emulator is combined with PID con-troller to simulate the Looper height control dynam-ics human tuned PID gains of looper control system.Then, methods to update the RNN model by usinglearning algorithm will be proposed.2 Looper Height Control in HotStrip RollingThe looper angle is determined by the diﬀerence ofstrip velocities between adjacent rolling stands. In thefollowing, the mathematical model of looper controlin hot strip rolling, strip thickness control and looperheight control are described.2.1 Mathematical Model for Hot RollingThe fundamental equations for hot rolling processare described as follows.Pi = σiqR0i(Hi − hi)Qi (1)Fi =12arctanrHi − hihi− π8shiR0ilnhiR0i(2)Qi =rhiHi − hiÃπ2arctanrHi − hihi−sR0ihilnhφihi+12sR0ihilnHihi!− π4(3)R0i = R³1 +cPiHi − hi´(c = 0.214× 10−3) (4)　 hi = si +PiM(5)φi =shiR0itanFi (6)fi =12φ2i³2R0ihi− 1´(7)bi =hiR0i(1 + fi)− 1　 (8)where, Pi is rolling force, σ is flow stress, Hi is en-try strip thickness, hi is exit strip thickness, Ri is rollradius, si is roll gap, fi is forward slip ratio, bi is back-ward slip ratio, Mi is mill modulus, and subscript idenotes ith stand. Using fi and bi led by solving aboveequations, exit strip speed vfi and entry strip speed vbican be obtained as followsvfi = VRi(1 + fi) (9)vbi = VRi(1 + bi) (10)where VRi is the rolling velocity of ith mill.2.2 Mathematical Model for Looper Sys-temAs shown in Fig. 1, the distance between mills isL = L1 + L2，exit strip speed of ith mill is vfi ,andentry strip speed of (i + 1)th mill is vbi+1. AssumingL1 = L2 and θ = θ0, the strip loop angle θ can beobtained as followssec θ = 1 +1LZ t0(vfi − vbi+1)dt (11)where the integral is started when the strip gets threads(i + 1)th mill. The strip loop figure can be approxi-mated as isosceles triangle. Thus, and looper angle αis given bysinα =1l³L2tan θ + δ´(12)Fig. 1: Looper and interstands schematicsVariables vfi, vbi, θ0, θ,α, δ, l, L, L1, L2 are explaimedin Fig. 1Yoshihiro ABE et al. MEM.FAC.ENG.OKA.UNI. Vol.40172.3 Mass Flow Model for Rolling veloc-ityMass flow rule is used in order to determine set pointof rolling velocity. Mass flow rule can be described asho1VR1(1 + f1) = ho2VR2(1 + f2) (13)where hoi is the desired value of strip thickness at ithstand.2.4 Strip Thickness Control ModelGauge meter equation is written byhi = si +PiM(14)where hi, si, Pi andM are exit strip thickness, roll gap,rolling force and mill modulus. The control scheme ofGauge Meter AGC(Automatic Gauge Control) is givenby∆hi = hi − hoi (15)∆si = −ki∆hi (16)where ki is AGC gain. AGC is started to operate soonafter the head end of strip arrives at the next stand.3 Problem description of LooperControl System3.1 PID Control of Looper AnglePID control is described asm(t) = Kp³e(t) +1TiZe(t)dt+ Tdde(t)dt´(17)where m(t) is manipulated variable and in this case,e(t) is error and means looper deviation, Kp is propor-tional gain, T i is integral time, and Td is derivativetime of PID control. In simulator, PID control is usedwith velocity form algorithm and lagged derivative.un = un−1 +Kph(en − en−1) +TsTien +∆μni(18)ηn = μn−1 +∆μn (19)∆μn = (γβ − 1)μn−1 + β(en − en−1) (20)β =TdTs + γTd(21)where Ts is sampling time instance, en is error at sam-pling instance nTs, en−1 is error at sampling instance(n− 1)Ts. and 1γ is derivative gain.3.2 Inter Stands Looper DynamicsThe problem treated in this paper consists of twostands and one looper facility between them. Thelooper angle is controlled by changing rolling speed ofthe upstream stand. In the following, construction ofthe problem for hot strip looper height control systemwill be stated.Fig. 2 shows two stands hot strip mill system withcontrollers. The block diagram showing dynamic char-acteristics of inter stands looper are given in the lowerpart of Fig. 3.Fig. 2: Hot Strip MillFig. 3: Block Diagram of Hot Strip Mill with Con-trollersIn this paper, based on the model in Fig. 3, numericalsimulations are carried out to generate looper dynam-ics for the construction of gain tuning system.4 Auto Tuning of PID Gains byRNNThe Construction of Gain Tuning System is shownin Fig. 4. the upper part of Fig. 4 shows real plant in-volving hot strip looper and PID controllers. The lowerpart of Fig. 4 shows the proposed gain tuning mecha-January 2006 RNN Based Auto-tuning of PID Control Gains in Hot Strip Looper Controller18Fig. 4: Construction of Gain Tuning Systemnisms. As shown here, neuro emulator is employed togenerate emulated looper angle dynamics. The resultsof emulation are estimated in estimator whose outputsare used for the inputs to RNN model. RNN gener-ates gains for PID controller. The parameters in neuroemulator are updated such that whose output becomessimilar to the looper angle of hot rolling mills.4.1 Neuro Emulator modelThe structure of neuro emulator model is shown inFig. 5.Fig. 5: Structure of Neuro Emulation modelThe inputs to a neuro emulator are time series dataof looper inputs, deviation of rolling speed, and pastLooper angles. These data are stored in data base oflooper dynamic characteristics and used for identifica-tion and traing of connecting weights in neuro emula-tor.The methods of trainig connecting weights in neuroemulator, λ(2)kj and λ(1)ji and descibed in the followingequations.λ(1)ji = λ(1)ji +∆λ(1)ji 　 (22)λ(2)kj = λ(2)kj +∆λ(2)kj (23)∆λ(2)kj = −η1∂E1∂λ(2)kj(24)∆λ(1)ji = −η1∂E1∂λ(1)ji(25)∂E1∂λ(2)kj= (αˆ[N ]− α[N ])y(2)j [N ] (26)∂E1∂λ(1)ji= (αˆ[N ] − α[N ])λ(2)kj [N ](1−y(2)j [N ])y(2)j [N ]y(1)i [N ] (27)E1 =12(αˆ[n]− α[n])2 (28)when, E1 is diﬀerence between α and αˆ, η1 is gain oftraing, y(1)i is the output of ith neuron in the inputlayer, y(2)j is the hidden of jth neuron in the outputlayer. Thus, the looper dynamics can be representedby neuro emulator. As show in Fig. 6, looper dynamicscan be replaced by neuro emulator. In the simulationfor gaintuning, neuro emulator is connected to loopercontroller as show in Fig. 7.Fig. 6: Replacement of looper dynamics by Neuro Em-ulatorFig. 7: Connecting method of neuro emulator with con-trollerYoshihiro ABE et al. MEM.FAC.ENG.OKA.UNI. Vol.40194.2 RNN ModelThe structure of RNN model is shown in Fig. 8. Thenetwork has three layers. The first layer is the inputlayer, which consist of two parts. The one is the planlayer, which represents input evaluation value Ii(i; 1 ∼5) respectively.Fig. 8: Structure of RNN ModelThe other is the context layer at number of rollingof N 0, which is expressed byck =N 0Xm=1dN0−mgk[m] ; k = 1 ∼ 3 (29)g1 : Kp, g2 : Ti, g3 : Td (30)where d is a positive constant and less than 1, whichmeans forgetting eﬀect and N 0 is the rolling numberindicating N 0th preceding instant. As shown in Fig. 8,the context layer is the layer that the past output dataof RNN is stored.Then the output of input layer isx(1)i =(Ii if 1 ≤ i ≤ 5ci−5 if 6 ≤ i ≤ 8(31)The second layer is the hidden layer, which can beexpressed assj =6Xi=1w(1)ji x(1)i ; j = 1 ∼ 6 (32)x(1)0 = −1 (33)x(2)j =11 + e−sj; j = 1 ∼ 6 (34)where w(1)ji is the weight for the connection between ithneuron in the input layer and jth neuron in the hiddenlayer.The third layer is the output layer, which is descrivedas follows.sk =3Xj=0w(2)kj x(2)j ; k = 1 ∼ 3 (35)x(2)0 = −1 (36)gk = sk; k = 1 ∼ 3 (37)where w(2)kj is the weight for the connection betweenjth neuron in the hidden layer and kth neuron in theoutput layer.Control perfermances are evaluated quantatively byusing evaluation equations (38) to (42).I1 =Z T1T0| ααo− 1|dt (38)I2 =Z TT1| ααo− 1|dt, (39)I3 =1T − T1Z TT1t| ααo− 1|dt (40)I4 = Kαover − αunderαoK = 10 (41)I5 =tT − T1t : settling time (42)Evaluation value Iis(i; 1 ∼ 5) in eqs.(38) to (42) areshown in Fig. 9.Fig. 9: Evaluation valueIn the learning process of RNN model, weight pram-eters are optimised such that each evaluation value ap-proaches to its expected value. In the learning, Sumof the diﬀerences of evaluation values Is from their ex-pected values Ios.4.2.1 Method of PID Gains tuning by RNNThe structure of RNN model is updated reﬀering dif-ferences of evaluation values with their aimed values.January 2006 RNN Based Auto-tuning of PID Control Gains in Hot Strip Looper Controller20Details are descibed in the following.w(1)ji = w(1)ji +∆w(1)ji 　 (43)w(2)kj = w(2)kj +∆w(2)kj (44)∆w(2)kj = −η2∂E2∂w(2)kj(45)∆w(1)ji = −η2∂E2∂w(1)ji(46)∂E2∂wkj=5Xm=1(Im − Iom)∂Im∂gkx(2)j (47)∂E2∂w(1)ji=3Xk=1³ 5Xm=1(Im − Iom)∂Im∂gk´w(2)kj (1− x(2)j )x(2)j x(1)i　　 (48)where, E2 is defined byE2 =125Xm=1(Im − Iom)2 (49)η2 is gain of traing.4.3 Training of RNN ModelThe RNN model is trained by the back propagationalgorithm (BP). BP algorithm is described as follows.step1；initializationThe end condition of learning is determined, and ini-tial value of weight parameters w(1)ji s and w(2)kj s are de-termined by generating random number between 0 and1.step2；input and preprocessingThe evaluation values, Ii[N0](i; 1 ∼ 5) at N 0th rollingare input to the plan layer and PID gains at previousrolling number of rolling N 0 are input to the contextlayer. Where input to the context layer is 0 at N 0 = 1.step3；forward propagationBy Eqs.（29）to（37), the output x(2)j of hidden layerand the output g(3)k [N0 + 1] of output layer are calcu-lated.step4；back propagationEqs.(43) to (48) are used in back propagation to up-date the RNN model.5 Numerical ExperimentsAccording to iteration progress, PID gains simulta-neously approach to certain covergence values. Theseconvergent behaviors are shown in Fig. 10. As shownhere, PID gains Kp, Ti and Td are tuned to their opti-mal values during iterations.Fig. 10: Variation of PID gains during tuningFig. 10 shows oﬄine gain tuning results. Vaviationsof loooper angle during tuning are shown in Fig. 11.The looper angles shown here are calculated by neuroemulator. As shown here, looper behavior becomesperferable during iterations.Fig. 11: Variation of Looper Angle(αˆ) during tuningAt the same time, estimation values reach to theirobjective values as shown in Fig. 12. That is, by theeﬀect of selt learning of RNN model, optimizations ofcombining weights of RNN model are considered to bemade.Yoshihiro ABE et al. MEM.FAC.ENG.OKA.UNI. Vol.4021Fig. 12: Variation of Evaluation value during tuningFig. 13 shows simulated looper dynamics for eachPID gains obtained by RNN model comparing emu-lated result in Fig. 11. As shown here, with exceseof tuning, improvement of control performance is at-tained. Apperently, simulated results show the eﬀec-tiveness of the proposed gain tuning method by RNNmodel.Fig. 13: Variation of Looper Angle by tuning(αo =[30deg])6 ConclusionIn this paper, auto gain tunig method of PID con-troller for hot strip looper height control is proposed.Neuro emulator is newly employed to emulate the dy-namics of looper height dynamics during rolling. RNNwith self learing function is used to generate PID gains.As for the inputs to RNN model, evaluation functionsof control performances are adopted which enables re-flection of the human preferences. Throught numericalexperiments, the applicability of the proposed methodis confirmed. Combination of a neuro emulator andRNN is consider to be powerful tool of PID gain tun-ing for other control system.Bibliography[1] S. H.Asada et al, ”Adaptive and Robust Control-Method with Estimation of Rolling Characteristicsfor Looper Angle Control at Hot Strip Mill”, ISIJInternational, Vol.43, No.3(2003), pp358-365[2] I.M.Mujtaba et al, , ”Application of Neural Net-work to Generation of Robot Arm Trajectory”,AROB9th, pp.380-383,2003[3] Lakhmi C.Jain et al, ”INDUSTRIAL APPLICA-TIONS of NEURAL NETWORKS”, The CRCPress, 1999[4] Cihan H. Dagli, ”ARTIFICIAL NEURAL NET-WORKS for Intelligent Manufacturing”, ChapmanHall, 1994[5] S. Imajo et al. , ”Human Model for Gain Tuningof Looper Control in Hot Strip Rolling”, tetsu-to-Hagane,vol.90,No. 11,pp.933-940, 2004January 2006 RNN Based Auto-tuning of PID Control Gains in Hot Strip Looper Controller22

RNN Based Auto-tuning of PID Control Gains in Hot StripLooper Controller

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