基于模型参考自适应Smith预估器的反馈式AGC厚度控制系统翻译

Feedback automatic gauge control system using modelreference adaptive Smith predictorLI-Xun, SONG Dong-qiu, YU Shou-yi, GUI Wei-hua(1. School of Information Science and Engineering, Central South University,Changsha Hunan 410083, China;2. Southwest Aluminum (Group) Co, Ltd,Chongqing Sichuan 401326, China)Abstract: Based on the compensating principle of Smith predictor for the time-delay process, we build a model-reference-adaptive(MRA) Smith-predictor feedback control model for the automatic-gauge-control(AGC) system. The structure of the control system is determined, the design algorithm and the adaptive modulation principle are bining the MRA Smith-predictor feedback with the AGC control model, we can control the thickness-deviation at the output. Simulation results show that the AGC system with the MRA Smith-predictor feedback exhibits an excellent performance in controlling the thickness deviation of rolled aluminum strips. The limitation on the time-delay which originally affects the control performance is now eliminated, the thickness-variation at the output is removed, and the response rate is raised. In summary，the product specifications of aluminum strips are satisfied.Key words: rolling; Smith predictor; feedback automatic gauge control; model reference adaptive1 introductionModern single stand reversible four heavy cold rolling mill automatic gauge control system（AGC）has the feedforward AGC, seconds flow type AGC and feedback type AGC etc.. All kinds of AGC coordination control strategy in the application of rolling can make the plate product thickness and plate shape have higher control precision.But because there is a certain gap between the point where thickness gauge checks in the export side and the rolling bite,the feedback type AGC makes thickness control produce pure time delay,have a not ideal controlperformance. For reducing the delay time of the control process, it is necessary to compensate the pure time delay of the feedback type of AGC. Smith estimate is an effective control method to overcome pure delay, through the dynamic properties of the estimate object ,compensating time delay with a prediction model, Compensator and controlled object together constitute a no time delay's generalized controlled object, So as to effectively overcome the influence of pure delay. According to Smith predictor has a strong dependence on the accuracy of the mathematical model of controlled object , document[3] puts forward the method of the adaptive poles self-revised, document[4] puts forward the method of the adaptive fuzzy controller. The closed-loop control system with pure time delay link has greater overshoots and longer regulating time, When the controlled object be disturbed and leading to the change of the regulated quantity, the controller can't immediately barrage jamming. This paper, based on the model reference adaptive control principle, use the model reference adaptive Smith predictor to keep the model parameters under the control of the adaptive law the samewith the controlled object.2 The model reference adaptive Smith predictor2.1 Control theory of MRA-Smith predictorMRA-Smith predictor is presented in Figure 1. G(s)e-τs is the control system transfer function, G m(s)e-τms is Smith prediction model of the controlled object,G C1(s) is the main controller,often use the PI algorithm. G C2(s) in the dotted line box is the secondary controller,often use the PD algorithm, Primarily for regulating the integral process or configurating the poles of the static process.Gd is the disturbance compensation controller.GC2(s)used for stabilizing nonstatic integral process and configurating poles of dynamic process, makes the poles of the control system distribute in the right place，so there is a better control performance.Gd used to adjust the response characteristic of the disturbance d (t)，inhibits the static error of standard Smith predictor with external disturbance，enhances adjust ability in order to improve the anti-jamming performance of the Smith predictor. For larger pure time delay object, Smith predictor with the PD secondary controller and disturbance compensation controller has a bettter control performance than the standard Smith predictor. In the cold rolling process rolling speed is change, Smith predictor model parameters and rolling mill parameters will not completely match, so join model reference adaptive agencies regulate the prediction model parameters,in order to reach the parameters which match the control object. G(e; t) is the gain of the adjustable feedforward regulator，F(e; t) is the compensation gain of the feedback regulator.When not joining MRA-Smith predictor, the closed-loop transfer function and characteristic equations of the control system isBecause of containing pure time delay link e-τs, along with the increase of τ and the phase lag, the stability of the system is lowering, the control effect become poor, the bigger τis the more difficult to stablize the system. When MRA-Smith predictor model and the controlled object is exactly match,C m(t) = C(t),G m(s) = G(s) and e-τms=e-τs.The output of system isBy formula (4), set characteristic equations of the input closed-loop transfer function asAlready not containing time delay part, the system stability does not influence byτ, e-τs in formula (4) only let the system response delay timeτ.2.2Design of MRA-Smith predictorMost of the controlled object of production process can be simplified by first-order lag plus delay（FOLPD），The transfer function isIn the formula，k is quotient，τ is the delay time，assumeLet the formula （8）（9）plug in formula （4），and ignore the time delay part e-τs，then get the input closed-loop transfer functionAssumeSimplify formula （10）asaccording to the value of the given parameters kc，Ti，k and a，we can determine the value of the parameters η and c1, Ibrahim Kaya in the literature [10] put forward the relationship of d1 and c1 as following2.3Design of MRA principleBecause the time delay part can be calculated，ignore the compensation pure time factor part of the rolling mill and Smith prediction model. According to formula (7)，take the first order link of rolling mill as reference model,and the state equation isThen the Smith predictor model adjustable system and its state equation isThe equation of Feedforward regulator G(e,t) and feedback regulator F(e,t) isAccording to formula（15）（16），there is a adjustable system equationAssume system general error asAccording to formula （13）and（17），there is a generalized state error equation.ThereinDesign adaptive law of G (e，t) and F(e，t), make formula (19) asymptotically stable,when t→∞,e(t) →0, ψ(t) →0,φ(t)→0. Select the lyapunov functionIn the function:λ1 > 0, λ2 > 0,km > 0,then v(t)>0 establishes when t≠0,soAssumeThenEnsure system is asymptotically stable,differentiate formula (20)，and plug in formula (23) to get the system integral adaptive regulation law3Feedback AGC system based on model reference adaptive Smith predictor3.1 Feedback AGC systemAccording to the feedback type AGC system control principle, when there is incoming thickness deviation △H, rolled piece export thickness deviation isIn the formula: Q is the plastic stiffness of rolling piece, Cp is the longitudinal stiffness of rolling mill. To eliminate export thickness deviation, we need to adjust the amount of roll gap toSet the distance thickness gauge to rolling mill roll gap as L,mill speed as v,the delay time to getting the detection value asτ1=L/v. Thickness gauge and down device has certain response time is respectively τm and τh,the total pure delay time of the feedback AGC control system is3.2Exit-thickness deviation of MRA-Smith predictor feedback AGCsystemIn feedback AGC control model reference adaptive Smith predictor can compensate the pure time delay factor e-τs. Figure 1 getsAccording to formula(29),get the transfer function from Thickness deviation to roll gapIf Smith predictor model and rolling mill completematch:G(s)e-τs=Gm(s)e-τms,plug (30) in (31) to getPlug formula(33) and (34) in formula(32),then get the deviation value of the export thickness of rolled piecesFrom formula (35) we can see the disturbance input is small, can even be neglected,the disturbance controller Gd takes zero，the deviation value of rolled piece export thickness is simplified toGet △h to tend to 0,as long as configurating Gc2(s)=-1/Gm(s).4Simulation of control system4.1 Model structure of control systemIn the feedback AGC control system, the thickness controller center on integrator, including thickness dead zone and the limiter. Because integrator generates oscillation and limit cycle oscillations easily, the goal of setting the dead zone is to prevent deathlimit cycle oscillations, under the premise of ensuring the control accuracy to prevent hydraulic pressing device to produce false action. The limiter avoid the influence of the strip straightness of aluminum plate beacuse of the large amount of the roll gap regulating variable , ensure the precision of shape. MRA-Smith predictor is applied to the feedback AGC automatic thickness control, get the control system as shown in figure 2.4.2Simulation parameters of control systemAfter simplified, single stand reversible four heavy cold rolling mill AGC system can be approach to 1-st order delay system, the mathematical model express asSoτ/T=5.6,within the limits of 0.05≤τ/T≤6，according to the ITAE optimal PID controller design experience formulaGet the feedback AGC traditional PID controllerRolling mill thickness gauge response time, feedback delay time and hydraulic pressure under device response time together is 0.3 s, set the sum of the input signal is the unit step signal. According to the above design principles, get MRA-Smith feedback AGC thickness control system parameters as shown in table 1.4.3Simulation result of control systemAccording to the figure 2 build the SIMULINK simulation diagram ofMRA-Smith predictor of the feedback AGC control system,then get aluminum sheet exports thickness deviation curve as shown in fig.3.Figure 3 (a) show that the traditional PID feedback AGC control system in aluminum sheet rolling process, because pure time delay characteristics is not compensated, aluminum sheet export thickness in about 3 s of the delay time do not reduce，thickness deviation curve is obviously oscillation. Conventional Smith feedback AGC control system can compensate for pure time delay characteristics of the rolling process, reduce oscillation of the exports thickness deviation curve, but there are a wave phenomenon, to a larger extent, slow reaction speed,after 2.5 s export thickness deviation reaches zero.The predictor model and rolling mill model does not fit, assume the time constant of the Smith predictor model is 0.7 s (the actual time constant of rolling mill is 1 s) get export thickness deviation curve of rolled pieces as shown in figure 3 (b). MRA-Smith predictor feedback AGC thickness control system can start feed-forward regulator and feedback regulator according to the self-adaptive law,onlineself-adaptive Smith predictor model parameters and rolling mill parameters tend tomatch, make thickness deviation of rolled pieces gradually reach a set error range, not only compensate pure time delay characteristics existing in the feedback control, thickness deviation curve does not exist oscillation phenomena, the stability of system increases quickly, convergence time is in 0.5 s, self-adaptive response is fast , can satisfy the production accuracy of aluminum sheet.5ConclusionFeedback AGC thickness control system with pure time delay characteristics restrict the improvement of the quality of the board strips products, using the Smith predictor to compensate pure time delay is a kind of effective method in engineering. But the traditional Smith predictor is more sensitive in model parameter uncertainty,when the model not completely matching the performance of the control system is not good.The MRA-Smith is able to solve this problem, the key is to build compensator model and realize pure delay link and design self-adaptive law. In this paper, we study the MRA-Smith prediction PI controller feedback AGC controlsystem’s application in aluminum sheet rolling process AGC control, AGC the results show that the Smith predictor with improved structure combined with the adaptive regulation law can solve the problem that the phenomena model parameters are not completely matching influences control performance,let rolled piece export thickness deviation be quickly in the allowable range in the fast time,the control response be fast, and effectively compensate for pure time delay characteristics of the traditional PI thickness control , rolled pieces thickness control have high accuracy, and there is engineering application value.。