Iterative Learning Control For Parabolic Distributed Parameter Systems With Time Delay

Since Arimoto proposed iterative learning control, in-depth academic researchfor all kinds of systems described by ordinary differential equations, put forward allkinds of control methods, such as the open loop P algorithm, PID algorithm for openloop; closed loop PD type algorithm, closed loop PID algorithm, and combinedcontrol, artificial intelligence and neural network control algorithm with wisdom, giveplay to their respective advantages in the practical engineering practice effectivelysolve many control problems. But the academic research in the distributed parametersystem is relatively less.For these reasons, this paper makes a study on two kinds of certain conditionsare satisfied with state delay parabolic distributed parameter system, puts forward twokinds of iterative learning control algorithm, the proof and simulation algorithm fordistribution to the miserable number system effectively control. For a class ofparabolic for Lipschitz nonlinear parabolic distributed parameter systems with statedelay and with multiple state delays, distributed parameter system respectively, thispaper presents a high order learning law and open P type learning law, to prove theeffectiveness of the algorithm, and gives the numerical simulation examples.For a class of satisfying the Lipschitz conditions with time-delay nonlineardistributed parameter system is a high order algorithm, the application of suchalgorithms in distributed parameter systems are rare. Because of the current academiccircles for distributed parameter systems with no effective method to distinguishalgorithm efficiency, efficiency and can't tell the difference between the algorithm andthe general PID algorithm, but the current iterative learning control trend is theexpansion of existing algorithms, this algorithm in the distributed application systemreference number or a more useful. For the linear systems with multiple state delays isproposed to open loop P control law. The effectiveness of the proposed controlalgorithm in the proof of the state time delay, the constant characteristic, according tothe basic idea of system state input estimation using the system, and according to thecharacteristics of the initial system state value, product classification techniques usingRiemann transform, successfully demonstrated the effectiveness of control algorithmis given.For the study of iterative learning control, is crucial for proving the validity ofthe algorithm, but the degree of attention to the continuous improvement of numericalsimulation system. The two class of distributed parameter systems are presented a numerical simulation. In the simulation process of the two system, the use of forwardEuler difference scheme for the partial differential equation is solved numerically, thesuccess of the system simulation.