Iterative Learning Control For Distributed Parameter Systems With Randomly Varying Trial Lengths

Iterative learning control(Iterative Learning Control,ILC),as an important branch in intelligent control,is suitable for systems that can continuously complete specified tasks repeatedly.It attempts to control the controlled system and corrects the non-ideal control signal with the tracking error of the system,so that the input signal of the system is continuously updated along the iteration axis,so as to achieve complete tracking of the desired trajectory.Traditional iterative learning control requires that the duration of each iteration must be consistent to meet the learning algorithm to be revised and improved in continuous control attempts.Therefore,as one of the strict repeatability requirements of traditional iterative learning control,a fixed batch length is our inherent requirement for systematic learning.However,in many practical situations,the running time under different batches may no longer be consistent,but vary randomly.Randomly changing batch length makes the strict repeatability requirements of traditional iterative learning control no longer met,resulting in hindered the development of iterative learning control in practical applications,which prompted us to start to consider iterative learning control under the environment where the batch length changes randomly Of applicability.In this paper,the distributed parameter system(Distributed Parameter System,DPS)described by the partial differential equation is selected as the research object.Unlike the centralized parameter system,which only considers a single time variable,the distributed parameter system contains both time and space variables It also makes it difficult to study the iterative learning control of distributed parameter systems.In addition,in computer simulation and computer-aided design,the use of digital computer analysis to solve the state equation of a continuous system,or computer control,often requires the continuous-time system to be discretized.Therefore,the research on discrete-time systems has practical application value.This paper takes the iterative learning control problem of the discrete distribution parameter system with batch length random change as the main research content.Among them,several types of distributed random iterative learning control algorithms are proposed based on the characteristics of random change of batch length,and detailed through strict theoretical analysis.The proof of the convergence of systematic errors is given.The effectiveness of the algorithm is verified in the given simulation.main tasks as follows:1.For the linear discrete first-order hyperbolic distributed parameter system,the problem of iterative learning control under the random change of batch length is studied.It is assumed that the range and probability distribution of the batch length that randomly changes in the system,and the expression of the probability that the systematic error occurs at a certain time is derived by means of probability statistical methods.Then,the distributed P-type and D-type iterative learning control algorithms are applied to the system without direct transmission channel respectively.In addition,the mathematical analysis methods such as discrete Gronwall and compression mapping principle are used to prove the convergence of the systematic error under mathematical expectation.Through numerical simulation,the effectiveness of these two distributed iterative control algorithms is verified.2.The problem of iterative learning control for discrete parabolic distributed parameter systems with batch length random changes is studied.In order to use the tracking information of all previous iteration processes to improve the performance of the current system,the iterative average operator is applied to the design of distributed learning laws.Then,based on the form of the general solution of the deviation fraction equation under the initial boundary value,the dimensionality reduction of the parabolic system under study is carried out.Using the traditional distributed parameter system iterative learning control analysis method and D'Alembert's discriminant theorem,it is proved that the system error under mathematical expectation converges along the iteration axis.The effectiveness of the proposed distributed iterative learning control algorithm is verified by the given numerical simulation.3.For linear discrete parabolic systems,a class of distributed learning algorithms with a screening mechanism is proposed.The algorithm makes the redundant tracking information missing and zero-filled no longer be collected and used for learning,but only uses the measurable useful information in recent iterations to improve the current system performance.Strict theoretical analysis proves that the convergence condition of system error is directly obtained.Finally,numerical simulation is given to verify the effectiveness of the proposed algorithm,and the comparison with the simulation results in Chapter 3 shows that the tracking error convergence speed of the algorithm is improved.