Research On Iterative Learning Control Algorithm For A Class Of Nonlinear Systems

Iterative learning control is an effective control method in systems with repeated operation characteristics.It uses the input value and output tracking error of the controlled system in the historical iteration to adjust the input value of the controlled system in the next iteration,so that the real-time output trajectory of the system completely tracks the desired output trajectory of the controlled system.In this thesis,aiming at a class of nonlinear controlled systems with the same macroscopic input-output nonlinear relationships,the following work has been done in broadening the application range of iterative learning control algorithms,improving the convergence speed and stability of controlled system output tracking error,and enhancing the robustness of the algorithm:The proportional-derivative type iterative learning control algorithm in the form of open-loop and closed-loop are improved respectively when the nonlinear controlled system meets the one-side Lipschitz condition and the quadratic inner bounded condition.Then the mathematical method which includes ? norm and its related characteristics and so on is used to analyze the convergence characteristics of the proposed algorithm,and the effectiveness of the proposed algorithm for tracking the output of such a nonlinear controlled system is proved theoretically,and the convergence conditions are given.In addition,simulation results show that the closed-loop iterative learning control algorithm performs more stable than the open-loop iterative learning control algorithm.Compared with the research on the iterative learning control algorithm under the classical local Lipschitz condition with high frequency,the improved algorithm research under the one-side Lipschitz condition weakens the constraints of the iterative learning control algorithm on the controlled system and broadens the application scope of the iterative learning control algorithm in nonlinear systems.An exponential variable gain iterative learning control algorithm with initial state shift compensation is proposed when the initial state shift exists in a nonlinear controlled system.The algorithm uses the previous part of the controlled system running time interval to compensate for the output error caused by the system initial state shift,and this part of the interval will tend to zero as the iteration progresses.The compression mapping method is used to analyze the output tracking error convergence of the controlled system under the action of the algorithm and the convergence conditions of the algorithm are given.Simulation results show that the algorithm can well handle the initial state shift of the controlled system.At the same time,the exponential variable gain makes the controlled system output tracking error converge faster and more stable than the output tracking error of the controlled system under the control of the general variable gain algorithm.