Research On Discrete-time Adaptive Control Algorithm For Nonlinear Systems With Hysteresis

In recent years,with the rapid development of advanced manufacturing industry,intelligent materials are widely used in different scientific fields.Smart materials,such as smart material driver,piezoelectric positioning platform and piezoelectric ceramic driver,have gradually become the focus of research.However,the hysteresis characteristics of these smart materials usually lead to errors or oscillations in the control system,or even instability.In addition,in most control systems,time-delay is common.When the time-delay is large enough,the operation performance of the system will be reduced and even the control system will lose stability.The research on these two phenomena is very extensive in the continuous-time system and very few in the discrete-time system.Therefore,it is of great theoretical and practical significance to study the discrete control algorithm for the nonlinear discrete system with hysteresis and the cascade nonlinear discrete system with hysteresis and time delay.In this paper,for the above two kinds of discrete-time nonlinear systems,the discrete adaptive dynamic surface algorithm is used to design the adaptive control scheme,and the stability analysis is carried out.Finally,the effectiveness of the algorithm is verified by simulation.The main research contents are as follows:(1)For a class of discrete-time nonlinear systems with hysteretic input,a scheme combining adaptive estimation inverse control and dynamic surface control is designed to realize precise tracking control.For this reason,the dynamic surface control technology of first-order digital low-pass filter is designed firstly,which does not need to transform the original discrete control system into an unknown special form.Therefore,the design process of the controller is greatly simplified.Secondly,a discrete-time estimation inverse compensator is constructed to eliminate the hysteresis nonlinearity.Finally,the computer control experiment is carried out on the hardware in the loop simulation platform to verify the effectiveness of the proposed adaptive control scheme.It is proved that all signals in the closed-loop system are semi global uniform and ultimately bounded.(2)For a class of nonlinear discrete-time systems with time-delay based on PI model,an adaptive estimation inverse quantization digital control scheme is proposed.Firstly,the time-delay problem in the system is solved by combining the approximation characteristics of fuzzy logic system and the famous finite cover theorem;secondly,the digital control of discrete-time system is realized by introducing the digital quantizer model;secondly,the influence of the hysteresis nonlinearity in the system is alleviated by constructing the hysteresis discrete-time estimation inverse compensator;finally,in the hardware in the loop simulation Computer control experiments are carried out on the platform to verify the effectiveness of the proposed adaptive control scheme.It is proved that all signals in the closed-loop system are semi global uniform and ultimately bounded.