Adaptive Dynamic Surface Control For Nonlinear System And Its Application

With the development of control system theories, the research of nonlinearsystems control has attracted more and more attentions of scholars. In recent years, asthe widely use of intelligent actuators such as piezoelectric actuator and giantmagnetostrictive actuator make the state characteristics of the nonlinear systembecome more and more complicated. Then, classical control theory have not beenable to achieve high accuracy, good stability, fast response control target. Dynamicsurface control (DSC) method was developed from backstepping method, through theintroduction of a first-order low-pass filter, the controller structure has been greatlysimplified, and it overcomes the actuator controller failure due to the continuousintegral. This paper aims to learn the application of the adaptive dynamic surfacecontrol in typical nonlinear systems with hysteresis and time delay, the main work isas follows:1. For a tuning metal cutting system with piezoelectric ceramic as the actuator,the mathematical model of the system is established. Then, we propose a dynamicsurface control scheme combing the RBFNN with the error transfer function, byusing the new scheme, the cutting precision can be arbitrarily prespecified, thecomputational burden can be greatly reduced and the explosion of complicityproblem inherent in the backstepping control can be eliminated. Simulation resultsshow that, the tracking error of cutting precision keep in the prespecified area, and it’smore convenient for real-time control.2. A Robust adaptive dynamic surface control for a class of nonlinear systemswith unknown parameters and external disturbances is proposed and applied to thegenerator excitation control system. Taking the increment of the power angle andaccessing point voltage as the output of the system, we design the generator excitationsystem controller and make simulation with Matlab, and then the effectiveness of thecontrol algorithm can be proved. Compared with other control methods, this scheme can ensure the stability of power system when it encountered some emergencieswithout linear transformation, and the quality of the motor power angle control can bearbitrarily prespecified.3. For a class of strict-feedback nonlinear systems with backlash-like hysteresisinput and unknown time-varying delay, a new adaptive dynamic surface controlscheme is proposed. By estimating the norm of unknown weighted vectors of theneural network instead of the weighted vectors, the number of estimated parametersand the design complexity can be greatly reduced. Using RBF neural network as theapproximator to the unknown nonlinear continuous Lipschitz function, and theunknown time-varying delays can be compensated through the introduction ofLyapunov-Krasovskii functional. The tracking precision can be prespecified inadvance by the proposed DSC scheme, simulation experiments show the correctnessof this control method.This paper has shown a special solution for the controller design problems ofseveral complex nonlinear systems, by using the improved dynamic surface method,the structure and the parameters of the control system can be totally unknown, and thetracking error performance can be arbitrarily prespecified. Stability analysis provedthat the new scheme can make the system uniformly ultimately bounded, andsimulation results show the effectiveness of the proposed control scheme.