Abstract
The control of nonlinear system is the hotspot in the control field. The paper proposes an algorithm to solve the tracking and robustness problem for the discrete-time nonlinear system. The completed control algorithm contains three parts. First, the dynamic linearization model of nonlinear system is designed based on Model Free Adaptive Control, whose model parameters are calculated by the input and output data of system. Second, the model error is estimated using the Quasi-sliding mode control algorithm, hence, the whole model of system is estimated. Finally, the neural network PID controller is designed to get the optimal control law. The convergence and BIBO stability of the control system is proved by the Lyapunov function. The simulation results in the linear and nonlinear system validate the effectiveness and robustness of the algorithm. The robustness effort of Quasi-sliding mode control algorithm in nonlinear system is also verified in the paper.
Highlights
With increasing demands on the improvement of the precision control, the control problem of nonlinear system is attracting more and more attention[1]
A single hidden layer neural network can approximate any nonlinear function to any prescribed accuracy if sufficient hidden neurons are provided[2]
The fuzzy logic system can approximate any nonlinear function to any prescribed accuracy, and it has the advantages in dealing with the time-delay, time-varying, multi input single output nonlinear system[4]
Summary
With increasing demands on the improvement of the precision control, the control problem of nonlinear system is attracting more and more attention[1]. Control algorithms of nonlinear system mainly contain the neural network control, fuzzy logic control, the sliding mode control and model free adaptive control (MFAC). The quasisliding mode control has important theoretical value and practical significance to study the variable structure control method for discrete-time nonlinear systems. The Model Free Adaptive Control (MFAC) is proposed to build the dynamic linearization model of nonlinear system, the algorithm is based on the theory of pseudo-partial-derivative (PPD), and the controller just uses the input and output information[8,9]. The paper combines the dynamic linearization ideology of MFAC and quasisliding mode control algorithm to build a precise model and the neural network is designed to obtain the optimal control law based on the above model. The control algorithm has the following advantages, (1) a better robustness; (2) a better tracking performance of system
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