Abstract

<p class="0abstract"><span lang="EN-US">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</span><span lang="EN-US"> of system</span><span lang="EN-US">. Second, the model error is estimated using the Quasi-sliding mode control algorithm</span><span lang="EN-US">, hence, the whole model of system is estimated</span><span lang="EN-US">. Finally, the neural network </span><span lang="EN-US">PID </span><span lang="EN-US">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 </span><span lang="EN-US">in</span><span lang="EN-US"> the </span><span lang="EN-US">linear and </span><span lang="EN-US">nonlinear system validate the effectiveness and robustness of the algorithm.</span><span lang="EN-US"> The robustness </span><span lang="EN-US">effort </span><span lang="EN-US">of </span><span lang="EN-US">Quasi-sliding mode control algorithm</span><span lang="EN-US"> in nonlinear system is also verified in the paper.</span></p>

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]

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Summary

Introduction

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

Dynamic linearization of the nonlinear system
A3: The system generalized
Model error estimation using Quasi-sliding mode algorithm
Control law design based on the artificial neural network
The stability and convergence of control algorithm
Simulation results
The convergence and robustness of algorithm in linear system
New algorithm Desired output Traditional pid algorithm
The convergence and robustness of nonlinear system
Conclusion
Authors
Full Text
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