scholarly journals The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1409
Author(s):  
Jiawen Li ◽  
Yi Zhang ◽  
Zhenghong Jin
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Singular System ◽  
Fuzzy Model ◽  
Switching Function ◽  
Covering Theorem ◽  
Function Type ◽  
Numerical Examples ◽  
Mode Control ◽  
Nonlinear Singular System

In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated based on the compound function type and simple function type. According to the solvability and the steps of two numerical examples, the method of solving the SPFM form of the nonlinear singular system with (and without) impulse are extended to the more general case. By using the Heine–Borel finite covering theorem, it is proven that a class of nonlinear singular systems with bounded impulse-free item (BIFI) properties and separable impulse item (SII) properties can be approximated by SPFM with arbitrary accuracy. The linear switching function and sliding mode control law are designed to be applied to the impulse elimination of SPFM. Compared with some published works, a human posture inverted pendulum model example and Example 3.2 demonstrate that the approximation error is small enough and that both algorithms are effective. Example 3.3 is to illustrate that sliding mode control can effectively eliminate impulses of SPFM.

scholarly journals Robust Fuzzy Sliding Mode Controller for Discrete Nonlinear Systems

2008 ◽  
Vol 3 (1) ◽  
pp. 6 ◽  
Author(s):  
Hafedh Abid ◽  
Mohamed Chtourou ◽  
Ahmed Toumi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Fuzzy Model ◽  
Uncertain System ◽  
Control Technique ◽  
Control Law ◽  
Mode Control ◽  
Equivalent Control ◽  
Fuzzy Sliding Mode ◽  
Discrete Nonlinear Systems

In this work we are interested to discrete robust fuzzy sliding mode control. The discrete SISO nonlinear uncertain system is presented by the Takgi- Sugeno type fuzzy model state. We recall the principle of the sliding mode control theory then we combine the fuzzy systems with the sliding mode control technique to compute at each sampling time the control law. The control law comports two terms: equivalent control law and switching control law which has a high frequency. The uncertainty is replaced by its upper bound. Inverted pendulum and mass spring dumper are used to check performance of the proposed fuzzy robust sliding mode control scheme.

Research on chaos control of permanent magnet synchronous motor based on the synthetical sliding mode control of inverse system decoupling

2020 ◽  
pp. 107754632093649
Author(s):  
Zhang Rongyun ◽  
Gong Changfu ◽  
Shi Peicheng ◽  
Zhao Linfeng ◽  
Zheng Changsheng
Keyword(s):  
Sliding Mode Control ◽  
Permanent Magnet ◽  
Motor System ◽  
Chaos Control ◽  
Sliding Mode ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Inverse System ◽  
Switching Function ◽  
Mode Control

This article focuses on realizing the chaos control of a permanent magnet synchronous motor by combining a pseudo-linear inverse system of the permanent magnet synchronous motor and synthetical sliding mode control. First, the permanent magnet synchronous motor dimensionless nonlinear mathematical model is established, and its chaos is analyzed by the Lyapunov exponent method. The permanent magnet synchronous motor parameter range when chaos appears is obtained. Then, the inverse system decoupling method is used to analyze the reversibility of the permanent magnet synchronous motor system, and the permanent magnet synchronous motor inverse system is obtained, which is compounded with the original system into a pseudo-linear inverse system that consists of two independent subsystems, including a first-order d-axis current system and a second-order rotational speed system, to decouple the permanent magnet synchronous motor system. Third, the first-order d-axis subsystem is controlled by sliding mode control with a hyperbolic tangent function as the switching function, and the second-order speed subsystem is controlled by super-twisting sliding mode control with a hyperbolic tangent function as the switching function, which is called the synthetical sliding mode control. The permanent magnet synchronous motor pseudo-linear inverse system is controlled by using the synthetical sliding mode to realize the chaos control of the permanent magnet synchronous motor. Finally, three kinds of permanent magnet synchronous motor chaos control systems are established in MATLAB/Simulink software, and the experimental tests are implemented. The results show that the proposed permanent magnet synchronous motor chaos control system has good performance, which can effectively eliminate chattering in sliding mode control and control chaos in the permanent magnet synchronous motor system.

scholarly journals Stability Analysis of a Class of Second Order Sliding Mode Control Including Delay in Input

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Pedro R. Acosta
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Second Order ◽  
Control Input ◽  
Sliding Surface ◽  
Numerical Examples ◽  
Mode Control ◽  
Second Order Sliding Mode

This paper deals with a class of second order sliding mode systems. Based on the derivative of the sliding surface, sufficient conditions are given for stability. However, the discontinuous control signal depend neither on the derivative of sliding surface nor on its estimate. Time delay in control input is also an important issue in sliding mode control for engineering applications. Therefore, also sufficient conditions are given for the time delay size on the discontinuous input signal, so that this class of second order sliding mode systems might have amplitude bounded oscillations. Moreover, amplitude of such oscillations may be estimated. Some numerical examples are given to validate the results. At the end, some conclusions are given on the possibilities of the results as well as their limitations.

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