Fuzzy Adaptive Fixed-time Sliding Mode Control with State Observer for A Class of High-order Mismatched Uncertain System
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Fuzzy Adaptive Fixed-time Sliding Mode Control with State Observer for A Class of High-order Mismatched Uncertain Systems Ali Soltani Sharif Abadi*, Pooyan Alinaghi Hosseinabadi, and Saad Mekhilef Abstract: Using state observer has attracted a notable interest of researchers in control community to provide an on-line state estimator for control systems instead of measuring them physically by sensors which is costly, inaccurate, and easy to contaminate by noise. Some challenges ahead to design state observer in control systems are using estimated data by observer in the designed controller as well as the system stability analysis by using controller and observer simultaneously. This paper proposes Fuzzy Adaptive Fixed-time Sliding Mode Control (FAFSMC) technique for trajectory tracking of a class of high-order nonlinear systems with mismatched external disturbances and uncertainties. Meanwhile, the fixed-time state observer is proposed to incorporate with the controller for estimating the unmeasured even states (velocity) and providing on-line data in the controller. A proper candidate Lyapunov function is defined to verify the system global fixed-time stability by considering designed control law, state observer term, and adaptive law, simultaneously. The simulation results of three simulation examples, ship course system, two-link robotic manipulator, and three-link robotic manipulator, are carried out in Simulink/MATLAB to reveal the effectiveness of the proposed FAFSMC scheme compared with the other three conventional methods for solving trajectory tracking problem. Two performance criteria, Integral of the Square Value (ISV) and Integral of the Absolute value of the Error (IAE), are used to make a comprehensive comparison among the proposed FAFSMC method with state observer and the other three methods. Keywords: Adaptive, fixed-time, fuzzy, mismatched uncertainties, sliding mode, state observer.
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INTRODUCTION
The existence of the parametric external disturbances and uncertainties is one of the issues in modeling of many practical high-order systems, because the accurate modeling of nonlinear systems is impossible to establish and considering the established high-order models is very complex [1]. To deal with this problem, different nonlinear control techniques have been used in many fields such as adaptive control methods [2–7], and robust control methods [8–13], etc. In [14], a robust controller H∞ has been proposed for a single input and single output linear systems. In [15], a robust adaptive fuzzy tracking controller has been proposed by utilizing the recursive back-stepping approach for non-affine stochastic nonlinear switched systems. Furthermore, Lyapunov stability theory has been widely used to investigate the system stability analysis. In [16], Lyapunov function theory has been interestingly
used to combine with a robust backstepping method to design a finite-time adaptive decentralized control method. In [17], the stability of the fau
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