Abstract
Combining adaptive fuzzy sliding mode control with fuzzy or variable universe fuzzy switching technique, this study develops two novel direct adaptive schemes for a class of MIMO nonlinear systems with uncertainties and external disturbances. The proposed control schemes consist of fuzzy equivalent control terms, fuzzy switching control terms (in scheme one) or variable universe fuzzy switching control terms (in scheme two), and compensation control terms. The compensation control terms are used to relax the assumption on fuzzy approximation error. Based on Lyapunov stability theory, the parameters update laws are adaptively tuned online and the global asymptotic stability of the closed-loop system can be guaranteed. The major contribution of this study is to develop a novel framework for designing direct adaptive fuzzy sliding mode control scheme facing model uncertainties and external disturbances. The derived schemes can effectively solve the chattering problem and the equivalent control calculation in that environment. Simulation results performed on a two-link robotic manipulator demonstrate the feasibility of the proposed control schemes.
Highlights
Some nonlinear systems, such as robotic manipulator, inverted pendulum, and electrical machines, are often highly coupled and time-varying systems, and suffer from structured and unstructured uncertainties 1, 2
A thorough knowledge of the plant dynamics is required for this purpose
Combining adaptive fuzzy SMC with fuzzy or variable universe fuzzy switching technique, this paper proposes two novel direct adaptive control schemes for a class of MIMO nonlinear systems with uncertainties and external disturbances
Summary
Some nonlinear systems, such as robotic manipulator, inverted pendulum, and electrical machines, are often highly coupled and time-varying systems, and suffer from structured and unstructured uncertainties 1, 2. The control of these systems is an important topic in the field of control. Sliding mode control SMC is an effective control scheme to deal with these problems 3–6. This control scheme suffers mainly from two disadvantages. The other is Mathematical Problems in Engineering the difficulty involved in the calculation of the equivalent control 7. In the real world, there are many complex industrial processes whose accurate mathematical models are not available or difficult to formulate
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