Research On Fuzzy Adaptive Second-Order Sliding Mode Control

Sliding mode control has been favored by researchers both domestically and internationally for its simplicity,strong disturbance rejection,and robustness.However,traditional sliding mode control algorithms are generally of first order,and they suffer from severe chattering issues,which limit the development of sliding mode control.The second-order sliding mode control algorithm extends the relative order to the second order,which solves the inherent chattering problem.Moreover,the second-order sliding mode control method inherits the advantages of traditional sliding mode control and provides higher control accuracy for closed-loop systems.However,commonly used second-order sliding mode control methods often assume that the system’s uncertainties are bounded by constants,resulting in non-adaptive gain adjustment and excessive chattering,which significantly hinders the promotion of second-order sliding mode control algorithms.Therefore,this paper focuses on uncertain nonlinear systems and proposes a fuzzy adaptive second-order sliding mode control algorithm to address issues such as finite-time stability,fixed-time stability,and output constraints within the framework of second-order sliding mode control.Additionally,a portion of the control algorithm theory is applied to the inverted pendulum.The main research content and innovations of this paper are as follows:(1)To address the issue of system uncertainties,fuzzy adaptive techniques are utilized to approximate the unknown functions of system uncertainties.Based on the second-order sliding mode dynamic model,a novel finite-time second-order sliding mode control algorithm is developed using the techniques of power integral,backstepping,and finite-time theory.This algorithm resolves the problem of unknown uncertainties in second-order sliding mode control,avoids excessive disturbance estimation,and reduces chattering.(2)The finite-time fuzzy adaptive second-order sliding mode control is extended to fixed-time domain,significantly improving the convergence speed of the system.The algorithm achieves convergence independent of the initial state and provides an upper bound on the time required for the system to reach a steady state.(3)To address the issue of output constraints,a tangential barrier Lyapunov function class is selected,and a novel fixed-time fuzzy adaptive controller is designed by combining power integral techniques and fixed-time theory.The derivative of the barrier Lyapunov function is embedded in the controller as the control gain,which is continuously updated based on the output of the system,effectively limiting the output variables.(4)For the linear first-order inverted pendulum,a fixed-time second-order sliding mode controller is constructed under output constraints.The inverted pendulum is first modeled and analyzed for forces,and then a second-order sliding mode controller is designed for output constraints.The proposed algorithm is validated through simulations,demonstrating fixed-time stability in the presence of output constraints.