To solve the regulator problem of a class of uncertain MIMO nonlinear systems subject to control input constraint, three types of time-varying sliding mode control laws are proposed. The sliding surfaces pass the initial value of the system at the initial time, and are shifted/rotated towards the predetermined ones. The controller parameters are optimized by genetic algorithm (GA). Lyapunov method is adopted to prove the stability and robustness to the parameter uncertainties and external disturbance. By mean of time-varying sliding mode control law, the reaching phase in the conventional sliding mode control is eliminated, and the system is guaranteed to have robustness from the very beginning. Taking the control of two-link manipulator and attitude tracking of rigid spacecraft as two examples, we illustrate the features of the time-varying sliding mode control. The simulation results show the validity of the control law to a class of uncertain MIMO systems. Better robustness against the uncertainties and external disturbance could be achieved by time-varying sliding mode control without violating the constraint on control input.
CitationJin Y Q, Liu X D, Qiu W, et al. Time-varying sliding mode control for a class of uncertain MIMO nonlinear system subject to control input constraint.CSMC would shorten the reaching phase, but so doing will result in severe chattering problem. To improve the robustness of CSMC during the reaching phase, Choi [4] put forward a stepwise time-varying sliding mode control for simple second-order SISO systems. The control strategy proposed reduced the reaching phase extremely, and achieved better robustness than CSMC did. Andrzej [5] presented continuous timevarying sliding mode control based on [4], eliminated the reaching phase, and offered the system work the robustness all the time. In [6] he presented three types of time-varying sliding mode control-constant acceleration sliding mode control, constant velocity sliding mode control and terminal slider controlfor second-order SISO system subject to control input constraints. They eliminate the reaching phase, and guarantee the robustness all the time. Refs. [7][8][9][10][11] applied the time-varying sliding mode control to position control system, hydraulic servo system, induction motor control and robust stabilization of linear unstable plants with saturating actuators. Metin [12] presented sliding mode control with time-varying sliding surfaces for a class of nonlinear systems, which was transformed into a linear time invariant (LTI) system by frozen-time approach, and sliding mode control design for LTI was used. Simulation results showed the global stability of the nonlinear system. But the robustness against the uncertainties and external disturbances was not discussed. Kim [13] presented SMC of robot manipulator with a timevarying sliding surface whose slope was varying according to an exponential function of time. To sum up, we are facing with the following problems: (1) except for [13], we failed to find many applications ...
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