Time-varying sliding-coefficient-based terminal sliding mode control methods for a class of fourth-order nonlinear systems

This paper presents a decoupled terminal sliding mode control (DTSMC) and a nonsingular decoupled terminal sliding mode control (NDTSMC) method for a class of fourth-order nonlinear systems. First, the nonlinear fourth-order system is decoupled into two (primary and secondary) second-order subsystems. The sliding surface of each subsystem was designed by utilizing time-varying coefficients, which are computed by linear functions derived from the input–output mapping of the one-dimensional fuzzy rule bases. Then the control target of the secondary subsystem was embedded to the primary subsystem by the help of an intermediate signal. Thereafter, the DTSMC and the NDTSMC methods were utilized separately to ensure that both subsystems converge to their equilibrium points. The inverted pendulum system was used in the simulations and results were given to show the effectiveness of the proposed methods. It is seen that the proposed methods exhibit a considerable improvement in terms of a faster dynamic response and lower IAE and ITAE values as compared with the existing decoupled control methods in the literature.