This paper presents time-varying sliding-coefficient-based approaches for a class of fourth order nonlinear systems: decoupled terminal sliding mode control (DTSMC) and nonsingular decoupled terminal sliding mode control (NDTSMC) methods. Cart-pole system (inverted pendulum) which is a fourth order nonlinear system is used in the simulations. The system is decoupled into two subsystems as the primary and secondary subsystems. Then, the sliding surfaces are designed for each subsystem. An intermediate signal is used to embed the control target of the secondary subsystem into the primary subsystem. Simulation results are provided to show the effectiveness of the proposed methods against the existing decoupled control method defined in the literature. Faster dynamic response and lower error values show that the proposed methods achieve a considerable improvement when compared with the existing decoupled sliding mode control (DSMC) method.
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