In a multi-input multi-output nonlinear system, because the system is subjected to the impacts of external disturbances and parametric uncertainties, its output response may not be able to satisfy the desired specification or even may make the system unstable. The H∞-ERL sliding mode controller proposed in this paper is motivated to solve these problems. This controller utilizes the concept of sliding mode controller with ERL (Exponential Reaching Law) as its major framework, and then uses Lyapunov stability theorem to ensure the closedloop stability when the system encounters prescribed external disturbances and parametric uncertainties. For the optimal selection of the adjustable parameters in the proposed sliding mode controller with ERL, the H∞ control methodology and the Lag-Lead compensator are formulated together in the proposed control scheme to find optimal control gains, which are used to minimize the ill-effect of external disturbances and plant parametric uncertainties on the controlled output. The closed-loop poles of the augmented system are then placed on the specified region to match the desired performance. The Popov criterion is then applied to handle the uncanceled dynamics caused by the unmodeled uncertainties so that the system robustness can be guaranteed. Finally, an ROV (Remotely Operated underwater Vehicle) is controlled and simulated by the proposed controller. The simulation results reveal that the proposed control law is robust to plant uncertainties and disturbances while the desired specifications assigned by the users are matched.
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