A novel arrangement of feedback linearization, sliding mode control, multi-objective optimization and fuzzy logic for nonlinear under-actuated systems

In this research, a novel fuzzy optimal robust control approach based on the feedback linearization scheme is introduced for a nonlinear under-actuated ball-wheel system. At first, the feedback linearization idea is employed to transform the nonlinear formulations of the ball-wheel system to the linear terms via changing variables instead of approximating them. Then, a robust sliding mode control technique is directed to stabilize the respected under-actuated system. The optimum values of the parameters associated to the designed controller are obtained via a multi-objective optimization process established on the Non-dominated Sorting Genetic Algorithm II (NSGA II). Eventually, a fuzzy logic-based system is designed to enhance the performance of the control system. Comparison of the simulations obviously indicates that the recommended schemes including the sliding mode control, multi-objective optimization and fuzzy system are valid approaches to improve the stabilization task of the feedback linearization control idea for nonlinear systems such as the ball-wheel system.