Intelligent Control of Four-order Under-Actuated Nonlinear System viaStrength Pareto Evolutionary Algorithm (SPEA-II)

In this paper a novel Intelligence Control System proposed for a nonlinear ball and wheel system. Initially,by implementation of feedback linearization technique the stability of the ball on the wheel was guaranteed.Due to the nonlinear nature of control parameters, combination with the sliding mode control was applied forfurther boosting effects in the case of any uncertainties. In the following, to develop the performance ofhybrid sliding mode control, some innovative methods, such as an adaptive mechanism, gradient search andthe chain rule of differentiation were used so as to minimize the sliding surfaces and take advantage of bothhybrid and PD controllers, simultaneously. Alongside, The Strength Pareto Evolutionary Algorithm (SPEAII)was utilized to ascertain the optimal parameters of the proposed controller with regard to design criteria.Consequently, the results and analysis of diagrams demonstrated the proper performance of the proposedcontroller in respect of stability, minimum tracking error, overshoot and optimal control efforts incomparison with other two controllers. Afterwards, the time responses of the (SPEA-II) results werecompared with other three Algorithms. The results were proved that SPEA-II yields better outcomes incomparison with other evolutionary algorithms.

Keywords:

Strength Pareto Evolutionary Algorithm (SPEA-II) , Artificial Intelligence Control , Chain Ruleof Differentiation , gradient search.