Abstract
In the present study, to attain an approximate feedback linearization based optimal robust control of an under-actuated cart-type inverted pendulum system with two-degree-of-freedom (2DOF) having time-varying uncertainties is desirable. To reach such a goal, at first, the governing dynamical equations of the cart-type inverted pendulum are presented. Then, using an approximate feedback linearization method, the dynamics of the nonlinear system are changed to those of the linear one. In order to simultaneously stabilize the both degrees of freedom, a robust sliding mode controller is designed for this under-actuated system. Finally, the control law is improved with aid of a novel adaptive approach based on an approximating function found via a multiple-crossover genetic algorithm so that the system always will be optimally robust against time-varying parametric uncertainties. The results are displayed to show how the proposed controller improves the settling time and overshoot of the system outputs. In addition, such an improvement in the values of the selected objective functions is clearly evident.
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