-+Improving the behavior of the sliding mode controller by using an innovative mathematical method for controlling an under-actuated system

The present paper studied on improved sliding mode controller in combination with a feedback linearization (IMSMC-FBL) for controlling the behaviour of an under-actuated inverted pendulum system based on Lyapunov theory. The most important type is that concerning the stability of solutions near to a point of equilibrium by using two innovative mathematical techniques, one is adaptive mechanism and the other one is the gradient search method based on the chain rule of differentiation. These techniques minimized the sliding surfaces and chattering, and also taking advantage of both sliding mode and FBL controllers leads us to stability, simultaneously. Alongside, the strength pareto evolutionary algorithm (SPEA-II) optimization was used to ascertain the optimal parameters of the proposed controller with regard to design criteria. The deigned control parameters demonstrated stability, minimum tracking error, overshoot and optimal control efforts in comparison with IMSMC and FBL. Afterwards, the settling time and overshoot of the mentioned two other controllers were compared with proposed controller, where it was proved that the proposed controller yields better results in comparison with other ones.

کلیدواژه ها:

: Improved sliding mode controller ، Lyapunov theory ، Adaptive mechanism ، optimal parameters ، Chain rule of differentiation.