Sliding Mode Control for a Pendulum based on Reaching Laws

Abstract

The position control of physical systems presents a difficult problem due to the presence of model nonlinearities and the effects of disturbances of internal or external origin. Sliding mode control has proved its effectiveness through various theoretical studies and practical engineering achievements. The advantage of this approach is its great robustness against the disturbances and uncertainties of modeling. However, this technique has a major drawback which is the phenomenon of 'chattering' caused by the discontinuous part of this control law and which can cause harmful effects on the control inputs of the process. It's in the sense attenuate the effect of the chattering problem, we consider in this paper, to underline the effect of the choice of the sliding function. We propose to apply the switch function and the hyperbolic tangent function as one of the approximations of the switch term for the control of position of an ideal pendulum (without friction). The control law is derived on the basis of the Lyapunov stability theory.