Sliding Mode Control Algorithm with Adaptive Gain and Implementation on Inverted Pendulum System

Abstract

Sliding mode control algorithm is an efficient control strategy to control systems with bounded nonlinearities and parameter uncertainties. However, if the knowledge about the bounds is unknown, sliding mode control fails to guarantee its claimed robustness. The effects of external disturbances, with large magnitudes, can be tackled by using a high value for the controller gain, but with a consequence of increased level of chattering, an unwanted high frequency switching phenomenon occurring in the neighborhood of the sliding surface. In order to mitigate the above mentioned problems, an adaptive law is used to update the controller gain so that the sliding mode controller can track the desired output successfully. This paper demonstrates the design principles of a sliding mode controller with an adaptive law for updating the gain. The gain is so updated that the sliding mode algorithm successfully tracks the desired reference within finite time and does not overestimate the magnitude of external disturbances, thus preventing high level of chattering. The designed controller can track the desired reference value even if the bounds of the external disturbances are unknown. The controller is implemented on a mathematically modeled real time inverted pendulum system and the output responses are obtained. It is concluded that the sliding mode controller with adaptive gain can tackle systems with unknown bounds and also it takes care of the unwanted chattering effect.