A gain adaptive Variable Structure Control methodology for second order nonlinear dynamic systems

This paper presents a Variable Structure Control (VSC) law with a gain adaptation mechanism for second order nonlinear dynamic systems which contain parametric uncertainties and external disturbances. The proposed method exhibit improved settling time compared to Sliding Mode Control (SMC), and has the ability to converge to a given set point switching only once. The controller achieves this by adapting its gain in real-time to match the effects of changing external disturbances and parametric uncertainties. The acceleration of the system is always directed towards the origin of error phase plane, and the trajectory of the error dynamics follow a parabola like path during control, improving the settling time as a result. Simulations and experiments are carried out on an inverted pendulum system to prove the performance and the practical applicability of the proposed method.