A smooth integral sliding mode controller and disturbance estimator design

Integral sliding mode control eliminates the reaching phase of the traditional sliding mode and is therefore robust from the start. However, the phenomenon of chattering inherent to the sliding mode control technique is not eradicated and may result in chattering at the control input. In this work a novel integral sliding mode controller is formulated where the discontinuous control law is based on inverse hyperbolic function and provides variable gain which is a function of the sliding manifold. As the system states converge towards the surface the gain of the discontinuous controller reduces and results in relatively smoother control effort at the steady state. The proposed controller is robust against parameter variations, perturbations and is also used for the disturbance estimation and rejection. Stability of the proposed controller is proved with the help of Lyapunov method. The proposed controller is used to design the controllers for two different problems. The DC motor speed control where the chattering elimination and disturbance cancellation are shown with the help of simulations. In the second problem a digital phase locked loop is designed by using proposed controller where the phenomenon of oscillator pulling is eradicated by the rejection of the injection tone which is treated as a disturbance. Experimental results show eradication of the chattering phenomenon as well as the disturbance.