Smooth Sliding Mode Control and its Application to the Phase Locked Loops

Abstract

Sliding mode control is a well established control systems design technique. Its robust-ness against parametric changes and matched uncertainties is well known. Sliding mode control is also used for the disturbance estimation and rejection. Unlike other control sys-tems techniques its control action is discontinuous and results in the unwanted oscilla-tions known as chattering effect. Chattering in general is considered harmful. In Mechan-ical systems chattering can result in heat loses and wear of the actuator and plant. In elec-trical systems it may cause heat loses which may shorten the life of the semiconductors. Besides it can excite the fast or un modeled dynamics in the system which can result in the unwanted results or may result in the instability. Smooth chattering free sliding mode control addresses the issue of chattering and provides smooth control action thereby re-moving the chattering from the sliding mode controller. The methods used for this pur-pose is the boundary layer control laws or by using the variable gain or adaptive sliding mode techniques. The resulting control action losses the robustness to some extent how-ever for all practical purposes the system is considered as robust. In this work a novel smooth chattering free variable gain sliding mode reaching law has been proposed. The proposed reaching law is robust against parametric changes, matched uncertainties and disturbances. It is based on the inverse hyperbolic function where the gain is a function of the sliding surface. With the convergence of the sliding surface the gain reduces and hence the chattering also reduces. The work rigorously proves the sta-bility, robustness and the chattering elimination behavior of the proposed control law. A novel disturbance estimation and rejection framework based on the proposed smooth in-tegral sliding mode control has also been proposed. Finally the novel control technique is applied to design the digital phase locked loop where the phenomenon of oscillator pull-ing and injection locking have been eradicated. The experimental results endorse the mathematical formulations.