Chaos Control of Third Order Phase Locked Loop Using Sliding Mode Nonlinear Controller

Abstract

The nonlinear dynamics of a third-order phase locked loop (PLL) reveals a chaotic behavior for range values of loop parameter. Using bifurcation theory, it has been verified through mathematical analysis and simulation that such behavior pulls the PLL to an undesirable and unstable out-of-lock state. This paper aims to control such chaotic behavior and drive the PLL to the in-lock state, by applying a nonlinear controller based on sliding mode control theory to the PLL under consideration. The design process involves two phases. In the first phase, a sliding surface is designed such that the sliding motion meets the design specifications. In the second phase, a high-speed switching control law is selected such that the system state trajectory reaches the sliding surface. The validity of the proposed controller is tested through simulations. Results show the effectiveness of the designed nonlinear controller in stabilizing the system and driving the PLL to the phase locked state.