Abstract
In this chapter we investigate how time-delayed feedback control (TDFC) techniques can be exploited in controlling chaos and bifurcation in a digital phase-locked loop (DPLL) and thus improve its system response. We use both the TDFC techniques: The conventional one and its extended version. Using local stability analysis, two parameter bifurcation studies and two parameter Lyapunov exponent spectrum we explore the nonlinear dynamics of conventional and controlled DPLLs. A condition for the optimum value of the system control parameter is derived analytically for a TDFC based DPLL. We describe the implementation of the extended time-delayed feedback control (ETDFC) technique in a DPLL. It is observed that the application of the delayed feedback control technique on the sampled values of the incoming signal results in the nonlinear time-delayed feedback control on the phase error dynamics. We establish that, for some suitably chosen control parameters, an ETDFC based DPLL has a broader stability zone in comparison with a DPLL and its TDFC version.
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