Abstract :
It is well known that first-order phase-locked loops exhibit a static phase error which acts as a delay between the input and output signals. The phase error approaches zero as the gain is increased, but the system also becomes unstable (as it enters a chaotic regime). Second-order phase-locked loops overcome this problem by incorporating a first-order filter, rather than just a gain. In theory, if we apply a chaos control scheme to the first-order loop, the system can be stabilized for high values of gain, possibly leading to better phase acquisition properties and lower steady-state phase error. In this note, we illustrate this idea using digital phase-locked loops (DPLLs), and investigate whether the scheme can be implemented in practice
