Optimum Strategies for Minimum Time Frequency Transitions in Phase-Locked Loops

Pontryagin´s maximum principle is applied to minimize the time for a phase-locked loop to lock to a step change in frequency. In particular, a Type II phase-locked loop is considered in detail. Phase control and frequency control of the input signal are analyzed with the nonlinearity of the phase detector taken into consideration. It is shown that application of Pontryagin´s maximum principle offers a decided advantage in shortening this time by proper control.