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The problem of minimum time frequency transitions in phase-locked loops with both phase and frequency controls applied is investigated using Pontryagin's maximum principle. Typically, a type II secondorder loop with a damping ratio of 0.707 subjected to a step change in the frequency of its input signal is considered and switchless control strategies that force the transients in the loop to settle down in minimum time are obtained.
Aerospace and Electronic Systems, IEEE Transactions on (Volume:AES-5 , Issue: 6 )
Date of Publication: Nov. 1969