Second order phase lock loop with feedback for rapid acquisition

A method for reducing the acquisition time (AT) of a phase lock loop (PLL) is considered. The method is (mathematically) optimal in the sense that for given PLL parameter values the AT is the shortest which can be achieved. It is possible to control the AT independently of other parameters, such as bandwidth or time constant, in the post-acquisition period. The considered method gives an optimal solution for every initial state of the PLL and, therefore, can be implemented in feedback form. It is shown that the basic PLL can be modified by addition of a feedback controller which minimizes the acquisition time. Analysis of this controller is carried out by using the maximum principle to derive an optimal system. A suboptimal system is also presented. The suboptimal system is simpler and more attractive for practical realization.