An integral resonant controller approach to frequency locking an optical cavity

This paper presents the application of an integral resonant controller (IRC) to the problem of frequency locking an optical cavity. Such frequency locking is necessary to ensure maximum constructive interference inside the cavity. This is achieved by altering the resonant frequency of the optical cavity to match the frequency of the input laser. The optical cavity is characterized as a negative imaginary system in the desired frequency range and a strict negative imaginary IRC is designed for locking such a cavity. We show in simulation that the internal stability of the positive feedback interconnection of the plant and the IRC is guaranteed as long as a certain DC gain condition is satisfied, as mentioned in previous theoretical results. Experimental frequency response data for the plant, comprising of a three-mirror ring cavity and a piezoelectric actuator is used. This data is used to obtain a model for the plant using methods of system identification which is then used to design an IRC. A unit step response is obtained to check for the performance of the controller in closed-loop.