Damping measurement of oscillators using adaptive phase control

This paper describes a method for the highprecision and fast measurement of the damping of a linear oscillator by using harmonic vibrations. The measurement is based on the evaluation of the vibration frequency that corresponds to a specific phase shift. A phase-locked loop controls the phase shift using the excitation frequency as control signal. Since the dynamics of the frequency adjustment is dependent on the damping of the oscillator itself, adaptive control mechanisms are necessary to enable a fast and effective measurement. However, the control loop is a nonlinear system, thus classical adaptive control methods cannot be applied. Therefore, a linearization of the analytic description of the control system is performed to develop controller design rules that provide a simple adaption mechanism using the damping as single adaptive parameter. The performance of an adaptive PID controller and a compensator is investigated by simulations with the original nonlinear system. The results prove that the linearization is an excellent approach for the controller design. Simulations show that the adaptive controller provides a fast, robust and high-precision damping measurement which is useful in a lot of sensor applications or system identification tools.