Analysis and design of resonance tuning systems

Abstract

A control system that tunes the resonant frequency of a lightly damped resonator to its excitation frequency in the face of detuning disturbances is investigated. The resonance tuning is achieved by adaptively controlling the resonant frequency of the resonator using the error between the excitation frequency and resonant frequency. Assuming that the parameters of the resonator are slowly time-varying, a nonlinear time-varying model that accurately predicts the tuning performance of the system is developed. This developed model is subsequently linearized to obtain a linear time-invariant model that facilitates both analysis and design of the resonance tuning system. Based on the developed linear time-invariant model, guidelines for designing the resonance tuning system are provided. The results are illustrated by examples.

Resonance seeking control in an event-triggered discrete-time domain

“…As such, the stability of this class of systems can be analyzed using Lyapunov's second method. In prior work on resonance seeking control [8], [9], [11], [12], the closed-loop stability analysis assumes that the plant (i.e. harmonic oscillator) is always at steadystate (or quasi-steady-state).…”

Adaptive resonance tuning through feedback

“…1 is considered and an analysis method for the resonance tuning system is developed. The approach is very similar to the one used in our earlier work [1], [2].…”

“…Two methods to overcome this problem have been investigated in our earlier work [1], [2]. A third method to overcome the same problem is proposed in [3], where the lightly damped second order system is placed inside a feedback loop as shown in Fig.…”

“…Two adaptive resonance tuning methods have been investigated in our previous work [1], [2]. The first method used a phase locked loop to adaptively tune the excitation frequency of a second order system to its resonant frequency, while the second method used a phase detector to adaptively tune the resonant frequency of a second order system to its excitation frequency.…”

“…A wide variety of systems, such as ultrasonic motors, piezoelectric transducers, induction heating loads, resonant inverter loads, microelectromechanical gyroscopes, cavity resonators and cyclotrons, can be modelled as lightly damped second order systems (see [1], [2], and the references therein). Such systems must be driven at their resonant frequencies in order to achieve optimal performance.…”