Resonance Control

Professor Cevat Gokcek

Michigan State University

Department of Mechanical Engineering

Resonant systems arise in many areas of science and engineering. Some examples of resonant systems include ultrasonic motors, piezoelectric transducers, induction heating loads, resonant inverter loads, vibrational gyroscopes, microwave heating loads, cavity resonators, plasma processing loads, cyclotrons, accelerometers, biological and chemical agent detectors, and bandpass wireless communication loads. For optimal performance (maximum power transmission, maximum resonance amplification, maximum signal selectivity or maximum measurement resolution), these systems must be excited at their resonant frequencies. However, even if these systems are driven initially at their resonant frequencies, disturbances, such as temperature change, load variation, manufacturing variability, aging, fatigue damage, electromagnetic detuning, microphonics or analyte deposition, can cause their resonant or excitation frequencies to drift over time and significantly impair their performance. This necessitates employment of a control system that maintains lock between the excitation frequency and resonant frequency in the face of such inherent disturbances.

In this talk, several resonance control methods for second and higher order systems are presented. For second order systems, the error between the excitation and resonant frequencies obtained by a phase detector is used to adaptively match these frequencies. For higher order systems, the driving frequency is adaptively controlled using the estimated derivative of the average power delivered to the system with respect to the driving frequency. The estimate of the derivative of the average power is obtained by sinusoidally perturbing the driving frequency and synchronously demodulating the average power delivered to the system. In both cases, a nonlinear model that accurately predicts the performance of the resonance control 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 control system. Based on the developed linear time-invariant model, guidelines for designing the resonance control system are also provided. The developed results are illustrated by several examples.

Friday, December 7, 2007

3:30 – 4:30 p.m.

Rm. 1500 EECS