Analysis and Design of Delayed Resonator in Discrete Domain

The delayed resonator (DR) is a new active vibration absorption technique that uses time-delayed partial state feedback to generate ideal resonance on a passive vibration absorber. It has many attractive features such as real-time tunability, ease of implementation, and total suppression of vibration for tonal frequency disturbances. The DR controller has been developed in continuous domain until now. In this paper, discrete domain analysis is presented. Simulation results indicate an expected dependency of stability on the sampling period for this active control strategy. A major advantage of discrete domain analysis is the reduction of characteristic roots from infinite to finite numbers and consequent simplicity in the analysis and design of the controller. It is shown that discrete domain control design for DR yields better vibration suppression considering the sampled control structure in implementations.