We propose a novel method for controlling vibrations within a resonant structure equipped with piezoelectric transducers. The scheme uses a parallel connection of modulated and demodulated controllers, each designed to damp the transient oscillation corresponding to a single mode. This technique allows multiple modes to be controlled with a single actuator. A simulation example is presented and design considerations for the scheme are discussed. Experimental results obtained from a piezoelectric laminate cantilever beam confirm the theoretical analysis.
It has been known for some time that real nonminimum phase zeros imply undershoot in the step response of linear systems. Bounds on such undershoot depend on the settling time demanded and the zero locations. In this note, we review such constraints for linear time invariant systems and provide new stronger bounds that consider simultaneously the effect of two real nonminimum phase zeros. Using the concept of zero dynamics, we extend these results to a class of nonlinear systems.
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