Comparison of negative and positive position feedback control of a flexible structure

Abstract

Two modal control techniques, negative position feedback (NPF) and positive positionfeedback (PPF), are applied to reduce multi-mode vibration of a lightly damped flexiblebeam using a piezoelectric sensor and piezoelectric actuators. The NPF and PPFcontrollers are constructed by respectively feeding back the generalized displacementresponse from the sensor in a negative and a positive sense to the actuators through secondorder high pass and low pass filters. PPF is well known while NPF is new forthis application and is in fact an electrical realization of a dynamic vibrationabsorber. The choice of the parameters for controllers of both types is made easy bya robust modal control technique that offers an optimal performance for NPFcontrol and a near-optimal performance for PPF control. Explicit forms of thecontroller parameters are presented. Experiments are conducted on a cantilever beamembedded with a matched pair of PZT (lead zirconate titanate) patch actuatorsand a collocated PVDF (polyvinylidene fluoride) patch sensor. The experimentsdemonstrate that it is possible to realize an electrical dynamic absorber using thegeneralized displacement sensor. It is further demonstrated that NPF can be a goodalternative control strategy particularly when multiple modes are to be controlled.