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

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