An Approach to Flexible Modes Identification and Control

Abstract

Abstract An approach is given for flexible mode identification and robust control. It was successfully implemented and tested in a lab experiment that consists of a simply supported aluminum plate with four piezo-electric actuators and four piezo-electric sensors. The approach is based on measuring mode shapes and using a frequency weighted LQR controller that permits reduced order plant modeling. Lab tests show the first four modes were reduced significantly. The discussion includes derivation of the equations for the model identification scheme. A detailed description is given of the LQR frequency weighting and plant augmentation technique. A fourth order roll-off of control authority was used to gain-stabilize high frequency unmodeled dynamics. The observer uses only mode shape information but no modal frequency information. This provides the controller with robustness to modal frequency changes. Robustness is shown to changes in modal frequency (+/−10%), as well as modal gain and damping.