Vibration Suppression of Flexible Manipulator by Combining Modified Input Shaping and Adaptive Positive Position Feedback Control

A vibration suppression strategy is developed for an unconstrained flexible manipulator with a collocated piezoelectric sensor/actuator pair. Dynamic modeling of the flexible manipulator is first shown and then a control law is developed. A proportional derivative (PD) controller is combined with various modified input shapers (MIS) to control the rigid mode and attempt to suppress the vibrations of the flexible mode. In order to suppress vibrations of a strucuture with frequency uncertainties, a positive position feedback (PPF) control law is augmented with an adaptive parameter estimator based on the recursive least squares method which updates the natural frequencies of the structure online.