Smart Material Based Complex Mode Active Control of Flexible Manipulators with Kinematic Redundancy

An active control methodology is presented for suppressing the vibratory response of flexible redundant manipulators with bonded piezoceramic actuators and strain gage sensors. Firstly, the dynamic equation of the manipulator is decoupled by means of the complex mode theory and the state-space expression of the controlled system is developed. Secondly, a continuous linear quadratic regulator (LQR) state feedback controller is designed based on the minimum principle. Thirdly, a full-order Luenberger state observer featuring an assigned degree of stability is determined via the duality between control and estimation. Finally, a numerical simulation is carried out on a planar 3R flexible redundant manipulator. The simulation results reveal that the dynamic performance of the system is improved rapidly and significantly.