Semi-active vibration control using piezoelectric-based switched stiffness

A switched stiffness semi-active vibration attenuation method implemented with a simple relay-type control logic for flexible mechanical structures is presented. A single degree of freedom system is considered for validation of the switched stiffness concept. The method is then applied to a flexible beam with moving base, representing the last link of a Cartesian-type robot manipulator. A piezoelectric actuator, attached on the top surface of the flexible beam, is switched between open and short circuit configurations. This switching introduces a change in stiffness, which, in turn, can remove energy from the overall system by directly affecting the stored potential energy in the flexible beam. The control logic for switching stiffness is based on the position and velocity feedback of the tip of the flexible beam. Implementation of this control logic is hindered by the lack of velocity sensors. A numerical differentiator may be utilized, but may degrade the vibration suppression performance due to the phase lag introduced by filters utilized for conditioning the resultant noisy signal. In order to remedy this, a novel output feedback variable structure velocity observer scheme applicable for a general nonlinear mechanical system, with unknown system dynamics is utilized. Simulation results show superior vibration attenuation for both the single degree of freedom oscillator and the cantilever flexible beam systems with velocity observer.