A substructuring approach to derive dynamic models for closed-loop mechanisms is applied to model a flexible-link planar parallel platform with Lead Zirconate Titanate (PZT) transducers. The Lagrangian Finite Element (FE) formulation is used to model flexible linkages, in which translational and rotary degrees of freedom exist. Craig-Bampton mode sets are extracted from these FE models and then used to assemble the dynamic model of the planar parallel platform through the application of Lagrange’s equation and the Lagrange multiplier method. Electromechanical coupling models of surface-bonded PZT transducers with the host flexible linkages are introduced to the reduced order dynamic models of flexible linkages. The assembled system dynamic model with moderate model order can represent essential system dynamic behavior and maintain kinematic relationships of the planar parallel platform. A Proportional, Integral, and Derivative (PID) control law is used as the motion control law. Strain rate feedback (SRF) active vibration control is selected as the vibration control law. Motion control simulation results with active vibration control and simulation results without active vibration control are compared. The comparison shows the effectiveness of active vibration control.
