Modeling and Inverse Compensation for Coupled Hysteresis of an XYΘ-Type Flexure-Based Mechanism

Parallel XYΘ-type flexure-based mechanisms are widely utilized for planar manipulation missions. However, modeling and control of such mechanisms face challenges including hysteresis of piezoelectric actuators (PEAs), couplings between input axes (input couplings), and coupled linear and angular motions of the end effector (output couplings). This paper focuses on addressing the hysteresis of PEA and input coupling effects of XYΘ-type flexure-based mechanism. A coupling modified Prandtl-Ishlinskii (CMPI) model is proposed to characterize the hysteresis and input couplings of the mechanism driven by PEAs. Based on the CMPI, a decoupling inverse MPI (DIMPI) is proposed as a feedforward compensator for decoupling control, and the PID controller is used as a feedback controller. Experiments validate that the proposed method can effectively reduce the coupled hysteresis between the three input axes of the mechanism driven by PEA.