Model Predictive Control Based on the Generalized Bouc-Wen Model for Piezoelectric Actuators in Robotic Hand With Only Position Measurements

Hysteresis nonlinearity is known to typify piezoelectric actuators and systems. If not appropriately accounted for in the control law, it can lead to the closed-loop’s performance loss or even instability. Several studies have proposed various techniques to design control laws with explicit consideration of this nonlinearity. However, they are limited to symmetrical hysteresis, and their efficiency is no longer ensured in the face of asymmetrical ones. This letter proposes to model the strong asymmetrical hysteresis in a piezoelectric actuator devoted to robotic hands using the generalized Bouc-Wen model. A Hammerstein structure is employed to also account for its dynamics. Then, we propose an output feedback control law consisting of nonlinear control and a nonlinear model predictive control. To get an estimate of the hysteresis signal used for feedback, we design a nonlinear observer. The observer and controls together stabilize the closed-loop output. The efficiency of the proposed control technique is finally demonstrated through several simulations.