Hysteresis measurement of pneumatic artificial muscle actuators and error-constrained adaptive compensation using a rate-dependent Bouc–Wen model

Accurate dynamic displacement measurement is essential for the characterization, calibration, and closed-loop operation of pneumatic artificial muscle (PAM) actuators. However, their inherent rate-dependent hysteresis poses significant challenges to accurate modeling and controller design. This paper proposes a rate-dependent Bouc–Wen model and a composite control method to address the complex hysteresis of PAM actuators. First, an experimental measurement platform is established to synchronously acquire the input voltage and output displacement, and the hysteresis loops are measured under different excitation frequencies, amplitudes, loads, and input waveforms. Then, a relaxation function is incorporated into the classical Bouc–Wen model to improve its ability to capture rate-dependent hysteresis. Finally, based on the developed model, an inverse-compensation feedforward controller is designed, and a composite control strategy is developed by integrating it with an adaptive feedback controller that incorporates error constraint. Using Lyapunov stability theory, the stability of the system is established and the corresponding convergence condition is derived. Theoretical results show that the proposed control scheme not only guarantees the asymptotic convergence of the tracking error, but also confines it within a prescribed bound over the entire control process. Comparative experiments demonstrate that the proposed method improves the accuracy of hysteresis modeling and the compensation performance of the controller.