High-Order Hysteresis Derivative Bouc-Wen Model for Piezoelectric Actuators at High Frequencies and Its Control Compensation

The classical BOUC-WEN model(CBW) is applicable only to symmetric and rate-independent hysteresis phenomena, exhibiting comparatively low modelling accuracy under high-frequency conditions. This limitation restricts its application within piezoelectric actuator systems. To address this issue, this paper proposes a novel higher-order hysteretic derivative Bouc-Wen model (HODBW) for describing the asymmetry and velocity-dependent nonlinearity of piezoelectric actuators under high-frequency conditions. This model incorporates higher-order hysteresis derivatives to construct a dynamic representation capable of precisely describing complex hysteresis behaviour at high frequencies. Concurrently, to reduce model complexity, Principal Component Analysis (PCA) is employed to determine the minimal number of polynomial coefficients. Based on this, a polynomial fitting method is applied to accurately determine the specific form of the input voltage , thereby enhancing the model’s precision. Additionally, the Particle Swarm Optimisation (PSO) algorithm was employed to identify the unknown parameters within the HODBW model. For the proposed HODBW model, a customised feedforward-feedback composite control strategy has been designed. The feedfor-ward section employs an inverse model to establish a hysteresis observer, whilst the feedback section utilises an HOSMC strategy to achieve effective compensation for model errors. The results demonstrate that the HODBW model exhibits superior modelling accuracy compared to both the CBW model and conventional 1 modified models, whilst the proposed control strategy also delivers outstanding performance. This thereby validates its superiority and applicability under high-frequency conditions.