Discrete-Time Linear Quadratic Optimal Tracking Control of Piezoelectric Actuators Based on Hammerstein Model

To address the issue of hysteresis nonlinearity adversely affecting the tracking accuracy of piezoelectric actuators, an improved particle swarm optimization (PSO) algorithm is proposed to improve the accuracy of hysteresis model parameter identification. Additionally, a discrete-time linear quadratic optimal tracking (DLQT) control strategy incorporating hysteresis compensation is developed to improve tracking performance. This study employs the Hammerstein model to characterize the nonlinear hysteresis behavior of piezoelectric actuators. Regarding parameter identification, the conventional PSO algorithm tends to suffer from premature convergence and being trapped in local optima. To address this, a cross-variation mechanism is introduced to enhance population diversity and improve global search ability. Furthermore, adaptive and dynamically adjustable inertia weights are designed based on evolutionary factors to balance exploration and exploitation, thereby enhancing convergence and identification accuracy. The inertia weights and learning factors are adaptively adjusted based on the evolutionary factor to balance local and global search capabilities and accelerate convergence. Benchmark function tests and model identification experiments demonstrate the improved algorithm’s superior convergence speed and accuracy. In terms of control strategy, a hysteresis compensator based on an asymmetric hysteresis model is designed to improve system linearity. To address the issues of incomplete hysteresis compensation and low tracking accuracy, a DLQT controller is developed based on hysteresis compensation. Hardware-in-the-loop tracking control experiments using single and composite frequency reference signals show that the relative error is below 3.3% in the no-load case and below 4.5% in the loaded case. Compared with the baseline method, the proposed control strategy achieves lower root-mean-square error and maximum steady-state error, demonstrating its effectiveness.