Piezoelectric Hysteresis Modeling Under a Variable Frequency Based on a Committee Machine Approach

Piezoelectric actuators, widely used in micro-positioning and active control systems, show important hysteresis characteristics. In particular, the hysteresis contribution is a complex phenomenon that is difficult to model when the input amplitude and frequency are time-dependent. Existing dynamic physical models poorly describe the hysteresis influence of industrial mechatronic devices. This paper proposes a novel hybrid data-driven model based on the Bouc-Wen and backlash hysteresis formulations to appraise and compensate for the nonlinear effects. Firstly, the performance of the piezoelectric actuator was simulated and then tested in a complete representative domain, and then using the committee machine approach. Experimental campaigns were conducted to develop an algorithm that incorporated Bouc-Wen and backlash hysteresis parameters derived via genetic algorithm (GA) and particle swarm optimization (PSO) approaches for identification. These parameters were combined in a committee machine using a set of frequency clusters. The results obtained demonstrated an error reduction of 23.54% for the committee machine approach compared with the complete approach. The root mean square error (RMSE) was 0.42 µm, and the maximum absolute error (MAE) appraisal was close to 0.86 µm in the 150-250 Hz domain via the Bouc-Wen sub-model tuned with the genetic algorithm (GA).