Data-driven model-free predictive control for microstage with coupling and hysteresis nonlinearities

Abstract

The precision motion control problem is investigated in this paper for microstages with cross-axial coupling and hysteresis. Cross-axis coupling generally results in stress-stiffening effects, thereby causing time-varying dynamics in the microstages. Additionally, when a microstage is driven by piezoelectric actuators (PEAs), the hysteresis effect of the actuator itself must also be considered. Modeling the microstages becomes complicated when both nonlinear characteristics, coupling and hysteresis, coexist. To address this challenge without the need for modeling, a novel data-driven model-free predictive control scheme called first-order tensor-vector product polynomial approximation based model-free predictive control (TPPA ${}_1$-MFPC is proposed. TPPA ${}_1$-MFPC solely relies on the sampling input/output (I/O) data of the systems. The main concept behind TPPA ${}_1$-MFPC is to derive a linear approximation model using the I/O data collected during operation. This linear approximation model then serves as a nominal model in a predictive controller, enabling the control of the microstages. Finally, the effectiveness of the proposed TPPA ${}_1$-MFPC scheme and the performance improvement over existing model-free schemes, for example, proportion integration differentiation control (PID), model-free adaptive control (MFAC), model-free adaptive predictive control (MFAPC), data-dependent LMI (DDLMI), and data-enabled predictive control (DeePC) are demonstrated in the simulation examples with a 2-degree of freedom (DOF) multileaf spring-based microstage driven by PEA.