Sampled-Data Model-Free Adaptive Control of Piezoelectric Actuators with Input Rate Constraint Using Extended State Observer

This paper investigates the motion tracking problem for piezoelectric actuators (PEAs) using a sampled-data control method known as sampled-data model-free adaptive control (SMFAC). The fundamental architecture of the proposed scheme is based on input-output data, and the sampling period is an integral part of the design. PEA with the Bouc-Wen hysteresis model is first considered to obtain a sampled-data nonlinear model using the integral mean value theorem and the discrete-time Euler approximation. Then, a sampled-data control rule subject to input rate constraint is constructed by applying a sampled-data extended state observer (SESO) and a sampled-data parameter estimation technique. The SESO is used to estimate the unknown residual nonlinearity and external disturbances. The convergence of the tracking error is proven through theoretical analysis. Experimental results confirm the adequate performance of the proposed scheme.