Prescribed Performance Control for Nonlinear Systems With Sensor Faults and Actuator Hysteresis

This paper investigates the prescribed performance control (PPC) issue in nonlinear systems involving actuator hysteresis, sensor fault, and unavailable states. Firstly, an inverse model is formulated by leveraging the properties of the analytic inverse of the asymmetric Prandtl-Ishlinskii (PI) model. Subsequently, the approximation capabilities of neural networks are harnessed to address entirely unknown nonlinear terms. Next, a novel adaptive observer is constructed to estimate the system states, hysteresis parameters, and sensor faults information. Moreover, the PPC strategy in conjunction with a shifting function, ensures that the tracking error converges to a specified region. This proposed approach effectively mitigates hysteresis and fault, rendering all signals of the closed-loop system semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the algorithm is verified through a simulation and an experiment. Note to Practitioners—Piezoelectric ceramic micro-positioning platforms find extensive application in high-precision positioning technology areas like fluid machinery, automated driving, and automated precision machining production due to their benefits of quick response speed, high displacement resolution, good stiffness, favorable frequency characteristics, and high positioning accuracy. Despite the advantages of piezoelectric ceramic actuators, hysteresis issues can arise, leading to significant positioning errors. Therefore, implementing a suitable control scheme is essential to address this challenge. Additionally, in the automotive and industrial fields, sensor faults can easily happen as a result of different external factors, potentially resulting in serious accidents. Consequently, effective fault management holds significant importance. The performance control method presented in nonlinear systems aims to ensure convergence time, overshoot, convergence accuracy, and other parameters within the predefined range, thereby guaranteeing optimal system performance. This strategy can be extended and applied to piezoelectric driven positioning systems.