Extended state observer–based fractional order sliding-mode control of piezoelectric actuators

Abstract

<jats:p> Tracking control of piezoelectric actuators is considered in the article. A Hammerstein model is used to depict the rate-dependent hysteresis characteristics of piezoelectric actuators, in which a Bouc–Wen model is to describe the static hysteresis characteristic, and a linear time-invariant system is to describe its rate-dependent characteristics. An inverse Bouc–Wen model connected in series with the piezoelectric actuator is used to compensate the static hysteresis nonlinearity of piezoelectric actuators. Furthermore, an extended state observer–based fractional order sliding-mode control is designed to deal with higher order unmodelled dynamics and inverse compensation errors. Moreover, the bounds of the estimation error of the extended state observer are estimated, and the convergence of the proposed control strategy is proved. Experimental results show that the proposed scheme can track both single and composite input signals within a certain frequency range. Compared with extended state observer–based conventional sliding-mode controller, the proposed scheme has faster response time and smaller tracking error. </jats:p>

Third‐order integral sliding mode control of piezoelectric actuators based on rate‐amplitude‐dependent Prandtl‐Ishlinskii model

“…Assumption 1 (31). Assume that the rate of change 𝜑 of the total disturbance of the system is bounded, that is, |𝜑| ⩽ M 1 , M 1 > 0.…”

“…To this end, this article designs an integral non‐singular fast terminal sliding mode surface, and a new third‐order integral sliding mode controller (3‐ISMC) based on this surface. At the same time, an extended state observer (ESO) 31 is used to accurately estimate the disturbance in the system dynamic process. In short, this article designs a new third‐order integral sliding surface, which can ensure the absolute convergence of the tracking error in a finite time and avoid singular problems.…”

Robust fractional‐order fast terminal sliding mode control with fixed‐time reaching law for high‐performance nanopositioning

“…In addition, the needs of designing high performance controller for piezoelectric positioner with high‐order model can be satisfied. The benefits of this study include but are not limited to that the following academic questions can be solved so as to realize high performance positioning for piezoelectric positioner 50,51 . For example, how to combine high order sliding mode and fractional calculus to design a robust, stable, non‐singular, global fast convergent controller?…”

“…The benefits of this study include but are not limited to that the following academic questions can be solved so as to realize high performance positioning for piezoelectric positioner. 50,51 For example, how to combine high order sliding mode and fractional calculus to design a robust, stable, non-singular, global fast convergent controller? How to ensure its stability, even fixed time stability?…”

Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

“…These systems have been used in several fields e.g. soft robotics [2], drug delivery [3], multi-agent systems [4], vibration [5], wheeled mobile robot [6], soccer dynamics [7], electromagnetic problems [8], piezoelectric actuators [9], hydraulic servo [10], cable-driven manipulators [11], and power grid [12].…”