Robust Performance Enhancement Using Disturbance Observers for Hysteresis Compensation Based on Generalized Prandtl–Ishlinskii Model

Abstract

This paper presents an approach employing disturbance observers to enhance the performance of inverse-based hysteresis compensation based on the generalized Prandtl–Ishlinskii model in feedback control reference-tracking applications. It is first shown that the error resulting from inexact hysteresis compensation is an L∞-bounded signal. Hence, a disturbance observer (DOB) is designed to cancel its effect and improve the closed loop robust tracking performance in the presence of plant dynamics uncertainty. The design of the DOB makes use of an equivalent internal model-based estimation of exogenous disturbances, where the internal model dynamics is designed to have at least an eigenvalue at the origin. The synthesis is then formulated as an H∞ weighted-sensitivity optimization for static output feedback (SOF) gain of a Luenberger observer. A linearization heuristic is then implemented to solve the bilinear-matrix-inequality (BMI) constrained semidefinite program (SDP) for a (sub)optimal static gain. Simulation results indicate that tracking performance is indeed improved using the combined inversion-based compensation and the DOB.

Sliding mode disturbance observer-based adaptive integral backstepping control of a piezoelectric nano-manipulator

“…Most of these methods treat the inverse compensation error as a bounded disturbance, where disturbance attenuation methods are used to reduce the impact of disturbances. Alternatively, disturbance observer based control has been demonstrated to be effective in canceling the effect of the inverse compensation error in [24]. Note that the control schemes mentioned above are developed to handle the inverse compensation error for the rate-independent Prandtl-Ishlinskii models.…”

“…Although the inverse compensation error is also treated as a bounded disturbance in this case, we explore the improvement of transient performance of the piezoelectric nano-manipulating system. Different from existing results such as [24], the convergence rate of the disturbance observer is concerned in our design, where a sliding mode disturbance observer is introduced to cancel various disturbances and model uncertainties. With this, the disturbance estimation error is guaranteed to converge to zero in a finite time.…”

High precision tracking of a piezoelectric nano-manipulator with parameterized hysteresis compensation

“…Recall that in [13], a linear disturbance observer was introduced to cancel the hysteresis compensation error, where an H ¥ controller was designed for the linear system with the bounded disturbance. In the present paper, the mechanical nonlinearity (nonlinear stiffness) and the rate dependent hysteresis are handled in an adaptive control framework with enhanced tracking performance, which will be experimentally demonstrated in the next section.…”

“…Many existing results in the literature focus on the modeling and compensation of hysteresis nonlinearities [3] by investigating appropriate mathematical models, such as Bouc-Wen model [4], Preisach model [5], and Prandtl-Ishlinskii (PI) model [6][7][8][9][10][11][12][13][14][15][16]. Among these hysteresis models, the PI model is relatively simple and its analytical inverse can be derived for real-time applications.…”

“…Among these hysteresis models, the PI model is relatively simple and its analytical inverse can be derived for real-time applications. Most of the reported PI models (referring to [6][7][8][9][10][11][12][13]) are only used to compensate the rate-independent hysteresis nonlinearities. However the hysteresis loops of a piezoelectric nano-manipulating system may exhibit both asymmetric and rate-dependent characteristics, which is more eminent when the nano-manipulator is performing large range trajectory tracking (with certain frequencies).…”