Precise tracking control of piezoelectric actuators based on a hysteresis observer

A nonlinear observer-based adaptive robust control approach for a class of uncertain asymmetric hysteretic systems

“…Note that all the parameters of the dynamic model (7)–(9) in the design of the reported hysteresis observer 19 are required to be known, such as a 1 , a 2 , and a 3 . Moreover, the design of the previous hysteresis observer 19 does not consider the adverse effect of the external disturbance d . Unlike Ji et al, 19 the new hysteresis observer in equation (28) is designed by combining the adaptive terminal sliding mode control technique in consideration of the external disturbance, where the parameters of the dynamic model (7)–(9) are adaptively estimated.…”

“…To overcome the drawback, a hysteresis observer was proposed to estimate the unknown hysteresis state. 19 However, the design of the proposed hysteresis observer is required to satisfy the condition that all the model information is known, and the proposed hysteresis observer is sensitive to the parametric uncertainties and external disturbances. Accordingly, it is still a challenge for control design to provide a robust estimate of the unmeasurable hysteresis state.…”

“…In this study, the asymmetric Bouc–Wen model is employed to characterize the hysteresis phenomenon, and a new nonlinear observer is designed to compensate the asymmetric hysteresis. Compared with the existing hysteresis observer, 19 the designed hysteresis observer dramatically reduces dependency on the whole dynamic model and improves the robustness against the parametric uncertainties and external disturbances. With a combination of both the terminal sliding mode control and the adaptive control, a novel adaptive terminal sliding mode controller is developed to achieve the finite-time stabilization of the asymmetric hysteretic system, where a non-singular sliding mode function is proposed via the super-twisting algorithm such that the finite-time convergence of the system states to zero is guaranteed.…”

Periodic tracking for piezo‐actuated displacement stage based on disturbance rejection proportional integral derivative and repetitive control

“…Piezo-actuated displacement stage (PDS) is an effective instrument in micro-displacement systems, such as scanning probe microscopy, optical alignments and hard disk driver, due to its high output force, large bandwidth and fast response. [1][2][3][4] The performance of PDS is largely limited by the strong hysteresis nonlinearity, which is a property of piezoelectric materials inherent. This type of nonlinearity often causes delay response and significantly degrades the positioning performance of the actuator.…”

“…When a periodic reference is imposed to a PDS system, its mechanism model tells that the hysteresis effect in piezo-actuator is equivalent to a periodic input disturbance for the control system. 1,4 Both periodic reference tracking and disturbance rejection are required in the control system design. According to the internal model principle (IMP), 25 a periodic model with the same period as the reference signals is necessary to eliminate the tracking error gradually and the previous ADR methods [16][17][18][19][20][21][22] would be failed to perform such scanning task due to the lack of the internal model.…”