352 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 1, JANUARY 2014 Model Reference Adaptive Control With Perturbation Estimation for a Micropositioning System Qingsong Xu, Member, IEEE, and Minping Jia Abstract— This brief presents a scheme of model reference adaptive control with perturbation estimation (MRACPE) for precise motion control of a piezoelectric actuation microposi- tioning system. One advantage of the proposed scheme lies in the fact that the size of tracking error can be predesigned, which is desirable in practice. A second-order nominal system is assumed, and the unmodeled dynamics and nonlinearity effect are treated as a lumped perturbation, which is approximated by a perturbation estimation technique. A dead-zone modification of the adaptive rules is introduced to mitigate the parameter drifts and to speed up the parameter convergence. Moreover, the proposed MRACPE scheme employs the desired displacement trajectory rather than the voltage signal as the reference input. The stability of the closed-loop control system is proved through Lyapunov stability analysis. Experimental studies show that the MRACPE is superior to conventional proportional-integral- derivative control in terms of positioning accuracy for both set- point and sinusoidal positioning tasks, which is enabled by a significantly enlarged control bandwidth. Index Terms— Adaptive control, disturbance, hysteresis, micro/nanopositioning, motion control, piezoelectric actuators. I. I NTRODUCTION M ICRO/NANOPOSITIONING systems with piezoelec- tric actuation are widely employed in diverse applica- tions where an ultrahigh-precision motion within a microscale workspace is needed [1]. Piezoelectric stack actuators (PSAs) are usually adopted owing to their merits in terms of high resolution, fast response, and high force density. Hence, the aforementioned applications can benefit more from PSAs than other kinds of actuators. However, the main challenge of using piezoactuated systems arises from the piezoelectric hysteretic nonlinearity. Under an open-loop voltage-drive approach, the hysteresis can induce a positioning error which is greater than 15% of the stroke. To tackle this issue, various control techniques have been developed to ensure the robustness of the system in the pres- ence of dynamics model and hysteresis uncertainties [2], [3]. Considering that hysteresis modeling is often a complicated Manuscript received July 4, 2012; revised January 20, 2013; accepted February 6, 2013. Manuscript received in final form February 16, 2013. Date of publication March 7, 2013; date of current version December 17, 2013. This work was supported by the Macao Science and Technology Development Fund under Grant 024/2011/A and the Research Committee of University of Macau under Grant MYRG083(Y1-L2)-FST12-XQS. Recommended by Associate Editor G. Cherubini. Q. Xu is with the Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Macao, China (e-mail: qsxu@umac.mo). M. Jia is with the School of Mechanical Engineering, Southeast University, Nanjing 211189, China (e-mail: mpjia@seu.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2013.2248061 work, some approaches without modeling the hysteresis effect have been presented, such as the integral resonant control [1], H ∞ robust control [4], [5], sliding mode control [6], [7], and iterative learning control [8]. In particular, as compared with robust control approach, the adaptive control does not require a prior information about the bounds on uncertain or time- varying items. Hence, adaptive control paves a more straight- forward way to the precision control of micropositioning systems. Nevertheless, only limited work has been dedicated to the extension of adaptive controllers to micropositioning system control. In the literature, it has been shown that the hysteresis effect can be described by the Krasnosel’skii and Pokrovskii (KP) model and compensated for using the inverse KP model [9]. However, because of the accuracy limitation of the identified model, there always exist differences between the predicted and exact hysteresis. By considering the uncertainties caused by the inversion-model-based compensation as input distur- bances into the system, an adaptive hysteresis model has been established in [9] for a model reference control of active material actuators. Alternatively, by treating the hysteresis nonlinearity as an unknown disturbance to the ideal double- integral plant model, an active disturbance rejection control was employed to actively reject the nonlinearity based on an estimate provided by an observer [10]. However, seldom can a micropositioning system be represented by a simple double- integral model. Moreover, to develop a controller without modeling the complicated nonlinear effect, an adaptive robust controller was devised in [11]. Yet, uncertainty bounds are required to realize the control system. In previous work [12], a model reference adaptive control (MRAC) strategy was reported to compensate for the hysteresis effect of a micropositioning stage. Even though the adaptive controller was realized without modeling the hysteresis effect nor acquir- ing the uncertainty bounds, a Prandtl–Ishlinskii hysteresis model was required to convert the desired motion trajectory into a voltage input. More recently, a MRAC scheme based on hyperstability theory was presented for a piezoactuated system [13]. Nonetheless, a Bouc–Wen hysteresis model was still employed to identify the dynamics equation of the system. From a practical point of view, it is preferable to develop a MRAC scheme without modeling the complicated nonlin- ear effects. By considering the nonlinearity as perturbations to the system, several perturbation estimation methods have been reported to be integrated with MRAC schemes. To name a few, a MRAC with disturbance rejection strategy was presented for the systems that can be represented by parabolic or hyperbolic partial differential equations along with known disturbance model or constant disturbance [14]. 1063-6536 © 2013 IEEE