IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 9, SEPTEMBER 2013 3927 Identification and Compensation of Piezoelectric Hysteresis Without Modeling Hysteresis Inverse Qingsong Xu, Member, IEEE Abstract—This paper presents a new approach for hysteresis identification and compensation of piezoelectric actuators by re- sorting to an intelligent hysteresis model. In particular, a least squares support vector machine (LSSVM)-based hysteresis model is developed and used for both purposes of hysteresis identification and hysteresis compensation. By this way, the hysteresis inverse is not needed in the feedforward hysteresis compensator since the hysteresis model is directly used. To establish the LSSVM model, the problem of how to select input variables to convert the multivalued mapping into a single-valued one is addressed. The effectiveness of the presented idea is validated by a series of experimental studies on a piezoactuated system. Results show that the proposed approach is superior to the Bouc–Wen-model-based one in terms of both hysteresis modeling and compensation. The reported method is more computational effective than existing model-based hysteresis compensation approaches, and it is exten- sible to other smart actuator systems as well. Index Terms—Hysteresis model, micro-/nanopositioning, motion control, piezoelectric actuator. I. I NTRODUCTION S MART ACTUATORS based on smart materials (e.g., piezoelectric materials, shape memory alloys, magne- tostrictive materials, etc.) are popularly employed for actuation in various precision systems dedicated to micropositioning, micromanipulation, and microassembly. Particularly, as a typ- ical smart actuator, the piezoelectric actuator is attractive in both fields of academia and industry due to the merits of (sub)nanometer positioning resolution, rapid response speed, and self-sensing capability. Although numerous previous works have concentrated on research and applications of piezoelectric actuators [1]–[4], the nonlinear piezoelectric effect (in terms of hysteresis and creep) still remains a challenging problem nowadays. The hysteresis effect can be greatly alleviated by using a charge-driven approach or a capacitor insertion method [5], [6]; however, it is at the cost of stroke reduction. Hence, voltage actuation is widely adopted in practice. In order to identify Manuscript received December 30, 2011; revised March 5, 2012 and April 25, 2012; accepted June 18, 2012. Date of publication July 6, 2012; date of current version May 2, 2013. This work was supported in part by the Macao Science and Technology Development Fund under Grant 024/2011/A and in part by the Research Committee of the University of Macau under Grant MYRG083(Y1-L2)-FST12-XQS. The author is with the Department of Electromechanical Engineering, Fac- ulty of Science and Technology, University of Macau, Taipa, Macao, China (e-mail: qsxu@umac.mo). 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/TIE.2012.2206339 the hysteresis behavior, the establishment of a suitable hystere- sis model is required. For instance, hysteresis identifications using Preisach model [7], [8], Prandtl–Ishlinskii model [9], Bouc–Wen model [10], etc., have been widely carried out. On the other hand, to fulfill the requirements of ultrahigh-precision positioning, the piezoelectric hysteresis has to be suppressed by implementing an appropriate control scheme. Generally, the ex- isting hysteresis compensation schemes fall into two categories in terms of hysteresis model-free and hysteresis model-based methods. Concerning the first category, its main property lies in that no hysteresis model is required. The unmodeled hysteresis is considered as an uncertainty or a disturbance [11] to the nominal system, which is tolerated by an advanced robust or adaptive controller. For instance, the applications of sliding- mode control [12]–[15], H ∞ robust control [16], [17], fuzzy logic control [18]–[20], and neural network control [21] have been successfully reported. Generally, in the second category, a hysteresis model (e.g., Preisach model) is identified, and an inverse hysteresis model is constructed to implement a feed- forward (FF) compensator [22], [23]. It has been shown that the inverse-model-based compensation can achieve an accurate positioning, whereas the result is very sensitive to the model accuracy [24], [25]. Fortunately, the combination of FF with feedback (FB) control can be adopted to suppress the hysteresis as well as creep effects [26]. Although the compensation of hysteresis nonlinearity with- out modeling the hysteresis effect is realizable by designing advanced FB controllers, extensive knowledge on control en- gineering is needed to design such kinds of control strategies. It is commonly believed that an FF compensator based on a simple hysteresis model (with fewer model parameters) in combination with a simple FB controller (e.g., PID control) makes it more feasible to suppress the hysteresis nonlinearity. The reason lies in that the latter allows the relief of burden on developing complicated modern controllers. For example, it has been shown that, by modeling the hysteresis with the Bouc–Wen model, an FF compensator combined with a PID FB controller is capable of compensating the nonlinear hysteresis effectively [27]. A review of model-based hysteresis com- pensation approaches reveals that most of the existing works compensate for the hysteresis effect by employing an inverse hysteresis model. Thus, both a hysteresis model and an inverse hysteresis model are required for the hysteresis identification and compensation purposes. More recently, it has been shown that it is possible to mitigate the hysteresis effect by adopting a Bouc–Wen hysteresis model directly while without using the hysteresis inverse [28]. However, only the quasi-static (low frequency) hysteresis was treated in previous work [28]. 0278-0046/$31.00 © 2012 IEEE