IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 23, NO. 1, JANUARY 2015 297 Digital Sliding Mode Prediction Control of Piezoelectric Micro/Nanopositioning System Qingsong Xu Abstract—This brief presents the design, analysis, and ver- ification of a new scheme of digital sliding mode prediction control (DSMPC) for precise position control of piezoelectric micro/nanopositioning systems. Its implementation only needs input/output measurements, whereas the burdens on hysteresis modeling and state observer design are released. The robustness against piezoelectric nonlinearities and model disturbances is guaranteed by a devised digital sliding mode control (DSMC). As compared with DSMC, the DSMPC is capable of further attenuating the positioning error through an optimal control, which is provided by the predictive control strategy. Its stability is proved and ultimate tracking error bounds are evaluated analytically. The feasibility of the control scheme is validated by experimental investigations on a piezo-driven micropositioning device. Results exhibit that the DSMPC surpasses proportional- integral-derivative control and DSMC in terms of high-speed motion tracking accuracy, which is afforded by an increased bandwidth. Index Terms— Digital control, micro/nanopositioning, model predictive control (MPC), piezoelectric actuators, sliding mode control (SMC). I. I NTRODUCTION M ICRO/NANOPOSITIONING concerns the ultrahigh- precision positioning typically with micro/nanometer accuracy in a small working range [1]. Various micro/nanopositioning systems have been developed using diverse actuation principles. In particular, the approach of piezoelectric actuation has attracted extensive attentions from both industry and academia, demonstrating its emerging potential dedicated to the said applications. As compared with their counterparts, piezoelectric actuators exhibit a number of distinctive characteristics, including high force density, rapid response speed, and fine motion resolution. Meanwhile, piezoelectric actuators introduce unwanted nonlinear effects in terms of hysteresis and drift. Tackling these nonlinearities is vital to accomplish a micro/nanometer positioning accuracy. Different control techniques have been explored for the suppression of piezoelectric nonlinearities by releasing the burden on hysteresis modeling [2]–[6]. Particularly, sliding Manuscript received August 20, 2013; revised December 20, 2013; accepted March 4, 2014. Date of publication March 31, 2014; date of current version December 15, 2014. Manuscript received in final form March 9, 2014. This work was supported in part by the Macao Science and Technology Development Fund under Grant 070/2012/A3 and in part by the Research Committee, University of Macau, under Grant MYRG083(Y1-L2)-FST12- XQS and Grant MYRG078(Y1-L2)-FST13-XQS. Recommended by Associate Editor A. Behal. The author is with the Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, 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/TCST.2014.2311096 mode control (SMC) has demonstrated an efficient nonlinear control featuring ease of implementation and robustness in the presence of model disturbances [7]. As another approach, model predictive control (MPC) is capable of predicting the system performance in a specified time in the future and offer- ing an optimal control action with respect to a predefined cost criterion [8], [9]. Hence, by merging SMC and MPC, several combined control algorithms have been recently developed to achieve the advantages of both methods. For example, a hierarchical MPC scheme with integral sliding mode was pro- posed for continuous-time nonlinear systems [10]. However, the controller was developed in continuous-time form. In practice, the control scheme of a micro/nanopositioning system is usually realized using a digital system, such as computer or digital signal processor. Deploying a continuous- time controller directly to a digital system may cause insta- bility of the control system [11]. In addition, concerning SMC, the digital implementation of a continuous-time control deteriorates the invariance property exhibited by continuous- time SMC [12]. Hence, to implement a reliable control scheme on a sampled-data system, a digital control is adopted here. In previous works, a discrete-time sliding mode prediction control has been designed for the tracking control of uncertain systems [13]. In addition, two model predictive discrete-time SMC have been developed for the motion tracking of piezo- electric nanopositioning systems [14], [15]. Recently, more combined control algorithms have been established targeting different physical processes [16]. Majority of the SMC plus MPC algorithms have been developed on the basis of state feedback of the system. Since micro/nanopositioning systems are normally only able to afford position information by displacement sensors, a state observer needs to be constructed [13]–[15], [17], [18]. However, the observer design complicates the control design procedure, and an inappropriately designed state observer ren- ders unstable control system. In this sense, it is desired to elim- inate the use of state observer for the realization of the com- bined control scheme. Unfortunately, the investigation toward this issue has not been yet well established. In previous work, a sliding mode predictive control was developed in [19] based on an input/output model without using a state observer. It is applied to plants which have a variable time delay with non- minimum phase behavior. However, it is unclear whether this control is applicable to piezo-actuated micro/nanopositioning systems, which typically exhibit a higher order model preceded by hysteretic nonlinearities. To this end, a novel digital sliding mode prediction control (DSMPC) scheme is devised in this brief for 1063-6536 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.