2586 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 7, JULY 2013 Suppression of Hunting in an ILPMSM Driver System Using Hunting Compensator Wei-Hann Yao, Pi-Cheng Tung, Chyun-Chau Fuh, and Fu-Chu Chou Abstract—This paper presents the suppression of hunting in an ironless linear permanent-magnet synchronous motor (ILPMSM) driver system using a hunting compensator. In high-precision motion control servo systems, hunting induced by nonlinear el- ements such as friction and saturation will reduce the system performance. Hunting means that limit cycle occurs in the system, causing a series of sustained oscillations. The hunting compensator is designed based on the circle criterion to ensure system stability. The effectiveness of the proposed control scheme is verified by simulation and experimental results. The proposed algorithm is experimentally tested on an ILPMSM drive system, and the ex- perimental results confirm the ability of the hunting compensation scheme to suppress the effects of hunting. Index Terms—Hunting, hunting compensator, ironless linear permanent-magnet synchronous motor (ILPMSM). I. I NTRODUCTION I N HIGH-PRECISION motion control servo systems, the hunting induced by nonlinear elements such as friction and saturation will reduce the system performance. Hunting means that limit cycle occurs in the system, causing a series of sustained oscillations. To solve the problem of friction, friction models have been established to compensate for friction force over the past century. In general, friction models can be classified as either static, such as the Karnopp model [1], the Coulomb friction model [2], and Armstrong’s model [3], or dynamic, such as the Dahl model [4], the bristle model [5], and the LuGre model [6]. In the existing research on high-performance motion control servo systems of friction compensation, a novel adaptive wavelet fuzzy cerebellar model articulation control system is developed for the trajectory tracking control of voice coil motors proposed in [7]. In [8], a new antiwindup PID controller was proposed to improve the control per- formance of variable-speed motor drives and is experimen- tally applied to the speed control of a vector-controlled induction motor driven by a pulsewidth-modulated voltage Manuscript received October 25, 2011; revised December 23, 2011 and February 27, 2012; accepted April 8, 2012. Date of publication April 24, 2012; date of current version February 28, 2013. This work was supported by the National Science Council of Taiwan, R.O.C., under Grant NSC-99-2221-E- 008-029. W.-H. Yao, P.-C. Tung, and F.-C. Chou are with the Department of Mechan- ical Engineering, National Central University, Chungli 320, Taiwan (e-mail: 943403015@cc.ncu.edu.tw; t331166@ncu.edu.tw; fcchou@cc.ncu.edu.tw). C.-C. Fuh is with the Department of Mechanical and Mechatronic Engi- neering, National Taiwan Ocean University, Keelung 20224, Taiwan (e-mail: f0005@mail.ntou.edu.tw). 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.2012.2196014 source inverter. A digital-signal-processor-based cross-coupled intelligent-complementary sliding-mode control (ICSMC) sys- tem for the synchronous control of a dual linear motor servo system was proposed by Lin et al. [9]. In [10], a global- task-coordinate-frame-based integrated direct/indirect adaptive robust contouring controller for linear-motor-driven biaxial sys- tems that achieves both stringent contouring performance and accurate parameter estimations was also proposed. A direct/ indirect adaptive robust control for a class of nonlinear sys- tems with unknown input dead zones, combined with the desired compensation strategy to synthesize practical high- performance motion controllers for precision electrical drive systems having unknown dead-zone effects, was proposed by Kim et al. [11]. Lin et al. [12] investigated the scheme of a modified Elman neural network controller to control the mover of a permanent-magnet linear synchronous motor (PMLSM) servo driver to track periodic-reference trajectories. In [13], a field-programmable-gate-array-based ICSMC was proposed to control the mover of a servo-drive system with a PMLSM to track periodic-reference trajectories. In this paper, the suppression of hunting in an ironless linear permanent-magnet synchronous motor (ILPMSM) driver sys- tem using a hunting compensator is proposed. The compensator remains inactive provided that the parameter values of the PI controller remain below a certain designed value, which is equivalent to the upper bound of the system’s stable range. The stability conditions can be derived using nonlinear stability analysis tools such as the circle criterion [17]. An ILPMSM system velocity control experiment and simulation with the PI controller are illustrated to show the feasibility of the proposed compensation scheme. The remainder of this paper is organized as follows. Section II describes the dynamic modeling of the ILPMSM system. Section III presents the velocity control block diagram. Section IV introduces the hunting compensator con- trol scheme. Section V presents simulation results. Section VI shows experimental results. Finally, Section VII provides some brief concluding remarks. II. DYNAMIC MODELING The d- and q-axis voltage equations of the three-phase sym- metrical armature winding of the ILPMSM in a synchronously rotating frame can be expressed as [14]–[16] V d = L d d dt i d + R d i d − π τ vL q i q (1) V q = L q d dt i q + R q i q + π τ v(L d i d + λ) (2) 0278-0046/$31.00 © 2012 IEEE