IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 11, NOVEMBER 2008
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High-Performance Position Control of Induction Motor Using Discrete-Time Sliding-Mode Control ˘ Boban Veseli´c, Branislava Peruni˘ci´c-Dra˘zenovi´c, Senior Member, IEEE, and Cedomir Milosavljevi´c
Abstract—A new way of induction-motor position control for high-performance applications is developed in this paper using discrete-time sliding-mode (DSM) control. In addition to the main DSM position controller, the proposed control structure includes an active disturbance estimator (ADE), in which a passive filter is replaced by another DSM-controlled subsystem, in order to improve system robustness and accuracy. Furthermore, the application of an ADE makes possible the design of both controllers using the knowledge of the nominal system only. Experiments have verified high efficiency of the proposed servo system under the influence of large parameter perturbations and external disturbances in the presence of unmodeled dynamics. Index Terms—Discrete-time sliding-mode control (DSMC), disturbance estimator (DE), induction motors (IMs), position control, servo systems.
I. I NTRODUCTION
E
XCELLENT constructional features of the squirrel-cage three-phase induction motor (IM) such as reliability, high efficiency, ruggedness, low cost, and no need for maintenance make the use of an IM very attractive. However, due to their highly coupled nonlinear structure, IMs have been, for years, mainly used in unregulated drives. A real breakthrough in IM control was the design of the field-oriented control (FOC) principle [1], which enables the decoupled control of rotor flux and electromagnetic torque. This has opened a wide door to IM applications in velocity and positional systems, previously reserved only for dc motors. The following two methods have been used in FOC realization: direct (DFOC) and indirect (IFOC). IFOC is more popular than DFOC due to its implementation simplicity and has become the industrial standard. In IFOC, the required rotor flux vector position is evaluated using the estimated value of slip and the measured rotor position. Both control schemes also incorporate two orthogonal current controllers and decoupling circuits. IFOC is more sensitive to parameter uncertainties, particularly to the rotor resistance variation [2]. This affects the rotor flux orientation. Online parameter identification [3]–[5]
Manuscript received January 13, 2008; revised July 11, 2008. Current version published October 31, 2008. This work was supported in part by the Serbian Ministry of Science under Grant TR11029. B. Veseli´c is with the Faculty of Electronic Engineering, University of Ni˘s, 18000 Ni˘s, Serbia (e-mail:
[email protected]). B. Peruni˘ci´c-Dra˘zenovi´c is with the Faculty of Electrical Engineering, University of Sarajevo, 71000 Sarajevo, Bosnia and Herzegovina (e-mail:
[email protected]). ˘ Milosavljevi´c is with the Faculty of Electrical Engineering, UniverC. sity of Isto˘cno Sarajevo, 71000 Sarajevo, Bosnia and Herzegovina (e-mail:
[email protected]). Digital Object Identifier 10.1109/TIE.2008.2006014
may be applied to accurately determine rotor flux position and to provide a complete decoupling. Sliding-mode control (SMC) [6], the popular nonlinear robust control strategy, which is theoretically invariant to model uncertainties and external disturbances under matching conditions [7], is very attractive for IM control [8], [9]. Up to now, a lot of papers dealing with IM SMC have been reported in the literature. Modern approaches aim to reduce the number of sensors since they are expensive and sensitive to environment. This is the reason why the so-called sensorless control of IM has attracted attention of researchers [10], [11]. The main issue in servo applications is position control, which is essential for any motion control. A positional servo system in a high-performance industrial application must have fast response, preferably without overshoot, high steady-state accuracy, good external disturbance rejection, and robustness to parameter perturbations. SMC can in great deal meet those requirements. Unfortunately, the chattering, usually associated with the classical SMC design, is a serious impediment for SMC application. Various SMC algorithms have been devised for IM position control such as a passivity-based SMC [12], an adaptive robust switching controller design [13], and a DSM control method based on the reaching law principle [14]. This paper presents a new IM position control approach for high-performance applications. The proposed control system is based on discrete-time SMC (DSMC) that allows a simplified IFOC structure, where only rotor flux is indirectly regulated by d-axis stator current control. Torque current controller and decoupling circuits are not needed. These simplifications, as well as rotor resistance variation, are treated as system perturbations. High system robustness and accuracy in the presence of internal and external disturbances are obtained by applying an active disturbance estimator (ADE). The concept of ADE, initially presented at a conference [15], is here further developed and applied to a real challenging and actual control problem. An ADE uses a DSM-controlled subsystem instead of a conventional passive digital filter. Both controllers, in the main loop and within the ADE, are designed using the DSMC algorithm [16], which is enhanced by a specific integral action [17] that is active only inside the boundary layer. The proposed servo system ensures an excellent dynamic response and high accuracy in the presence of internal and external disturbances. The remainder of this paper is organized as follows. In Section II, an IM model is derived according to the discussed strategy. Section III describes ADE and the proposed positional servo system. The design of the chattering-free DSM tracking controller is given in Section IV. Experimental results are given in Section V, whereas Section VI gives some conclusions.
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 11, NOVEMBER 2008
Fig. 1. Block diagram of the proposed robust position control system using the simplified indirect rotor-flux-oriented vector control of an IM.
II. IM M ATHEMATICAL M ODEL An IM model in the d–q synchronously rotating frame, under commonly used assumptions, can be expressed as 2 ˙ids = − Rs + Rr Lm ids + ωe iqs σLs σLs L2r Rr Lm ωr Lm 1 φdr + φqr + uds 2 σLs Lr σLs Lr σLs Rs Rr L2m =− + iqs − ωe ids σLs σLs L2r +
i˙ qs
+
Rr Lm ωr Lm 1 φqr − φdr + uqs σLs L2r σLs Lr σLs
(1)
(2)
Rr Lm Rr = ids − φdr + (ωe − ωr )φqr Lr Lr
(3)
Rr Lm Rr φ˙ qr = iqs − φqr − (ωe − ωr )φdr Lr Lr
(4)
J θ¨m + B θ˙m + Tl = Te
(5)
φ˙ dr
Te =
3pp Lm (iqs φdr − ids φqr ) 2Lr
(6)
where uds and uqs are the d–q components of stator voltage, respectively; ids and iqs are the stator current components; φdr and φqr are the rotor flux components; Rs and Rr are the stator and rotor resistances, respectively; Ls , Lr , and Lm are the stator, rotor, and mutual inductances, respectively; σ = 1 − L2m /(Ls Lr ) is the leakage factor; pp is the number of pole pairs; ωe , ωr = pp ωm , and ωm = θ˙m are the synchronous, rotor electrical, and mechanical angular velocities, respectively; θm is the rotor shaft angle; Te and Tl are the electromagnetic and load torques, respectively; J is the moment of inertia; and B is the viscous friction coefficient. A sixth-order nonlinear model describes the IM in the d–q system. The vector control principle, usually implemented by rotorflux-oriented control, ensures decoupling of torque control and rotor flux control. Rotor flux is oriented toward the d-axis φdr = φr
φqr = φ˙ qr = 0.
(7)
Using (7), (3) and (4) are reduced to Tr φ˙ r + φr = Lm ids
(8)
ωs = ωe − ωr = ωe − pp ωm = Lm iqs /(Tr φr )
(9)
defining rotor flux dynamics and slip frequency. Tr = Lr /Rr is a rotor time constant. Rotor flux is generated only by the flux current component ids . Since the rotor flux should be constant, the d-axis current controller should ensure that ids keeps a desired constant value i∗ds . In steady state, the rotor flux is given by φr = Lm i∗ds .
(10)
Substituting (7) and (10) into (6), electromagnetic torque becomes kt = (3pp /2) L2m /Lr i∗ds . (11) Te = kt iqs , As a result, the electromagnetic torque is linearly dependent on the torque current component iqs , indicating that both rotor flux and electromagnetic torque can be controlled separately. In most so far described IM vector control applications, two current controllers, along with decoupling circuits, are used as part of inner control loops in addition to the position/velocity controllers. Usually, hysteresis or PI current controllers are applied. The resulting current dynamics is much faster than the dynamics of the mechanical part. Hence, in the outer control loop design, the current dynamics is usually neglected, and the IM model is a second-order plant, described by (5) and (11). In the proposed IM control scheme, shown in Fig. 1, there is only a flux current PI controller. Torque current controller and decoupling circuits are excluded. The rotor flux vector angular position θe is obtained using the slip estimate and the measured rotor position. Notice in Fig. 1 that the slip calculator is fed with the actual measured currents. The commonly used feedforward slip estimation, utilizing current commands i∗ds and i∗qs , cannot be implemented since there is no q-axis current controller. The simplest slip estimation is applied, ωs = iqs /(Tr ids ). The rotor resistance variation due to machine thermal changes results in inaccurate slip estimation and, consequently, in incorrect rotor flux position. This leads to a violation of ideal torque and flux decoupling, which deteriorates performance. This phenomenon has not been isolatedly handled in this paper, although there exist several online rotor resistance identification techniques [3]–[5] that overcome this problem. The impact of the rotor resistance variation is treated here as a system perturbation, which is submitted to the robustness of the proposed scheme. By virtue of (7), (9), (10), and (11), and under the assumption that a flux current controller ensures that ids = i∗ds ,
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