1178 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 11, NO. 5, SEPTEMBER 2000 Robust Backstepping Control of Induction Motors Using Neural Networks C. M. Kwan and F. L. Lewis Abstract—In this paper, we present a new robust control technique for induction motors using neural networks (NNs). The method is systematic and robust to parameter variations. Motivated by the well-known backstepping design technique, we first treat certain signals in the system as fictitious control inputs to a simpler subsystem. A two-layer NN is used in this stage to design the fictitious controller. Then we apply a second two-layer NN to robustly realize the fictitious NN signals designed in the previous step. A new tuning scheme is proposed which can guarantee the boundedness of tracking error and weight updates. A main advantage of our method is that we do not require regression matrices, so that no preliminary dynamical analysis is needed. Another salient feature of our NN approach is that the off-line learning phase is not needed. Full state feedback is needed for implementation. Load torque and rotor resistance can be unknown but bounded. Index Terms—Control, induction motor, neural networks (NNs). I. INTRODUCTION T HE INDUCTION motor is quite popular for fixed-speed applications. Since rotor currents are induced, no brushes and slip rings are needed. It is maintenance free, simple in op- eration, rugged and generally less expensive than either dc or synchronous motors [4]. On the other hand its model is much more complicated than other machines and because of this, it is considered as “the benchmark problem in nonlinear systems” by the Editorial Board of IEEE TRANSACTIONS ON AUTOMATIC CONTROL in comments on a recent paper written by Marino et al. [33]. Moreover, uncertainties such as load torque and rotor resistance are usually unknown and may have a large degree of variations (up to 50% change in rotor resistance) [33]. There are many approaches to control induction motors such as methods described in [2], [3], [14], [25]–[27], [35], [40], [43], and references therein. Here we briefly summarize induction motor control methods in the past few years. A method com- bining nonlinear damping and observer backstepping using a flux observer was used in [28]. Machine parameters were as- sumed to be known. An indirect field-orientation approach was used in [45]. Assumptions were similar to [28]. A recurrent neural-network (NN) approach to induction motor control was reported in [46]. In [47], an off-line approach to model an in- duction machine by an NN was proposed. The model was then validated by simulations. Assuming all the states are available and all motor parameters are known, a dynamic feedback lin- earization method was generated in [48]. An NN was used to Manuscript received April 23, 1999; revised January 21, 2000 and May 16, 2000. This work was supported by the National Science Foundation under Grant IRI-9216545. C. M. Kwan is with the Intelligent Automation Inc., Rockville, MD 20850 USA. F. L. Lewis is with the Automation and Robotics Research Institute, The Uni- versity of Texas at Arlington, Fort Worth, TX 76118 USA. Publisher Item Identifier S 1045-9227(00)06488-2. identify motor speed on-line for induction motor control [49]. Huang et al. [50] used two NNs: one for load torque estimation and one for model identification. No closed-loop stability anal- ysis was given. A recurrent NN was used to implement a pro- grammable cascaded low-pass filter, which synthesizes stator flux vector. The focus of the NN was for flux synthesis rather than closed-loop control. A method combining optimal regu- lator with neural-network estimator was proposed in [52]. The NN was essentially used as an observer. An adaptive flux ob- server was proposed for speed control of induction motor [53]. A controller based on a linearized model of the induction motor was used in [54]. States are needed for implementation. Ha and Sul [55] proposed a new method of estimating rotor flux angle from stator voltages and currents. The method might be com- bined with other control methods for closed-loop control. A new adaptive control scheme without flux measurement was pro- posed in [56]. Stability analysis was given. We also mention some recent related works on the control of motors. Chen and Paden [7] applied adaptive control tech- niques to hybrid stepper motor. Bodson et al. [5] developed a feedback linearization method to control a permanent magnet stepper motor. Burg et al.developed a velocity tracking con- troller for a dc motor [6]. Dawson et al. summarized various control approaches to different motors in [15]. Our current work concentrates on the robust control of induction motors using NNs. Whether it is possible or not to apply our approach to the above types of different motor systems requires further investi- gation. NNs have been applied to system identification [10], [19] or identification-based control [8], [9], [21], [24], [36]. Uncer- tainty on how to initialize the NN weights leads to the necessity for “preliminary off-line tuning” [8], [9], [12]. Recently many NN controllers have been proposed for various control applica- tions that can provide closed-loop stability ([9], [18], [30], [32], [37]–[39], [41], [44]). In the recent adaptive and robust control literature there has been a tremendous amount of activity on a special control scheme known as “backstepping” [22], [23], [28]. When used under some mild assumptions, many existing robust and adaptive control techniques can be extended to wide classes of applications. A major problem with backstepping approaches is that certain functions must be “linear in the unknown system parameters,” and some very tedious analysis is needed to determine a “regression matrix.” For instance, even for two robots within the same class (same number of links, revolute joints) but with different number of unknown parameters, minor changes in link lengths and masses, etc., one has to restart the whole tedious process of determining the regression matrix again. For a robot with six links, the job becomes even more difficult. Although symbolic computation may offer some help, one still has to manually manipulate and combine a lot of 1045–9227/00$10.00 © 2000 IEEE