776 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 4, JULY/AUGUST 1998 Switched Reluctance Motor Modeling with On-Line Parameter Identification Sayeed Mir, Member, IEEE, Iqbal Husain, Member, IEEE, and Malik E. Elbuluk, Senior Member, IEEE Abstract—A nonlinear model with on-line parameter estimation using recursive identification for switched reluctance motors (SRM’s) is presented. The model is robust toward parameter vari- ations in the motor or any system disturbances. The parameters of the model are adjusted to account for errors in rotor position, which allows the use of crude inexpensive position sensors. The proposed modeling approach allows self tuning of SRM’s in a production unit. The simulations and experiments performed to test the model demonstrate the accuracy of estimation of the model. Index Terms— Parameter identification, switched reluctance motor modeling, switched reluctance motors. I. INTRODUCTION T HE switched reluctance motor (SRM) is a simple, low- cost, and robust motor that makes it suitable for variable- speed and servo-type applications. With relatively simple converter and control requirements, the SRM is gaining in- creasing attention in the drive industry. The inherent nonlinearity of the SRM makes torque produc- tion highly dependent upon the geometry of the poles and is characterized by dual dependence on both the stator current and rotor position. In order to obtain high quality control in either torque or speed control applications, it is essential to have an accurate model of the motor that describes the torque characteristics. In the past, either a linear model of an SRM [1] or a nonlinear model based on stored current, position, and torque profiles [2]–[5] has been used to implement sophisti- cated control algorithms. The highly nonlinear nature of the SRM makes the linear model unsuitable for high-performance applications. The nonlinear SRM models described in [2]–[4], in general, use a function to represent the motor flux-angle- current characteristics based on off-line data collected from the motor under static conditions. The piecewise-linearized model, which accommodates some of the nonlinearities of the machine, has been discussed in [6]. The model is simpler than the more complicated nonlinear models, but is less accurate. All the SRM modeling schemes that have been discussed in the literature describe the motor characteristics using data Paper IPCSD 98–21, presented at the 1997 Industry Applications Society Annual Meeting, New Orleans, LA, October 5–9, and approved for publica- tion in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. Manuscript released for publication March 3, 1998. S. Mir is with the Electrical and Electronics Department, General Motors Research and Development Center, Warren, MI 48090 USA. I. Husain and M. E. Elbuluk are with the Department of Electrical Engineering, The University of Akron, Akron, OH 44325-3904 USA. Publisher Item Identifier S 0093-9994(98)05191-3. collected under static conditions. During the operation of the machine, the characteristics of the machine may change from its initial model, due to unmodeled dynamics and change of machine parameters. In such cases, algorithms based upon the static model no longer remain valid. Also, these models are highly dependent upon the rotor position information. Any inaccuracy in the position information can lead to inaccurate torque estimation and erroneous control. Tuning individual motors coming out of a production line is, in itself, an ever-existing problem for SRM’s. The operating principle of SRM’s forces each machine to have its own current-profiling controller in order to obtain a smooth motor torque. The phase current profiles are typically predetermined and stored in the memory to serve as reference currents. A high-bandwidth current regulator is typically required to force the phase currents to follow the reference currents. The strategy is analogous to field-oriented control of ac machines, except that an ac machine controller uses a favorable reference frame to obtain the reference phase currents [7]. Unlike field- oriented control of ac machines, no reference frame exists for SRM’s in which the motor currents are constants, which makes the design of controllers for SRM’s so complicated. A controller that would determine the optimal current waveforms in real time would be ideal for SRM’s. In the absence of such a controller, a torque observer that is not based upon predetermined parameters of a particular machine would significantly enhance the viability of the SRM in various applications. The torque observer will enable the design of a closed-loop torque controller within the speed loop. In this paper, a nonlinear model with on-line parameter es- timation using recursive identification is presented. The model serves as a torque observer, providing total torque, as well as phase torque. Changes in the parameters of the machine or inaccuracies in the rotor position information do not affect the model. Speed or crude rotor position information is sufficient to give an accurate estimation of the torque of the machine using this model, thereby eliminating the need for expensive resolvers or encoders required in the past. Most importantly, the presented model allows self tuning of a switched reluctance machine without additional instrumentation. The details of the model, including the estimation algorithm, and simulation and experimental results appear in the following sections. II. SRM MODELING Stator flux is used as the state variable for the modeling approach. The following aspects of the flux production of SRM’s are considered in selection of the model. 0093–9994/98$10.00  1998 IEEE