Adaptive control of variable reluctance motors: a spline function approach

This paper considers nonlinear adaptive control of a variable reluctance motor (VRM) in a low-velocity high-torque mode of operation. A simple dynamic model for the relationship among electric torque, rotor angular position, and phase currents is proposed. The model incorporates spline functions and a set of 'Fourier' sinusoids and captures several experimentally verified VRM characteristics, including flux saturation effects. based on this model, an adaptive controller is derived using the certainty equivalence principle. The controller provides asymptotic tracking of a desired rotor position trajectory. So-called 'torque-sharing functions' are employed to smooth the commutation among phases and to increase the peak torque available from the motor, when compared to 'hard' commutation that energizes only one phase at a time. Experimental results from a laboratory VRM provide motivation for the model and illustrate the controller's design and trajectory tracking performance. Index Terms - Adaptive control, asymptotic stability, nonlinear magnetics, numerical control, reluctance motors, rotating machine nonlinear analysis, spline functions.