Piece-wise Polynomial based Model for Switched Reluctance Motor

An analytical model is proposed for SRM phase flux-linkage, lambda in terms of phase current, i and rotor position, theta. The key contribution of this paper is that instead of fitting a global function to lambda(i, theta), it has been divided into four regions according to the physical characteristics. A two-stage polynomial fitting approach is used to capture each region: first, each flux-linkage vs rotor position curve at a constant current, Is captured by a fifth order polynomial in rotor position; then, variation of these polynomial coefficients with phase current is captured by another fifth order polynomial in current. Thus, each region is captured by 36 parameters and a total of 144 coefficients capture the complete flux-linkage data accurately, in an analytical formula. The other dynamic properties of SRM like, incremental inductance (partial derivative lambda/partial derivative i) and back-emf constant (partial derivative lambda/partial derivative theta) are obtained using the analytical model, which can be used for generating the feed-forward control signal in the torque controller design. An expression for instantaneous torque, T(i, theta) is derived from this flux-linkage model using co-energy principle and validated with experimentally obtained phase torque data. The accuracy and computational simplicity of the instantaneous torque model make it suitable for online torque estimator in closed-loop torque control applications.