Adaptive flux observer for permanent magnet synchronous motors

Abstract : The paper deals with the observer design problem for a flux in permanent magnet synchronous motors. It is assumed that some electrical parameters such as resistance and inductance are known numbers. But the flux, the angle and the speed of the rotor are unmeasurable. The new robust approach to design an adaptive flux observer is proposed that guarantees globally boundedness of all signals and, moreover, exponential convergence to zero of observer error between the true flux value and an estimate obtained from the adaptive observer. The problem of an adaptive flux observer design has been solved with using the trigonometrical properties and linear filtering which ensures cancellation of unknown terms arisen after mathematical calculations. The key idea is the new parameterization of the dynamical model containing unknown parameters and depending on measurable current and voltage in the motor. By applying the Pythagorean trigonometric identity the linear equation has found that does not contain any functions depending on angle or angular velocity of the rotor. Using dynamical first-order filters the standard regression model is obtained that consists of unknown constant parameters and measurable functions of time. Then the gradient-like estimator is designed to reconstruct unknown parameters, and it guarantees boundedness of all signals in the system. The proposition is proved that if the regressor satisfies the persistent excitation condition, meaning the “frequency-rich” signal, then all errors in observer exponentially converges to zero. It is shown that observer error for the flux explicitly depends on estimator errors. Exponential convergence of parameter estimation errors to zero yields exponential convergence of the flux observer error to zero. The numerical example is considered.