Stability analysis of q-axis rotor flux based model reference adaptive system updating rotor time constant in induction motor drives

q-axis rotor flux can be chosen to form a model reference adaptive system (MRAS) updating rotor time constant online in induction motor drives. This paper presents a stability analysis of such a system with Popov's hyperstability concept and small-signal linearization technique. At first, the stability of q-axis rotor flux based MRAS is proven with Popov's Hyperstability theory. Then, to find out the guidelines for optimally designing the coefficients in the PI controller, acting as the adaption mechanism in the MRAS, small-signal model of the estimation system is developed. The obtained linearization model not only allows the stability to be verified further through Routh criterion, but also reveals the distribution of the characteristic roots, which leads to the clue to optimal PI gains. The theoretical analysis and the resultant design guidelines of the adaptation PI gains are verified through simulation and experiments.