Speed observer of an induction machine based on the rotor flux linkage vector

Currently it is promising to create closed-loop asynchronous electric drives with frequency speed control without a phys-ical speed sensor on the AM shaft and instead use a speed observer. These sensorless electric drive systems have lower cost and dimensions and are more reliable if under operating conditions installing a speed sensor on the AM shaft is difficult or impossible. Well-known speed observers are synthesized as adaptive systems with a reference model (Model Reference Adaptive System – MRAS). These speed observers are most often used to form the adaptation function of the rotor flux linkage vector and estimation is obtained from the reference stator model and the adaptive rotor model. The observer structure is determined using a technique that uses the second Lyapunov theorem on the motion stability. At the same time, the problem of parametric synthesis, which consists in determining coefficients of the PI controller as part of the speed observer, is not even posed and solved in the literary sources known to the author. Therefore, the aim of the article was to propose a method for determining limits of the ranges of possible values of the controller coefficients. The criterion for selecting the controller parameters is the asymptotic stability of the observer. To determine stability of the observer the method of the first Lyapunov theorem on the motion stability was used. The original system of nonlinear equations of the observer was linearized. Then, to construct bound-aries of the stability region in the plane of two gain coefficients of the PI controller, roots of the characteristic equation of the linearized system were found in the nodes of the grid of the parameter plane. The need to use not only the integral but also the proportional component of the controller was justified, numerical values of these parameters and their relationship at different values of the rotor speed were determined.