This paper presents an adaptive state observer for a nonlinear induction motor model that accounts for viscous friction. The problem is solved using a modified version of the Dynamic Regressor Extension and Mixing (DREMBAO) method. The main idea is to reduce the original model to a regression-like model, where the vector of unknowns contains unknown parameters and state variables. After this step, it becomes possible to obtain a set of scalar linear equations with respect to the unknown state variables and parameters. Using these equations, parameters are estimated with gradient descent estimator, and state estimation is obtained using the gradient observer. Simulation results of an adaptive observer are presented, which demonstrate the effectiveness of the proposed approach.

The paper introduces a new state observer for the non-linear model of a voltage-fed induction motor (IM) with unknown rotor resistance and load torque. The only measurements available are the stator current and the control voltage. Compared to the recently introduced observer for IM, which is based on the Dynamic Regressor Extension and Mixing Adaptive Observer (DREMBAO) approach, the proposed observer estimates rotor speed and magnetic flux simultaneously, eliminating the need for a two-stage sequential estimation process. Additionally, the proposed solution considers viscous friction in the motor model, which is not taken into account in the aforementioned approach or other similar ones. The problem is solved using the Generalized Parameter Estimation-Based Observer (GPEBO) approach, which transforms the observer problem into a parameter estimation task. Simulations are also presented to support the theoretical claims and illustrate the performance of the solution.