Noninteracting optimal and adaptive torque control using an online parameter estimation with help of polynomials in EKF for a PMSM

This paper addresses a non-interacting torque control strategy to decouple the d- and q-axis dynamics of a permanent magnet synchronous machine (PMSM). The maximum torque per ampere (MTPA) method is used to determine the reference currents for the desired torque. To realize the noninteracting control, knowledge concerning the inductances L_d and L_q of the electrical machine is necessary. These two inductances are estimated by two extended Kalman filters (EKFs), which use a univariate polynomial as a model to describe the saturation effects of the PMSM. The Kalman filters (KF) are realized within a noninteracting control system to improve the observability of the inductance. Despite the non-perfect decoupling, thanks to the structural stochastic nature of the KFs, noninteracting cancellation errors are represented with its process noise and the inductances are estimated sufficiently well. In this sense, we can speak about KFs for and within noninteracting control. Estimating inductances is fundamental for optimal torque control, which is a viable approach to reducing mechanical vibration and disturbance. Moreover, the control strategy of model-based techniques must be adaptively tuned to work properly. Starting from the existing literature, a viable control structure is proposed in which the stability of the control loop using a Proportional Integral (PI) controller is shown for the resulting time-varying system. In fact, the model is represented as a time-varying system because of the presence of the variable inductances L_d and L_q and because of the presence of the velocity of the rotor which is not considered as a state. In this paper, a forward Euler discretization is used to realize the observer in the discrete experimental setup. Measures realized with hardware in the loop (HIL) show interesting results in the context of inductance estimation, due to the advantage of the reduction of the dimensions of the two decoupled EKFs resulting from the noninteraction control. Using the HIL simulator, the proposed torque control strategy is investigated, showing promising results in terms of increasing observability due to decoupling. This and the usage of univariate polynomials in EKF calculations lead to significant reduction of measurement points, reduction of oscillations and ripples, deviation between desired and achieved torque and reduction of disturbances. Moreover, the proposed control strategy using a very limited calculation load, at the same time, maintains the ripples inside the technical limits of the obtained torque. Both effects are due to the decoupled EKFs with simplified and reduced order of the models using univariate polynomials, which require significantly fewer measuring points in the run-up to the creation of the model of the inductances L_d and L_q.