Hybrid Dynamical Modeling and Control of Permanent Magnet Synchronous Motors: Hardware-in-the-Loop Verification

Abstract

The stabilization of a permanent magnet synchronous motor using digital controllers requires the design of both the feedback law and an appropriate sampling frequency. Moreover, the design approach must be robust against existing uncertainties, such as disturbances and parameter variations. In this paper, we develop a stabilizing state feedback nonlinear control scheme for the permanent magnet synchronous motor. Moreover, we consider the case where the feedback signal is transmitted over a digital platform, and we derive the stabilizing sampling frequency, such that the stability of the closed-loop system is maintained. We design the controller by emulation, where the closed-loop stability is first established in continuous time; we then take into account the effect of sampling. The feedback law consists of two parts: feedback linearization and robust linear quadratic regulator for the linearized mode. The robustness is achieved by augmenting the state space model, with additional states representing the tracking errors of the motor speed and the motor current. Then, to cope with sampling, we estimate the maximally allowable sampling interval to reduce the sampling frequency while preserving the closed-loop stability. The overall system is modeled as a hybrid dynamical system, which allows handling both the continuous-time and discrete-time dynamics. The effectiveness of the proposed technique is illustrated by simulation and verified experimentally using a hardware-in-the-loop setup. Upon implementing the proposed approach, the obtained sampling interval was around 91 ms, making it suitable for digital implementation setups.