Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors Considering Current and Torque Constraints

Abstract

In various permanent magnet synchronous motor (PMSM) drive applications the torque dynamics are an important performance criterion. Here, time-optimal control (TOC) methods can be utilized to achieve highest control dynamics. Applying state-of-the-art TOC methods leads to unintended overcurrents and torque over-and undershoots during transient operation.To prevent these unintended control characteristics while still achieving TOC performance the time-optimal model predictive control (TO-MPC) is proposed in this work. The TO-MPC contains a reference pre-rotation (RPR) and a continuous control set model predictive flux control (CCS-MPFC). By applying Pontryagin's maximum principle, the TOC solution trajectories for states and inputs of the PMSM are determined neglecting current and torque limits. With the TOC solution, a flux linkage reference for the CCS-MPFC is calculated that corresponds to a pre-rotation of the operating point in the stator-fixed coordinate system. This pre-rotated flux linkage reference is reached in minimum time without overcurrents and torque over-as well as undershoots by incorporating current and torque limits as timevarying softened state constraints into the CCS-MPFC. Simulative and experimental investigations for linearly and nonlinearly magnetized PMSMs in the whole speed and torque range show that, compared to state-of-the-art TOC methods, overcurrents and torque over-as well as undershoots are prevented by the proposed TO-MPC.

Continuous Control Set Model Predictive Torque Control with Minimum Current Magnitude Criterion for Synchronous Electric Motor Drive

“…This is due to the effects of the backelectromotive-force, that is present in E i (see (1)), as shown in Fig. 3 in [24].…”

“…In order to keep the current vector magnitude lower than the nominal current, avoiding over-currents during transients operations, a linear current constraint has to be defined due to the linearly-constrained quadratic programming problem implementation. Therefore, the circular current constraint has to be linearized as proposed in [24]. The linear time-varying current constraint, which is function of the instantaneous current i k dq , implemented in this paper is:…”

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors in the Whole Speed and Modulation Range Considering Current and Torque Limits

“…During online operation, a set of nonlinear equations, cf. (26), must be numerically solved in order to determine the time-optimal stator voltages [5], [6], [9]. Hence, control methods that do not solve the TOC problem, such as PI-FOC [4], direct torque control [11], conventional model predictive controllers (MPC) [12]- [15], or deadbeat direct torque and flux control [16], may not reach the reference in the fastest way, resulting in time-suboptimal control behavior.…”

“…3]. To prevent these undesired characteristics, the TOC methods [8], [9] are considering current and torque limits but are restricted to the linear modulation range during steady-state operation. The deadbeat flux control (DBFC) proposed in [10] is to the authors' best knowledge the only TOC method that can reach the entire overmodulation range up to six-step operation.…”

“…Current and Time-optimal Overmodulation torque limits control and six-step • allow a seamless transition in the entire modulation range including six-step operation. The TO-HRG makes use of the reference pre-rotation (RPR) method [9] and the harmonic reference generator (HRG) method [2] to obtain the respective advantages of the control methods [9] and [2], see Tab. 1.…”