PMSM model discretization for Model Predictive Control algorithms

Abstract

Drives based on permanent magnet synchronous machines become more and more popular in many industrial applications. In most high-performance applications classical vector control is currently used. While this control method is usually reliable it has some limitations especially in controllers tuning and constraints handling. New control methods like Model Predictive Control become feasible in connection with increasing computational power of controller hardware. The paper deals with enhanced discrete time PMSM model which can be used for efficient predictive control implementation. The other objective of the paper is discussion of prediction horizon length impact on the drive control performance.

Model Predictive Control for Power Converters and Drives: Advances and Trends

“…However, non-linear systems require a more complex approach [85]. A trade-off between the model quality and complexity defines several discretization techniques, the most common being Euler approximation and Taylor series expansion [86]. Another approach consists of a first step where the system is discretized using a one-step or multiple-step Euler approximation.…”

Novel Lexicographic MPC for Loss Optimized Torque Control of Nonlinear PMSM

“…Minimizing losses is the goal of various MPC approaches for PMSM control including e.g. [6], [17]- [19]. However, usually a trade-off is found by incorporating the two control objectives in the cost function as a weighted sum.…”

“…The substitution procedure removes the additional equality constraint imposed by the system model (19) from the optimization problem. The optimization problem is only constrained by the inequality constraint induced by the inputs.…”

Prediction Error Analysis of Finite-Control-Set Model Predictive Current Control for IPMSMs

“…In general, the shorter the prediction stepsize, the better is the steady-state performance; this has been empirically shown by experimental results in literature [15,16]. In particular, when system variables and inputs change rapidly, a long prediction stepsize cannot respond immediately and may yield large tracking errors [11]. However, the prediction stepsize cannot be reduced indefinitely due to the hardware limitations and the power level of applications [17].…”

“…In Reference [10], a modified Euler integration method was adopted to achieve higher model accuracy, which actually transformed the implicit Tustin approximation to an explicit one by combining with forward Euler approximation. In Reference [11], two-order Taylor series expansion was utilized to achieve faster signal propagation from input changes to all controlled states, especially the mechanical speed, and relative degree one could be obtained [12]. In References [13,14], a discretization method was proposed considering the PWM pulse patterns within each sampling period for deadbeat predictive control to obtain an accurate discrete model.…”