Robust Commutation Design: Applied to Switched Reluctance Motors

TL;DR

This work addresses torque ripple in SRMs caused by manufacturing variations in the rotor teeth and the torque-current-angle relation $T=\mathbf{g}(\phi)\mathbf{u}$. It proposes a robust, low-order commutation function design that parameterizes the SRM model as $\hat{\mathbf{g}}^{\top}(\phi,\boldsymbol{\theta})=\boldsymbol{\psi}_g(\phi)\boldsymbol{\theta}$ and the control map as $\mathbf{f}^{\pm}(\phi,\boldsymbol{\alpha})=\boldsymbol{\psi}_f(\phi)\boldsymbol{\alpha}^{\pm}$ with a Matérn-like kernel enforcing periodicity. The optimization minimizes the expected torque ripple $\tilde{\mathcal{J}}(\boldsymbol{\alpha})$ subject to linear positivity constraints, yielding a convex problem solved offline for a universal driver. Across Monte Carlo simulations on $M=100$ SRMs and experimental trials, robust commutation reduces tracking error and torque ripple under tooth-to-tooth and machine-to-machine variations, enabling a single low-memory driver with reduced acoustic noise and improved performance in mass-produced SRMs.

Abstract

Switched Reluctance Motors (SRMs) are cost-effective electric actuators that utilize magnetic reluctance to generate torque, with torque ripple arising from unaccounted manufacturing defects in the rotor tooth geometry. This paper aims to design a versatile, resource-efficient commutation function for accurate control of a range of SRMs, mitigating torque ripple despite manufacturing variations across SRMs and individual rotor teeth. The developed commutation function optimally distributes current between coils by leveraging the variance in the torque-current-angle model and is designed with few parameters for easy integration on affordable hardware. Monte Carlo simulations and experimental results show a tracking error reduction of up to 31% and 11%, respectively. The developed approach is beneficial for applications using a single driver for multiple systems and those constrained by memory or modeling effort, providing an economical solution for improved tracking performance and reduced acoustic noise.

Figures (7)

• Figure 1: Schematic overview of an SRM with three coils. Sequentially applying currents to the coils attracts rotor teeth, generating torque. When control designs involve commutation functions that rely on incorrect or incomplete models, torque ripple occurs, degrading tracking performance.
• Figure 2: Control scheme for an SRM $P$: The SRM's nonlinear dynamics are linearized using a commutation function $\mathbf{f}$ to achieve $\hat{\mathbf{g}}\mathbf{f}=\pm 1$, enabling the use of a linear feedback controller $C(z)$. Solid lines and dashed lines depict continuous-time and discrete-time signals, respectively.
• Figure 3: Torque-current-angle relationships $\mathbf{g}(\phi,\boldsymbol{\theta}_i)$ of the simulated SRMs ($\lambda=1$). The average $\mathbf{g}(\phi,\boldsymbol{\theta}^\circ)$ is shown in bold.
• Figure 4: The developed robust commutation functions $\mathbf{f}^-$ (solid) and conventional functions $\mathbf{f}_{\text{conv}}^-$ (dot-dashed). The developed commutation functions exhibit much more overlap, leading to careful switching of the currents in the face of model uncertainty.
• Figure 5: Torque ripple of all SRMs. Commutation functions $\mathbf{f}^-$ and $\mathbf{f}_{\text{conv}}$ are designed to invert $\mathbf{g}(\phi,\boldsymbol{\theta}^\circ)$ so the torque ripple is expected to be low with both $\mathbf{f}^-$ () and $\mathbf{f}_{\text{conv}}$ () for the average SRM. However, since each simulated SRM is different with $\boldsymbol{\theta}_i\neq \boldsymbol{\theta}^\circ$, each SRM exhibits torque ripple. The robust $\mathbf{f}^-$ exhibits significantly less torque ripple () than $\mathbf{f}_{\text{conv}}$ () because the model uncertainty is taken into account in the design.