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Structured physics-guided neural networks for electromagnetic commutation applied to industrial linear motors

Max Bolderman, Mircea Lazar, Hans Butler

TL;DR

The paper tackles commutation errors from position-dependent parasitics in high-precision motion systems by introducing physics-guided neural networks (PGNNs) to identify the electromagnetic part from force data and then analytically invert the PGNN to obtain an improved commutation law. It also develops an input transformation to operate when currents cannot be directly controlled, and validates the approach on an industrial coreless linear motor, achieving about a 10x reduction in commutation error and a 4x improvement in position tracking MSE over classical methods. The PGNN preserves physical interpretability by structuring the model around a physics-based gain matrix plus a cogging term, while learning parasitic effects with neural networks and providing an analytically tractable inversion for real-time control. The work demonstrates a practical, data-driven pathway to enhance industrial mechatronics performance and sets the stage for integrating the PGNN-based commutation with feedforward control and reduced reliance on force sensing.

Abstract

Mechatronic systems are described by an interconnection of the electromagnetic part, i.e., a static position-dependent nonlinear relation between currents and forces, and the mechanical part, i.e., a dynamic relation from forces to position. Commutation inverts a model of the electromagnetic part of the system, and thereby removes the electromagnetic part from the position control problem. Typical commutation algorithms rely on simplified models derived from physics-based knowledge, which do not take into account position dependent parasitic effects. In turn, these commutation related model errors translate into position tracking errors, which limit the system performance. Therefore, in this work, we develop a data-driven approach to commutation using physics-guided neural networks (PGNNs). A novel PGNN model is proposed which structures neural networks (NNs) to learn specific motor dependent parasitic effects. The PGNN is used to identify a model of the electromagnetic part using force measurements, after which it is analytically inverted to obtain a PGNN-based commutation algorithm. Motivated by industrial applications, we develop an input transformation to deal with systems with fixed commutation, i.e., when the currents cannot be controlled. Real-life experiments on an industrial coreless linear motor (CLM) demonstrate a factor 10 improvement in the commutation error in driving direction and a factor 4 improvement in the position error with respect to classical commutation in terms of the mean--squared error (MSE).

Structured physics-guided neural networks for electromagnetic commutation applied to industrial linear motors

TL;DR

The paper tackles commutation errors from position-dependent parasitics in high-precision motion systems by introducing physics-guided neural networks (PGNNs) to identify the electromagnetic part from force data and then analytically invert the PGNN to obtain an improved commutation law. It also develops an input transformation to operate when currents cannot be directly controlled, and validates the approach on an industrial coreless linear motor, achieving about a 10x reduction in commutation error and a 4x improvement in position tracking MSE over classical methods. The PGNN preserves physical interpretability by structuring the model around a physics-based gain matrix plus a cogging term, while learning parasitic effects with neural networks and providing an analytically tractable inversion for real-time control. The work demonstrates a practical, data-driven pathway to enhance industrial mechatronics performance and sets the stage for integrating the PGNN-based commutation with feedforward control and reduced reliance on force sensing.

Abstract

Mechatronic systems are described by an interconnection of the electromagnetic part, i.e., a static position-dependent nonlinear relation between currents and forces, and the mechanical part, i.e., a dynamic relation from forces to position. Commutation inverts a model of the electromagnetic part of the system, and thereby removes the electromagnetic part from the position control problem. Typical commutation algorithms rely on simplified models derived from physics-based knowledge, which do not take into account position dependent parasitic effects. In turn, these commutation related model errors translate into position tracking errors, which limit the system performance. Therefore, in this work, we develop a data-driven approach to commutation using physics-guided neural networks (PGNNs). A novel PGNN model is proposed which structures neural networks (NNs) to learn specific motor dependent parasitic effects. The PGNN is used to identify a model of the electromagnetic part using force measurements, after which it is analytically inverted to obtain a PGNN-based commutation algorithm. Motivated by industrial applications, we develop an input transformation to deal with systems with fixed commutation, i.e., when the currents cannot be controlled. Real-life experiments on an industrial coreless linear motor (CLM) demonstrate a factor 10 improvement in the commutation error in driving direction and a factor 4 improvement in the position error with respect to classical commutation in terms of the mean--squared error (MSE).
Paper Structure (13 sections, 1 theorem, 37 equations, 11 figures, 2 tables, 2 algorithms)

This paper contains 13 sections, 1 theorem, 37 equations, 11 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Closed--loop control architecture
  5. Classical commutation
  6. Data--based calibration
  7. Problem statement
  8. Physics--guided neural networks for commutation
  9. Suitable selection of control inputs
  10. PGNNs for identification of the electromagnetic part
  11. An analytical commutation solution
  12. Experimental results
  13. Conclusions

Key Result

Proposition 4.1

Consider the PGNN eq:PGNN_Electromagnetics_SingleCoilset, eq:GainMatrix_Cogging written as eq:PGNN_Rewritten_LIP with identification cost function eq:Identification_CostFunction. Let $\Lambda$ be diagonal and choose $\theta_{\textup{phy}}^{l^*}$ to represent the classical model eq:Electromagnetics_S Then, it holds that Moreover, eq:LowerCostFunction holds with strict inequality if and only if

Figures (11)

  • Figure 1: Schematic overview of the closed--loop control architecture.
  • Figure 2: Industrial coreless linear motor.
  • Figure 3: Schematic top--view of the CLM.
  • Figure 4: Position reference $y^*(t)$ (top window), and the commutation error in driving direction $F_y(t) - F_y^*(t)$ measured on the CLM using commutation law \ref{['eq:Commutation_Solution_Ideal']} with data--based calibrated parameters.
  • Figure 5: Schematic overview to control $i^l(t)$ via ${F_y^l}^*(t)$ and $\Delta^l(t)$.
  • ...and 6 more figures

Theorems & Definitions (8)

  • Remark 2.1
  • Remark 4.1
  • Remark 4.2
  • Proposition 4.1
  • proof
  • Remark 4.3
  • Remark 4.4
  • Remark 5.1