Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Accounts of using the Tustin-Net architecture on a rotary inverted pendulum

Stijn van Esch, Fabio Bonassi, Thomas B. Schön

TL;DR

The paper investigates identifying a rotary inverted pendulum using a physics-informed neural network, the Tustin-Net, and compares it to a first-principles Euler–Lagrange grey-box model on a real Quanser Qube Servo 2. It identifies limitations of standard Tustin-Net training and proposes a transfer-learning workflow—pre-training on transient data, freezing early layers, and fine-tuning final layers—to boost accuracy, especially under imbalanced data. Results show that a TL-trained Tustin-Net achieves RMSEs comparable to or better than the Euler–Lagrange model and with less reliance on detailed physical knowledge, demonstrating practical viability for data-driven mechanical system identification. The approach enhances generalization across operating conditions and offers a scalable path for physics-based deep learning in real hardware settings.

Abstract

In this report we investigate the use of the Tustin neural network architecture (Tustin-Net) for the identification of a physical rotary inverse pendulum. This physics-based architecture is of particular interest as it builds on the known relationship between velocities and positions. We here aim at discussing the advantages, limitations and performance of Tustin-Nets compared to first-principles grey-box models on a real physical apparatus, showing how, with a standard training procedure, the former can hardly achieve the same accuracy as the latter. To address this limitation, we present a training strategy based on transfer learning that yields Tustin-Nets that are competitive with the first-principles model, without requiring extensive knowledge of the setup as the latter.

Accounts of using the Tustin-Net architecture on a rotary inverted pendulum

TL;DR

The paper investigates identifying a rotary inverted pendulum using a physics-informed neural network, the Tustin-Net, and compares it to a first-principles Euler–Lagrange grey-box model on a real Quanser Qube Servo 2. It identifies limitations of standard Tustin-Net training and proposes a transfer-learning workflow—pre-training on transient data, freezing early layers, and fine-tuning final layers—to boost accuracy, especially under imbalanced data. Results show that a TL-trained Tustin-Net achieves RMSEs comparable to or better than the Euler–Lagrange model and with less reliance on detailed physical knowledge, demonstrating practical viability for data-driven mechanical system identification. The approach enhances generalization across operating conditions and offers a scalable path for physics-based deep learning in real hardware settings.

Abstract

In this report we investigate the use of the Tustin neural network architecture (Tustin-Net) for the identification of a physical rotary inverse pendulum. This physics-based architecture is of particular interest as it builds on the known relationship between velocities and positions. We here aim at discussing the advantages, limitations and performance of Tustin-Nets compared to first-principles grey-box models on a real physical apparatus, showing how, with a standard training procedure, the former can hardly achieve the same accuracy as the latter. To address this limitation, we present a training strategy based on transfer learning that yields Tustin-Nets that are competitive with the first-principles model, without requiring extensive knowledge of the setup as the latter.
Paper Structure (18 sections, 26 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 18 sections, 26 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. First-principles model
  3. Setup
  4. Euler-Lagrange grey-box model
  5. Parameters identification
  6. Shortcomings
  7. Physics-based deep learning model
  8. The Tustin-Net architecture
  9. Standard training procedure
  10. Improving training with transfer learning
  11. Step 1. Network pre-training
  12. Step 2. Weights freezing
  13. Step 3. Fine-tuning
  14. Numerical results and discussion
  15. Euler-Lagrange model
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Rotary pendulum system: picture of the lab apparatus (left) and schematic overview (right).
  • Figure 2: Scheme of the Tustin-Net model.
  • Figure 3: Free-run simulation of the Euler-Lagrange model \ref{['eq:mechanical:statespace']} with (orange dashed line) and without (purple dotted line) spring model, compared the ground truth (blue continuous line) on one of the validation experiments.
  • Figure 4: Free-run simulation of the Tustin-Net model \ref{['eq:tustin:statespace']} learned via Algorithm \ref{['alg:transfer_learning']} (red dashed-dotted line) compared to the ground truth (blue continuous line) and to standard training procedure (Section \ref{['sec:tustin-net:intro']}) on a validation dataset.
  • Figure 5: Performance comparison of the Tustin-Net model learned by Algorithm \ref{['alg:transfer_learning']} (red dashed-dotted line) and Euler-Lagrange model (orange dashed line) on the validation dataset.

Theorems & Definitions (3)

  • remark thmcounterremark
  • remark thmcounterremark
  • remark thmcounterremark