Scaleable Open Source Labs

Preamble

Motivations

System identification (SysID) is a fundamental skill in modelling and control, enabling us to select and tune mathematical models of real-world systems from experimental data.

In this lab, you will explore both:

1. A physics-informed approach — where you construct a model based on assumed system dynamics, and tune parameters based on real-world data, and,
2. A black-box approach, where you select a candidate transfer function based on the response and directly fit it’s parameters to suit measured input–output data.

By engaging with both approaches, you will build an appreciation for the trade-offs between interpretability, accuracy, and effort in modelling real systems. You will also develop practical skills in experimental design, data acquisition, and parameter estimation.

Learning Outcomes

Upon completing this lab, you will be able to:

1. Design and conduct experiments to obtain dynamic response data from a real physical systems,
2. Interpret free-response behaviour to estimate parameters of a physical system model,
3. Fit and evaluate black-box transfer function models using measured input–output data,
4. Compare physics-informed and black-box modelling approaches, including their assumptions and limitations,
5. Process and visualise experimental data to support model development and validation, and,
6. Critically assess model fidelity and sources of error in system identification.

Generative AI Use

[!CAUTION] This laboratory is unassessed, and exists only to help you develop fundamental skills in experiment design, data collection, processing, systems modelling, and parameter estimation. Aspects of this laboratory can be trivially completed using generative AI. Using genAI to complete this lab will only rob you of a valuable learning experience. You are strongly encouraged to complete this lab without the assistance of genAI.

System Background

This lab centres on the canonical, idealised mass-spring-damper system, shown in Figure 1.

Figure 1: Mass–spring–damper experimental rig

The system entails:

1. A mass m which moves rectilinearly between two fixed endpoints,
2. Springs $k_1$ and k_2, each attached to both the mass and one endpoint, and,
3. Friction acting on the mass, which can be modelled by dampers b_1 and b_2.

The system parameters (m, k_1, k_2, b_1, and b_2) are unknown to you.

Physical Lab Rig

This ideal system has been realised in the form of a handheld, scaleable lab rig that you are free to use. The rig:

• contains a sliding ‘mass’, tension springs, and frictive elements,
• is approximately the size on an iPhone and can be disturbed by hand using the ‘plectrum’,
• measures the instantaneous position of the mass and displays this on a digital readout, and,
• has the ability to record this position over a short time window and provide a .csv file to your computer for copying and analysis by presenting as a USB drive.

The rig is encased in acrylic and is intrisically safe. You do not need to complete a risk assessment to use the rig.

Your Task

[!NOTE] This is a note callout.

[!TIP] This is a tip.

[!IMPORTANT] Key information goes here.

Hand Calculations

To begin

Taking Measurements

Data Processing

System Identification (SysID)

Teardown