Peltier Digital Twin: an open-source CPS benchmark

Reference artefacts for the paper

An Open-Source CPS Benchmark Architecture with a Thermoelectric Digital-Twin Use Case Lorenzo Raspaolo, Riccardo Berta, Luca Lazzaroni, Sandro Pastore, Francesco Bellotti ApplePies 2026, Bologna. Springer, Lecture Notes in Electrical Engineering.

The paper defines a seven-component benchmark architecture for open-source cyber-physical systems and instantiates it on a Bi2Te3 Peltier thermoelectric cooler. This repository is the reproducibility package R of that architecture: every artefact the paper refers to is here.

The seven components

Symbol	Component	Where it lives
P	Physical plant	materials/, plus the bill of materials in report/
S/A	Sensors and actuators	materials/, implementation/Driver_FW/
C	Embedded controller	implementation/Driver_FW/Driver_FW.ino
D	Digital twin	implementation/Peltier_DigitalTwin.slx
F	Formal model	modelling&verification/Peltier_UPPAAL.xml
L	Logs and datasets	implementation/dataset/
R	Reproducibility package	this repository

Layout

implementation/
  Driver_FW/          firmware and serial logger
  Peltier_DigitalTwin.slx
  dataset/            released telemetry + column dictionary
  scripts/            regenerate the paper figures and metrics
modelling&verification/
  Peltier_UPPAAL.xml  timed automata + the four verified CTL queries
materials/            component datasheets
report/               full course report the paper derives from
figures/              created on first run of the scripts

Each directory has its own README with the details.

Reproducing the published results

matlab -batch "run('implementation/scripts/run_validation.m')"   # Table 3
python3 implementation/scripts/make_fig_results.py               # Fig. 2
python3 implementation/scripts/make_fig_pipeline.py              # Fig. 1

Expected output, over the 4560 active-phase samples of the released dataset:

Phase	MAPE	RMSE	N
SP1 = 22 degC	1.4 %	0.32 K	1800
SP2 = 20 degC	2.8 %	0.58 K	1800
SP3 = 18 degC	7.2 %	1.31 K	960
Active total	3.2 %	1.38 K	4560

For the formal model, open modelling&verification/Peltier_UPPAAL.xml in UPPAAL 5.x and run the four stored queries: all four are satisfied, each in under 1 s.

Testbench at a glance

• Bi2Te3 Peltier module, 16 mm side, characterised in situ: alpha = 0.0152 V/K, R = 2.04 ohm, K = 0.52 W/K
• 2x PT100 on MAX31865 SPI converters, Rref = 430 ohm
• AOD4184A MOSFET, software PWM at 100 Hz
• Arduino UNO Q (Cortex-M33, Zephyr RTOS), 1 Hz control and telemetry super-loop
• Passive aluminium heat sinks, no fan
• Safety threshold T_h,max = 60 degC, shared by firmware and formal model

Tooling

MATLAB/Simulink R2024b or later, UPPAAL 5.x, Python 3.10 or later with matplotlib, numpy and h5py, Arduino IDE 2.x with the Arduino UNO Q core and the Adafruit_MAX31865 and PID_v1 libraries.

Citing

Please cite the ApplePies 2026 paper above. A BibTeX entry will be added once the volume DOI is assigned.