ode45 Simulation of Temperature Sensor Thermal Response with Different Time Constants

Project info

• Field of studyInstrumentation and Sensors
• LevelMaster's thesis (S2)
• Method typeNumerical Simulation
• Estimated build time± 5 working days
• Toolsode45, odeset (MATLAB inti)
• PriceUS$28 - US$172

Research goal

Simulate sensor measured temperature with Differential Equations with ode45 and examine its sensitivity to thermal time constant and heat transfer coefficient.

Variables

Example result

• 66Accepted steps
• 0.606Mean step (s)
• 5.518Max of state 1
• 9.729Oscillation period (s)
• 0Max error vs tight solution
• 397Function evaluations

ode45 solves the Sensor measured temperature and Thermal time constant system in 66 adaptive steps (mean 0.606 s) with a maximum error of 5.0e-05 against a tight-tolerance reference; the oscillation period is about 9.73 s.

Computed from illustrative synthetic data, not from a real study.

About Differential Equations with ode45

ode45 solves non-stiff ordinary differential equations with an adaptive fourth/fifth-order Runge-Kutta method. It is used to simulate dynamic models such as populations, chemical reactions, and mechanical systems in engineering or science theses.

Steps

1. 1Write the equations as a first-order system dy/dt = f(t,y)
2. 2Define the derivative function and initial conditions
3. 3Set tolerances with odeset (RelTol, AbsTol)
4. 4Call ode45 over the desired time span
5. 5Verify the result (conserved quantity or analytic solution)
6. 6Plot the solution against time and the phase portrait

Assumptions to check

• The system is non-stiff (use ode15s if stiff)
• The derivative function is smooth over the integration range
• Tolerances are tight enough for the required accuracy

Reading and reporting the results

Report the model, parameters, initial conditions, solver tolerances, and numerical verification. Show the solution plots and interpret the resulting dynamic behaviour.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

% Lotka-Volterra predator-prey model
a = 1.1; b = 0.4; d = 0.1; g = 0.4;
f = @(t, y) [a*y(1) - b*y(1)*y(2); d*y(1)*y(2) - g*y(2)];
opts = odeset('RelTol', 1e-8, 'AbsTol', 1e-10);
[thermal_time_constant, sensor_measured_temperature] = ode45(f, [0 60], [10; 5], opts);   % time, states

% Conserved quantity V = d*x - g*ln(x) + b*y - a*ln(y)
V = d*sensor_measured_temperature(:,1) - g*log(sensor_measured_temperature(:,1)) + b*sensor_measured_temperature(:,2) - a*log(sensor_measured_temperature(:,2));
fprintf('Steps taken: %d\n', numel(thermal_time_constant));
fprintf('Max drift of conserved quantity: %.2e\n', max(abs(V - V(1))));

figure;
subplot(1,2,1);
plot(thermal_time_constant, sensor_measured_temperature(:,1), thermal_time_constant, sensor_measured_temperature(:,2), 'LineWidth', 1.2);
legend('Prey', 'Predator'); xlabel('Time'); ylabel('Population');
subplot(1,2,2);
plot(sensor_measured_temperature(:,1), sensor_measured_temperature(:,2)); xlabel('Prey'); ylabel('Predator'); title('Phase portrait');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions