Simulink Project for Inverted Pendulum: Setup and Simulation

A Simulink project for inverted pendulum involves creating a dynamic model using blocks like Integrator, Gain, and Sum to represent the pendulum's physics, then designing a controller such as a PID to balance it. You simulate the system by running the model and observing the pendulum's angle and control input over time.

Syntax

The basic components for modeling an inverted pendulum in Simulink include:

• Integrator: To represent angular velocity and angle by integrating acceleration.
• Gain: To apply constants like gravity, mass, and length.
• Sum: To combine forces and torques.
• Scope: To visualize outputs like angle and control signals.
• PID Controller: To stabilize the pendulum by adjusting input force.

These blocks connect to form differential equations describing the pendulum's motion.

matlab

%% Simulink block setup pseudocode
% 1. Use 'Integrator' blocks to get angle (theta) and angular velocity (omega)
% 2. Use 'Gain' blocks for constants: g (gravity), m (mass), l (length)
% 3. Use 'Sum' blocks to calculate net torque
% 4. Connect blocks to form equations:
%    d(omega)/dt = (m*g*l*sin(theta) + control_input) / (m*l^2)
%    d(theta)/dt = omega
% 5. Add 'PID Controller' block to compute control_input based on theta
% 6. Use 'Scope' to monitor theta and control_input

Example

This example shows how to create a simple inverted pendulum model in Simulink and simulate it with a PID controller to keep it balanced.

matlab

% MATLAB script to open and run a simple inverted pendulum Simulink model
% Create a new model
model = 'inverted_pendulum_example';
new_system(model);
open_system(model);

% Add blocks
add_block('simulink/Commonly Used Blocks/Integrator',[model '/Integrator1']);
add_block('simulink/Commonly Used Blocks/Integrator',[model '/Integrator2']);
add_block('simulink/Commonly Used Blocks/Gain',[model '/Gain_g']);
add_block('simulink/Commonly Used Blocks/Sum',[model '/Sum']);
add_block('simulink/Commonly Used Blocks/PID Controller',[model '/PID']);
add_block('simulink/Commonly Used Blocks/Scope',[model '/Scope']);

% Set Gain value for gravity
set_param([model '/Gain_g'], 'Gain', '9.81');

% Connect blocks (simplified connections for demonstration)
add_line(model, 'Integrator2/1', 'Integrator1/1');
add_line(model, 'Gain_g/1', 'Sum/1');
add_line(model, 'Sum/1', 'Integrator2/1');
add_line(model, 'Integrator1/1', 'PID/1');
add_line(model, 'PID/1', 'Sum/2');
add_line(model, 'Integrator1/1', 'Scope/1');

% Save and run simulation
save_system(model);
sim(model, 10);

Output

Simulation runs for 10 seconds showing pendulum angle response in the Scope window.

Common Pitfalls

Common mistakes when building an inverted pendulum Simulink project include:

• Incorrectly setting the signs in the Sum blocks, which can cause the pendulum to diverge instead of stabilize.
• Not tuning the PID controller gains properly, leading to oscillations or failure to balance.
• Forgetting to initialize the pendulum angle and velocity, causing unexpected simulation results.
• Ignoring physical parameters like mass and length, which affect system dynamics.

Always verify block connections and parameter values carefully.

matlab

% Wrong sign in Sum block example
% Incorrect: torque = m*g*l*sin(theta) - control_input
% Correct: torque = m*g*l*sin(theta) + control_input

% PID tuning example
% Wrong: Kp=0, Ki=0, Kd=0 (no control)
% Right: Kp=100, Ki=1, Kd=20 (example tuned values)

Quick Reference

Key tips for your inverted pendulum Simulink project:

• Use Integrator blocks to model angular velocity and angle.
• Apply physical constants with Gain blocks.
• Combine forces correctly with Sum blocks, minding signs.
• Tune your PID Controller to stabilize the pendulum.
• Visualize results with Scope blocks.

Key Takeaways

Model the pendulum dynamics using integrators, gains, and sums to represent physics.

Use a PID controller block to balance the pendulum by adjusting input force.

Check all block connections and signs carefully to avoid unstable simulations.

Tune PID gains to achieve smooth and stable pendulum control.

Visualize angles and control signals with scopes to analyze system behavior.