Inverted-pendulum-on-a-cart

This project is a simulation and control implementation of an inverted pendulum mounted on a cart. The system's dynamics are modeled and controlled using MATLAB. The following files are part of this project:

1. InvPendOnCart.m: This MATLAB script contains the main code for simulating the inverted pendulum on a cart system. It sets up the system parameters, initializes the simulation, and visualizes the results. this functios give all states over time.

2. odeSolver.m: This MATLAB script contains a custom ordinary differential equation (ODE) solver used in the simulation. It include numerical integration methods to solve the equations of motion for the system. methods like Rhngekutta4,Euler ,ode45.

3. lqrControl.m: This MATLAB script implements the Linear Quadratic Regulator (LQR) controller for stabilizing and controlling the inverted pendulum system. It designs and applies the control law to maintain balance.

4. RK4.m: This MATLAB script contain the implementation of the Runge-Kutta 4th-order numerical integration method used in the simulation. this function output is next_state .

5. EnergyShaping_Lqr_SwingUp.m: This MATLAB script implement an energy-shaping control strategy combined with LQR to perform the swing-up and stabilization of the inverted pendulum.

Getting Started

To run this project on your local machine, follow these steps:

1. Ensure you have MATLAB installed on your computer.

2. Clone or download this repository to your local machine.

3. Open MATLAB and navigate to the project directory.

4. Run lqrControl.m or EnergyShaping_Lqr_SwingUp.m to see outputs

Usage

You can customize and extend this project in several ways:

• Adjust system parameters such as pendulum length, cart mass, and control gains in `You can customize and extend this project in several ways:

• Adjust system parameters such as pendulum length, cart mass, and control gains in EnergyShaping_Lqr_SwingUp.m or lqrControl.m.

• Modify the control strategy in lqrControl.m or EnergyShaping_Lqr_SwingUp.m to experiment with different control algorithms.

Contributing

If you would like to contribute to this project, please open an issue or submit a pull request. We welcome improvements, bug fixes, and new features.

Acknowledgments

Special thanks to JITENDRA SINGH for the paper "Model-Based Control Design for Swing-up & Balance of the Inverted Pendulum." The information from this paper was used in the design of the swing-up controller for this project.