Design, Modeling and Control of an Inverted Pendulum on a Cart

The Inverted Pendulum on a Cart is a classical control theory problem that helps understand the importance of feedback control systems for a coupled plant. In this study, a custom built pendulum system is coupled with a linearly actuated cart and a control system is designed to show the stability of the pendulum. The three major objectives of this control system are to swing up the pendulum, balance the pendulum in the inverted position (i.e. $180^\circ$), and maintain the position of the cart. The input to this system is the translational force applied to the cart using the rotation of the tires. The main objective of this thesis is to design a control system that will help in balancing the pendulum while maintaining the position of the cart and implement it in a robot. The pendulum is made free rotating with the help of ball bearings and the angle of the pendulum is measured using an Inertial Measurement Unit (IMU) sensor. The cart is actuated by two Direct Current (DC) motors and the position of the cart is measured using encoders that generate pulse signals based on the wheel rotation. The control is implemented in a cascade format where an inner loop controller is used to stabilize and balance the pendulum in the inverted position and an outer loop controller is used to control the position of the cart. Both the inner loop and outer loop controllers follow the Proportional-Integral-Derivative (PID) control scheme with some modifications for the inner loop. The system is first mathematically modeled using the Newton-Euler first principles method and based on this model, a controller is designed for specific closed-loop parameters. All of this is implemented on hardware with the help of an Arduino Due microcontroller which serves as the main processing unit for the system.