Abstract
The objective of this project is to control and stabilize an Inverted Pendulum (IP) Cart System by using two types of controllers: Linear Quadratic Regulator and Proportional Integral Derivative. LQR (Linear Quadratic Regulator) Controller and Proportional Integral Derivative Controller (PID) are used to control the Inverted Pendulum unstable system, and the performances of the controllers are analyzed. Initially, the hardware of the IP is taken into consideration and the system is modeled by deriving its Equation of Motion (EOM) using Lagrange's method. Subsequently each of the controllers are designed based on a common design specification and simulated to prove the controllers’ effectiveness in stabilizing the IP at its unstable equilibrium point. The Inverted Pendulum Cart System is modeled by its Equation of Motion (EOM) in Simulink/MATLAB. To compare the controller stabilization and robustness, two types of obstacles were introduced and the performance of each of the controller is analyzed.