Balancing Double Inverted Pendulum on A cart by Linearization Technique

Abstract

Double Inverted Pendulum on a cart (DIPC) is a classic problem in dynamics and control theory and is widely used in control laboratories to demonstrate the effectiveness of control systems as well as a benchmark for testing control algorithms. It is suitable to investigate and verify different control methods for dynamic systems with higher order nonlinearities. A controller is proposed to swing a double inverted pendulum to an unstable upright inverted position and stabilize around the point by using Linear Quadratic Regulator (LQR) technique. Linearization form of nonlinear system is obtained by Jacobian with proper cost function and the modeling of it is accomplished with the help of Euler – Lagrangian equation derived by specifying Lagrangian, difference between kinetic and potential energy of DIPC. Simulation results are retrieved by MATLAB