Swinging up and Stabilization of Cart Inverted Pendulum System Using Backstepping State Feedback Control Incorporating with GA

Abstract

The cart inverted pendulum system is an Underactuated system with one control input for two outputs degrees of freedom (DOF), highly nonlinear and inherently unstable. The pendulum is swinging from the pendant position to an inverted position when the cart is accelerated by force which is provided to the cart with a DC motor. In this thesis mathematical modelling of dynamics is derived by utilizing Euler-Lagrange’s equations and the system is decomposed into cart subsystem and pendulum subsystem. Since the system is highly nonlinear, it can validate different nonlinear and linear controllers. So, in this work, a combined backstepping and state feedback controller is optimized by a genetic algorithm (GA) is designed for the stabilization of the system in a comparison with linear quadratic regulator (LQR) and energy-based passivity swing up a controller for swinging the pendulum from the pendant position to near to upright position. Additionally, there are four scenarios considered for the cart’s position  1 meter and 45 degrees the angle of a pendulum for proposed control effectivity. From the results in the simulation, the proposed controller gives 2.53% overshoot, 1.1695 settling time for set point changes responses and 63.26% of overshoot, 49.5474 IAE for multiple set point changes. For disturbance rejection, the proposed controller  5N rejects disturbance applied at 2.0507 recovery time and 8.75519 IAE and robust to 40% change mass of pendulum to parameter uncertainty with 1.3106 and 1.8535 IAEU and IAE respectively. The performance of the controllers tuned with the genetic algorithm is measured using integral absolute error (IAE). The controller design is implemented in MATLAB.