Root Locus Analysis for Swinging Up and Stabilizing Inverted Pendulum Cart System

The paper presents swinging up and stabilization of inverted pendulum cart system (IPCS) and analysis of applied controller via root locus method. The IPCS is highly non-linear system which is analysed by the response after application of impulse input to the system. The controller which has combined feature of linear quadratic regulator (LQR) and conventional PID is proposed to handle the system. The root locus are drawn with and without application of the conventional PID and proposed controllers. It reveals that after application of controller, the roots shift towards left hand side (LHS) which are shown via root locus method. Initially, the system is merely controlled with conventional controller and then after LQR is incorporated in the feedback to control the system. The time specifications result are calculated and compared. The results reveal that the controller which is composed with PID and LQR shows better results as compared to the merely application of PID controller. The disturbance effect is also presented to show performance of the proposed controller. A number of simulated waveforms e.g. cart position and pendulum angle response are presented to show controller’s performance.