Stabilization of a cart inverted pendulum system using LQR, Partial Feedback Linearization and LQG control

Controlling of a cart inverted pendulum often becomes learning material for a control system. Several researchers have carried out about stabilization of inverted pendulum using numerous methodologies. However, the stabilization of the pendulum has just been conducted in the inverted area. The aim of this research was designing a control system to raise the pendulum from the lower area to the inverted area using Linear Quadratic Regulator (LQR) and Partial Feedback Linearization control in the Simulink MATLAB. Furthermore, the design was given a noise so that Linear Quadratic Gaussian (LQG) control was needed to make this system more robust. The model of cart pendulum with LQR control alone was unable to raise the pendulum from 0 degree to reach the angle at 180 degrees in an inverted area although the gain K and the voltage of DC motor were increased. For this reason, the Partial Feedback Linearization method was added to raise the pendulum by controlling the energy and slide mode on the cart. The strengthening of the system with the LQG design was carried out to reduce the noise signal that occurs in the DC Motor and sensor. The design was implemented in the simulation using Simulink MATLAB. It shows that the design of LQR and Partial Feedback Linearization control can make the pendulum stable at 180 degrees in 5.2 seconds and the cart is stable at 0 cm in 4.5 seconds. Whereas, the design of LQG control can reduce the noise well in the system.