Modeling and Control of Inverted Pendulum cart system using PID-LQR based Modern Controller

The paper proposes a modern controller i.e. combination of Linear quadratic regulator (LQR) and Proportional, integral and derivative (PID) to control a highly non-linear inverted pendulum cart system. The detailed mathematical modeling of the inverted pendulum cart system as well as the modern controller are discussed in this paper. The performance of the proposed controller is compared with the conventional PID controller. The comparative results are shown using several simulated waveforms as well as in terms of time response specifications such as rise time, settling time, and peak overshoot and undershoot under MATLAB/Simulated environment.