LQR Controller Design for Stabilization of Cart Model Inverted Pendulum

Optimal response of the controlled dynamical systems is desired hence for that is the optimal control. Linear Quadraticn Regulator (LQR), an optimal control method, and PID control which are generally used for control of the linear dynamical systems have been used in this paper to control the nonlinear dynamical system. The inverted pendulum, a highly nonlinear unstable system is used as a benchmark for implementing the control methods. In this paper the modeling and control design of nonlinear inverted pendulum-cart dynamic system with disturbance input using PID control & LQR have been presented. The nonlinear system states are fed to LQR which is designed using linear state-space model. Here PID & LQR control methods have been implemented to control the cart position and stabilize the inverted pendulum in vertically uprightposition. The MATLAB-SIMULINK models have been developed for simulation of the control schemes. The simulation results justify the comparative advantages of LQR control methods.