Design and Implementation of a State-feedback Controller Using LQR Technique

The main objective of this research is to design a state-feedback controller for the rotary inverted pendulum module utilizing the linear quadratic regulator (LQR) technique. The controller maintains the pendulum in the inverted (upright) position and is robust enough to reject external disturbance to maintain its stability. The research work involves three major contributions: mathematical modeling, simulation, and real-time implementation. To design a controller, mathematical modeling has been done by employing the Newton-Euler, Lagrange method. The resulting model was nonlinear so linearization was required, which has been done around a working point. For the estimation of the controller parameters, MATLAB LQR function has been utilized. Simulation has been performed for the designed controller and it also has been implemented and tested over the real inverted pendulum. From the results, it is vivid that the designed controller keeps the inverted pendulum in an upright position and rejects the disturbances and falling under gravitational force by adjusting the rotation of the horizontal link.