Controller for swing-up and balance of single inverted pendulum using SDRE-based solution

The study of underactuated systems, especially control of the Inverted Pendulum has always excited the control community. Various different controller schemes have been proposed and designed to achieve the task of swing-up and balance of the Inverted pendulum. This work studies one of the recently proposed methods for designing nonlinear controllers, State Dependent Riccati Equation (SDRE). This method works exactly the same way as Linear Quadratic Regulator (LQR), but in this case the plant and input matrices (A( x) and B(x) respectively) are state dependent instead of being constant. This flexibility helps us to gain more precise control over the systems.; This thesis analyzes the Inverted Pendulum and designs a SDRE-Based Controller. The performance of the controller is verified by performing an experimental real-time control on the Inverted Pendulum set-up in Automation & Robotics research institute. Since global stability of SDRE is not guaranteed, so this work also tries to determine the region of asymptotic stability and also tries to find a relationship between region of asymptotic stability and Julia sets. The real-time results obtained show the effectiveness of using SDRE in the design of nonlinear controllers.