Robust LQR Optimal Control Of The Inverted Pendulum

Inverted pendulum is commonly used as an experimental device in dynamics and control theory. It is a typical nonlinear, multivariable, high order and instable system that can effectively verify the feasibility of some control methods. Therefore, it serves as a benchmark for other systems, for example, aerospace applications that exhibit the similar dynamic behavior.In this thesis, both single and double inverted pendulum are studies with three different controllers, namely standard LQR, robust LQR and H∞robust LQR, in order to compare the robustness and robust stability of the controlled pendulum systems under different uncertainties. Simulation results show that, in the presence of uncertain quality of cart or rod, robust LQR control method has better performance than the standard LQR control method in terms of robustness and robust stability. While, H∞robust LQR control method has better capacity of resisting disturbance than robust LQR control method if there exists external disturbance on the rod or cart.The main contributions of the thesis can be described as follows. Based on H∞robust LQR control method, a minimum energy H∞robust LQR control method (MEHR) is proposed not only to ensure system robustness and stability, but also to make the control parameters of K controller much smaller, which is very important for real engineering applications. Simulation results show that the tradeoff between robustness and control energy can be achieved by the MEHR controller.