FO based-LQR stabilization of the rotary inverted pendulum

This work implements a feedback control system for stabilizing the RIP (Rotary Inverted Pendulum) using a FO (Fractional Order) based-LQR (Linear Quadratic Regulator) controller. That is, every derivative term of a classical LQR control law containing the Laplace variable s will be transformed into its FO derivative form sm, where m isa fractional number between 0 and 1. Experimental results obtained with LQR and FO LQR-based controllers demonstrated that all designed control systems were able to stabilize the pendulum with and without the action of disturbances and in the presence of a larger pendulum Link mass. However, the application of a FO LQR-based controller improves the robustness of the control system. Such control systems use direct measurement of pendulum and motor shaft positions. For LQR controllers, speeds were obtained by differentiation of the corresponding positions and passed through first order filters to reject high frequency noise. It was not required to use any additional filter for the FO LQR-based controller.