Design and control of spatial inverted pendulum with two degrees of freedom

Abstract

The inverted pendulum systems have inherently unstable dynamics. In order to stabilize the inverted pendulum at upright position, an actuation mechanism should generate fast-reactive motions at the pivot point of the system. This paper addressed the design and control of a spatial inverted pendulum with two degrees of freedom (DOF). The first part of the study consists of designing a novel planar two-DOF (PRRRR) actuation mechanism in order to balance the spatial inverted pendulum. The system is underactuated and has inherently extreme nonlinearity and also the restrictions on the actuators. Then, in the second part, a second-order sliding-mode and a linear quadratic Gaussian (LQG) controller have been proposed to control the pendulum within the equilibrium position. Finally the simulation results evaluated in terms of the robustness, time response and stability show that the second-order sliding-mode controller is more robust and has fast response performances in re-stabilizing the spatial inverted pendulum, while LQG controller is better in terms of keeping the system in equilibrium during the long period of time.