Control of a rotary inverted pendulum

AbstractThis work deals with the control of a rotary inverted pendulum (see Figure 1). This device is composed of the following: an arm rotating in the horizontal plane where one of its ends is mounted on a motor shaft and where a rod is mounted on its other end. The rod's lower end is mounted on the arm's free end in such a manner that, the rod is moving as an inverted pendulum in a plane that is at all times perpendicular to the rotating arm. The problem dealt with here is to find a control law to the motor's output torque such that the inverted pendulum motion will be stabilized about a vertical axis