Minimum-time swing-up of a rotary inverted pendulum by iterative impulsive control

The minimum time swing up of a rotary inverted pendulum is considered. For our rotary inverted pendulum, a DC motor rotates a stiff arm at one end in the horizontal plane. The opposite end of the arm is instrumented with a joint whose axis is along the radial direction of the motor. A pendulum is suspended at the joint. The task is to design a controller that swings up the pendulum and maintains it upright and maintains the arm position. From practical tuning point of view, a PID controller plus an impulse controller is proposed for the swing up control. An iterative tuning of the impulsive control actions is applied to achieve the minimum-time swing-up. To make the overall control strategy more robust, a new mode switching control method is also proposed. Compared to the existing dual mode nonlinear controller provided by the manufacturer, the swing up time is significantly reduced as demonstrated by extensive experimental results.