Rejection of a Strong Oscillatory Disturbance

The double pendulum dynamics and the dynamics of the spring-mass system are coupled. The spring-mass system causes a pole pair with a very small positive damping. With a H2 controller, this pole pair is shifted into the right half-plane and the closed-loop system becomes unstable: The oscillations of the mass become larger and larger and the pendulum falls down. With a carefully designed Hinf controller, the pole pair belonging to the spring-mass system remains in the left half-plane and the oscillation slowly come to rest. It should be noted that the torque caused by the oscillations is very large so that excellent disturbance rejection properties of the controller are required.