Uncertain Double Pendulum with a Hard Spring and an All-Pass: Stabilization and Disturbance Rejection

For the nominal plant, it is possible to design a H2 controller with good performance properties. When the rigid motor shaft is replaced by the elastic motor shaft with the hard spring, the performance of the H2 controller severely degrades: The closed-loop system gets oscillatory behavior. If also an all-pass will be added, the closed-loop system becomes unstable. A carefully designed Hinf controller is much better suited to stabilize the double pendulum with the hard spring but the closed-loop system gets an oscillatory behavior if the all-pass is added. This can be observed in the first part of the film. The robustfied version of this controller with the D-K iteration yields a mue controller. This controller has perfect disturbance rejection properties even in the presence of the hard spring and the all-pass. This will be demonstrated in the second part of the video clip.