This segment also shows how the controller behaves when the disturbance is small, but in the course of correction, the cart approaches the limits. In conclusion, it can be clearly seen that the controller can start the pumpup procedure from any initial conditions and is robust to any disturbance. The double link pendulum mechanizaton is a straightforward design. The links are modeled as rigid bodies, Thus the composite mechanical system has 3 degrees of freedom. The video demonstrates four controllers that work for all possible pendulum link configurations.
Integral state is added for better steady state performance.
H-infinity design was also carried out in Sepp's MSEE thesis, but it did not give any better result, visually at least. This is to be expected since a more robust design can easily result in poorer performance. Additional robustness tests could show the real benefit of robust design. However, for an unstable system, these results are very hard to present. Limit cycles due to the nonlinear friction make it yet more difficult.