State Observer for a Torsion Plant. Assume that the only measurable output for the system in Problem P10-4 is the angular velocity of the upper rotational inertia. Design a state observer that is at least an order of magnitude faster than the ideal closed-loop system.

Problem P10-4:

Controllability and Observability of a Torsion Plant. Determine the state controllability, output controllability, and observability of the rotational system depicted in Figure 7.17. Recall that the system parameters were provided in Table 7.1. The input is the torque and the outputs are the angular displacements of the two rotational inertias.