Robust exact model matching via P-D feedback with application to DC servo motor

The problem of exact model matching for single input single output linear systems with nonlinear uncertain structure, via an independent of the uncertainties P-D state and output feedback, is studied. The necessary and sufficient conditions for the problem to have a solution, are established. The general expressions of the feedback matrices solving the problem are derived. For the special case of static state feedback, the respective results are also derived. For a permanent magnet DC motor with uncertain load inertia and viscosity, an independent of the uncertainties P-D feedback law is applied to yield a closed loop system transfer function which is equal to that of a desired model's.