Nonlinear model matching: a local solution and two worked examples

The model matching problem consists of designing a compensator for a given system, called the plant, in such a way that the resulting input-output behavior matches that of a prespecified model. In a recent paper it was shown that in case the model is decouplable by static state feedback and generic conditions on the plant are satisfied, the model matching problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model around the equilibrium point. In this paper this local solution will be presented and we will investigate the question to what extent we can use the feedback that solves the corresponding linear model matching problem in order to approximately solve the original nonlinear problem. This will be done by means of two examples: the double pendulum and a two-link robot arm with a flexible joint.