Quasi-Polynomial Control of a Synchronous Generator

A simple dynamic model of permanent magnet synchronous generator, that is used for electrical energy generation is investigated in this work using a nonlinear technique based on the quasi-polynomial representation of the dynamical model. It is well known that dynamical systems with smooth nonlinearities can be embedded in a quasi-polynomial model. Quasipolynomial systems are good candidates for a general nonlinear system representation since their global stability analysis is equivalent to the feasibility of a LMI. Moreover, the stabilizing quasi-polynomial state feedback controller design problem is equivalent to the feasibility of a bilinear matrix inequality. The classical stabilizing state feedback problem for quasipolynomial systems has been extended in this work with the ability of tracking time-dependent reference signals. It is shown, that the stabilizing quasi-polynomial servo controller design is equivalent to a bilinear matrix inequality. The results are applied to the model of a synchronous generator.