Orbital stabilization of nonlinear systems via Mexican sombrero energy shaping and pumping-and-damping injection
For control engineers, it provides a new method for orbital stabilization, though the example only replicates existing results.
The paper modifies the interconnection and damping assignment passivity-based control method to solve orbital stabilization of nonlinear systems, achieving industry-standard field-oriented control for induction motors.
In this paper we show that a slight modification to the widely popular interconnection and damping assignment passivity-based control method---originally proposed for stabilization of equilibria of nonlinear systems---allows us to provide a solution to the more challenging orbital stabilization problem. Two different, though related, ways how this procedure can be applied are proposed. First, the assignment of an energy function that has a minimum in a closed curve, i.e., with the shape of a Mexican sombrero. Second, the use of a damping matrix that changes "sign" according to the position of the state trajectory relative to the desired orbit, that is, pumping or dissipating energy. The proposed methodologies are illustrated with the example of the induction motor and prove that it yields the industry standard field oriented control.