Orbital stabilization of nonlinear systems via Mexican sombrero energy shaping and pumping-and-damping injection

Bowen Yi (1, 2) , Romeo Ortega (2) , Dongjun Wu (2) , Weidong Zhang (1, 3)

1 Shanghai Jiao Tong University [Shanghai]
2 L2S - Laboratoire des signaux et systèmes
3 Pengcheng Laboratory = Peng Cheng Laboratory [Shenzhen]

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.

Domains: Engineering Sciences [physics]

Bowen Yi, Romeo Ortega, Dongjun Wu, Weidong Zhang. Orbital stabilization of nonlinear systems via Mexican sombrero energy shaping and pumping-and-damping injection. Automatica, 2020, 112, pp.108661. ⟨10.1016/j.automatica.2019.108661⟩. ⟨hal-03387984⟩