A new family of interconnection and damping assignment passivity-based controllers

Meng Zhang (1) , Roméo Ortega (2) , Zhitao Liu (1) , Hongye Su (1)

1 Institute of Cyber-Systems and Control
2 L2S - Laboratoire des signaux et systèmes

The by-now standard formulation of interconnection and damping assignment passivity-based control (for input-affine systems) proposes the solution of a partial differential equation (PDE) that defines the assignable energy functions and computes the control using the input matrix pseudo-inverse. However, in its original formulation—a more general design procedure was proposed, which was essentially abandoned because of the difficulties in solving the PDE. In this note, a new family of interconnection and damping assignment passivity-based controls is proposed by extending this method in the following directions: (i) It allows the desired interconnection and damping matrices to depend on the control signal, giving the possibility to shape the PDE to ensure its solvability; (ii) the PDE directly generates the control signal that have, in general, simpler expressions; and (iii) it is applicable for general nonlinear systems possibly not affine in the control. The technique is illustrated with three examples, including the well-known boost power converter for which it yields a simple, high-performance controller.

Domaines: Automatique; Automatique / Robotique

Meng Zhang, Roméo Ortega, Zhitao Liu, Hongye Su. A new family of interconnection and damping assignment passivity-based controllers. International Journal of Robust and Nonlinear Control, 2016, 27 (1), pp.50-65. ⟨10.1002/rnc.3557⟩. ⟨hal-01815732⟩