Tuning rules for passivity-preserving controllers

Abstract

Nonlinear Passivity-based control (PBC) algorithms for power converters have proven to be an interesting alternative for other, mostly linear, control techniques. The control objective is usually achieved through an energy reshaping process and by injecting damping to modify the dissipation structure of the system. However, a key question that arises during the implementation of the controller is how to tune the various parameters. From previous work we know that a PBC controller forces the closed-loop dynamics to behave as if there are artificial resistors connected to the real circuit elements. This has led to conservative tuning rules stemming from characteristic impedance matching conditions. In this paper an alternative solution is provided that uses the classical Brayton-Moser equations. The criteria derived from these equations result in fairly sharp and less conservative tuning rules to guarantee stability and non-oscillatory responses.Both criteria are compared and tested using the elementary single-switch boost converter.

A dual relation between port-Hamiltonian systems and the Brayton–Moser equations for nonlinear switched RLC circuits

“…This directly suggests application of similar controller design techniques as developed for PCH and Lagrangian systems with some additional advantages. For example, in contrast to the Lagrangian or Hamiltonian framework, a passivity-based feedback controller (see Jeltsema and Scherpen (2002) and Ortega, Jeltsema, and Scherpen (2002) for some ÿrst results regarding control in the BM framework) based on the BM equations requires state measurements in terms of currents and voltages directly. This is a major advantage since they correspond to the commonly used and available sensors because no complicated and performance degrading (due to unknown parameters) state transformations have to be made.…”

On mechanical mixed potential, content and co-content

“…An advantage of using the mixed potential function is that we can apply Brayton and Moser's stability criteria to investigate the stability of the equilibrium points of a mechanical system or use it to find tuning rules for feedback controllers, like the passivity-based control algorithms [5]. Also, in the proposed framework we are able to apply the recently developed novel nonlinear control technique, called Power Shaping, as proposed in [7], to the class of mechanical systems considered here.…”