Modeling and control of nonlinear networks : A power-based perspective

Increasing demands on efficient power management and conversion, together with demands on reduced harmonic generation, higher bandwidths, and reliability, make it necessary to design devices (e.g., controllers, compensators, filters etc.) that ensure a system to meet certain directives. Such devices are most often developed and studied using linear signal-based approaches. However, since virtually all modern systems are highly complex and inherently nonlinear, linear analysis and design techniques might become insufficient as to ensure certain predefined behaviors, robustness and reliability under all operating conditions, especially if the (controlled or compensated) system is subject to large set-point changes, disturbances, or errors that cause the system to deviate from its nominal point of operation. For that reason, the development of dedicated tools that take the systems nonlinearities into account is of utmost importance. This thesis is concerned with the development of new modeling, analysis and control methods for nonlinear electrical networks. A unified power-based framework that provides a systematic dynamical description of a broad class of networks, including switched-mode power converters, is presented. A major advantage of the method is that the underlying physical structure, like the interconnection of the individual elements, nonlinear phenomena and the power flow, are explicitly incorporated in the model. Taking the network power-flow as a starting point, the concept of passivity is considered from a fairly different point of view with respect to the existing energy-based approaches. The resulting passivity properties are of interest in network theory, but also have applications in control as they suggest a so-called Power-Shaping stabilization method which forms an alternative to the existing method of Energy-Shaping. In addition, useful relations with reactive power are established and lead to the notion of reactive Hamiltonians. In the context of the recently proposed Passivity-Based Control (PBC) strategy for switched-mode power converters, the power-based framework reveals and justifies a revised damping injection scenario that significantly improves the robustness of the closed-loop. Some preliminary steps are taken to extend the power basedmodeling and control approach to mechanical and electro-mechanical systems. The developments throughout the thesis heavily rely on the ideas of R.K. Brayton and J.K. Moser stemming from in the early sixties. Where applicable, the newly obtained results are compared with well-known existing energy-based methods, like the Lagrangian and Hamiltonian approach, and several structural relationships between the methods are established.