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Analysis and design of nonlinear control systems for switching networks

Project members: D. Jeltsema, J.M.A. Scherpen, J.B. Klaassens

Switching electrical networks are nowadays essential for high-performance energy control for a large variety of applications. This varies from simple DC-DC, AC-DC, DC-AC and AC-AC converter structures for use in commercial electrical apparatus, to high tech structures for use in, e.g., space and non-civilian applications. The basic ideal configuration of a power converter is generally based on the combination of controllable (semiconductor) switches and (filter) components in the form of passive components like inductors, capacitors and transformers.

In the last thirty years this area has undergone a wealth of practical and theoretical developments, mainly done in the field of power electronics. These developments and studies where mainly concerned with small signal analysis (linearizing) based on averaging techniques like pulse-width modulation (PWM), and related, linear PID control techniques, static behavior, ripple analysis, etc. The aim of this project is to consider the general structure of switching electrical networks. We approach these systems from a physical modeling point of view, i.e., we use physical system theoretic descriptions (large signal) based on the interconnection and energy properties of the system. For that, a general energy-based modeling procedure for (single and multiple) switched-mode electrical networks has been developed. The method is a synergy of the well-known Hamiltonian and Lagrangian formalism together with the Brayton-Moser equations. This technique is useful for, e.g., passivity-based control purposes and large signal stability analysis. As case studies, fundamental single switch DC-to-DC converters and multi-switch AC-to-DC rectifiers were used (see Figure 11). Further research includes the involvement of several classes of non-ideal physical elements into the framework.

Figure 11: Passivity-based controlled AC-to-DC Buck type converter.
\includegraphics[width=0.75\linewidth]{pics/bucky}

The general modeling framework will be used for analysis purposes, and for giving specific choices for the best physical variables for controller design. These choices are important to obtain a better overall performance (in terms of overshoot, disturbance rejection, etc.) of the closed loop system. The topology of the switching network is decisive for the (in-)stability of the zero-dynamics, i.e., for being a (non-)minimum phase system. Study of the zero-dynamics is mainly of importance for the controller design. Furthermore, we study possible improvements by developing (nonlinear) control schemes that are based on the physics and that are generally applicable to this type of systems. If possible, by the new set-up from a system and control point of view, new switching network topologies will be developed, resulting in converter structures that are fulfilling specific demands of high tech applications like in, e.g., space and non-civilian applications.


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