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
highperformance energy control for a large variety of applications.
This varies from simple DCDC, ACDC, DCAC and ACAC converter structures
for use in commercial electrical apparatus, to high tech structures for use
in, e.g., space and noncivilian 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 pulsewidth 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 energybased modeling procedure for (single and multiple)
switchedmode electrical networks has been developed. The method is a synergy
of the wellknown Hamiltonian and Lagrangian formalism together with the
BraytonMoser equations. This technique is useful for, e.g.,
passivitybased control purposes and large signal stability analysis. As
case studies, fundamental single switch DCtoDC converters and multiswitch
ACtoDC rectifiers were used (see Figure 11).
Further research includes the involvement of several classes of nonideal
physical elements into the framework.
Figure 11:
Passivitybased controlled ACtoDC Buck type converter.

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 zerodynamics, i.e., for being a
(non)minimum phase system. Study of the zerodynamics 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 setup 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 noncivilian applications.
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