Nonlinear dynamics of spacecraft power systems
This thesis pioneers the application of nonlinear dynamics to spacecraft power systems.
Two areas of general interest are addressed. On the one hand, the fundamental dynamics of
space power systems were investigated from a nonlineax dynamics perspective, and on the
other, nonlinear dynamics concepts were used to realise a practical engineering application.
The former examines four simple but relevant space power system models. The study
revealed a variety of bifurcations, coexisting attractors and chaotic behaviour that could
potentially shed light on some familiar but poorly understood effects in space power systems
operations, including bus voltage collapse, spurious oscillations, and chaotic 'noise'. Because
such behaviour manifests itself in nonlinear systems but could not be exposed by customary
linear systems theory, potential anomalies may remain unpredicted which could lead to
catastrophic consequences. As such, these results have important implications to reliability
issues, critical in space. The exposition of the concepts and tools used in this thesis would
serve the practising engineer by providing the basis and pave the way for studying larger
and more complex systems, in the quest for improved system performance and reliability.
In the course of this work, an algorithm to compute the maximum Lyapunov exponent
from differential equations with discontinuities was required to confirm chaos. Although
the concepts and tools for investigating smooth equations are well established, dynamics
of non-smooth systems have not been extensively studied. Here, the algorithm proposed
by Miiller to cope with the discontinuities in mechanics was reviewed and was found to be
applicable to power electronics in general. As a confirmation, this algorithm was applied
successfully to a well known Buck DC-DC converter.
Although the exploitation of nonlinear dynamics to engineer direct practical applications
is still in its infancy, one is presented in this thesis. A maximum power point tracker
was synthesised via nonlinear dynamics principles, simulated and experimentally verified.
Excellent static and dynamic performance were exhibited. In addition, a two-dimensional
stroboscopic map was derived which adequately described the fundamental dynamics of the
system. This is confirmed from the good agreement between the simulated and experimental
return maps. Via this map and further bifurcation study, preliminary design guidelines were