The motion of fluids, such as air or water, is central to many engineering systems of significant
economic and environmental importance. Examples range from air/fuel mixing in combustion engines
to turbulence induced noise and fatigue on aircraft. Recent advances in novel sensor/actuator
technologies have raised the intriguing prospect of actively sensing and manipulating the motion
of the fluid within these systems, making them ripe for feedback control, provided a suitable control
model exists. Unfortunately, the models for many of these systems are described by nonlinear,
partial differential-algebraic equations for which few, if any, controller synthesis techniques exist.
In stark contrast, the majority of established control theory assumes plant models of finite (and
typically small) state dimension, expressed as a linear system of ordinary differential equations.
Therefore, this thesis explores the problem of how to apply the mainstream tools of control theory
to the class of systems described by partial differential-algebraic equations, that are either linear,
or for which a linear approximation is valid.
The problems of control system design for infinite-dimensional and algebraically constrained
systems are treated separately in this thesis. With respect to the former, a new method is presented
that enables the computation of a bound on the n-gap between a discretisation of a spatially distributed
plant, and the plant itself, by exploiting the convergence rate of the v-gap metric between
low-order models of successively finer spatial resolution. This bound informs the design, on loworder
models, of H[infinity] loop-shaping controllers that are guaranteed to robustly stabilise the actual
plant. An example is presented on a one-dimensional heat equation.
Controller/estimator synthesis is then discussed for finite-dimensional systems containing algebraic,
as well as differential equations. In the case of fluid flows, algebraic constraints typically
arise from incompressibility and the application of boundary conditions. A numerical algorithm is
presented, suitable for the semi-discrete linearised Navier-Stokes equations, that decouples the differential
and algebraic parts of the system, enabling application of standard control theory without
the need for velocity-vorticity type methods. This algorithm is demonstrated firstly on a simple
electrical circuit, and secondly on the highly non-trivial problem of flow-field estimation in the
transient growth region of a flat-plate boundary layer, using only wall shear measurements.
These separate strands are woven together in the penultimate chapter, where a transient energy
controller is designed for a channel-flow system, using wall mounted sensors and actuators.