One of the main difficulties in control systems design is
undoubtedly the presence of delays, and more if the system to be
controlled is unstable in open loop and/or non minimum phase.

Temporal delays may be intrinsic to the process to be controlled,
such as in chemical and biological processes, distillation
columns, processes with thermal exchanges, and so on.  Delays can
also be introduced in the controller design itself (computation
time of the control algorithm, distributed systems, remote
control, communication networks, sensors and/or actuators induced
delays, etc.).

In general, the control system performance is very sensitive to
all these delays, even more than to other parameters in the model.
In fact, a closed-loop control system may become unstable as a
consequence of delays. The main limitation of systems with delays
in the control loop is due to the induced phase change, which
leads to instability with smaller gains than in the absence of
delay. This implies a limitation in the control action magnitude.
Systems with delay are infinite-dimensional, and thus their
transfer function has an infinite number of poles. It is thus very
difficult for a conventional regulator adjust these poles.

The Smith Predictor, as well as their multiple
extensions, and the technique of Finite Spectrum Assignment
, may be considered as the control strategies
more widespread for the control of linear systems with a delay in
the actuation and/or measurement.

Smith Predictor and Finite Spectrum Assignment, have in common
that they are based on a delay compensation by means of an output
or state prediction from a model of the process in consideration.
If the process to be controlled is unstable, the resulting
controls schemes do not fulfill the internal stability condition
and thus they will become unstable.

To be able to apply these techniques to the control of unstable
systems with delay, several modification of the original Smith
Predictor scheme have been proposed, generically denoted as Dead
Time Compensators (DTC). There also have been different approaches
to find a numerically stable implementation of the Finite Spectrum
Assignment technique. However, all these modifications consist on
partial solutions to the problem posed in both cases.


In this thesis, a generic solution for both problems has been
proposed. More concretely, the following items have been
developed:
A new methodology has been developed for the DTCs design for
the control of stable and/or unstable systems, either minimum or
non minimum phase, with delays. Contrary to other proposals, this
methodology allows the controller design without taking into
consideration the delay in the tuning of the characteristic
equation for reference tracking as well as in disturbance
rejection. With it, a substantial improvement is achieved with
respect to previous approaches.
The development of a robust prediction scheme for the implementation of the Finite Spectrum Assignment
 technique, avoiding the problem of numerical instability
 originated by the approximation of the prediction integral.
The experimental validation of all the developed algorithms with a 4 rotor mini-helicopter in free flight (with the development of an embedded system), and a lab prototype
 of a 4 rotor helicopter. To remark
 that, up to date, no real implementation of a prediction scheme or
 DTC for unstable systems has been found in the literature.