Process control, PID and adaptive control - Intelligent Buildings and Building Automation - page 137

The design problem is called the underlying design problem for systems with
known parameters. The block labelled ' Controller ' is an implementation of
the controller whose parameters are obtained from the control design.
The main reason for using an adaptive controller is that the process or its
environment is changing continuously. It is difficult to analyze such systems.
To simplify the problem, it can be assumed that the process has constant but
unknown parameters. The term self-tuning was used to express the property
that the controller parameters converge to the controller that was designed
if the process was known. An interesting result was that this could happen
even if the model structure was incorrect.
The tasks shown in the block diagram can be performed in many different
ways. There are many possible choices of model and controller structures.
Estimation can be performed continuously or in batches. In digital imple-
mentations, which are most common, different sampling rates can be used
for the controller and the estimator. It is also possible to use hybrid schemes
in which control is performed continuously and the parameters are updated
discretely. Parameter estimation can be done in many ways. There is also a
large variety of techniques that can be used for control system design. It is
also possible to consider nonlinear models and nonlinear design techniques.
Although many estimation methods will provide estimates of parameter
uncertainties, these are typically not used in the control design. The estimated
parameters are treated as if they are true in designing the controller. This is
called the certainty equivalence principle.
The choice of model structure and its parameterization are important
issues for self-tuning controllers. A straightforward approach is to estimate
the parameters of the transfer function of the process. This gives an indirect
adaptive algorithm. The controller parameters are not updated directly, but
rather indirectly via the estimation of the process model.
References
Åström, K. J. and Hägglund, T. (1995) PID controllers: theory, design and tuning ,
Instrument Society of America: Research Triangle Park, North Carolina.
Åström, K. J. and Wittenmark, B. (1995) Adaptive Control , Reading, Massachusetts:
Addison-Wesley Publishing Company.
Letherman, K. M. (1981) Automatic Controls for Heating and Air-conditioning:
principles and applications , Oxford: Pergamon Press.