Modeling

The Raison d'être for Models
The basic idea of feedback is tremendously compelling. Recall the mould level control problem from Chapter 2. Actually, there are only three ways that a controller couldmanipulate the valve: open, close or leave it as it is. Nevertheless, we have seen already that the precise way this is done involves subtle trade-offs between conflicting objectives, such as speedof response and sensitivity to measurement noise.

Model Complexity
In building a model, it is important to bear in mind that all real processes are complex and hence any attempt to build an exactdescription of the plant is usually an impossible goal. Fortunately, feedback is usually very forgiving and hence, in the context of control system design, one can usually get away with rather simplemodels, provided they capture the essential features of the problem.

We introduce several terms:
Nominal model. This is an approximate description of the plant used for control system design.Calibration model. This is a more comprehensive description of the plant. It includes other features not used for control system design but which have a direct bearing on the achieved performance.Model error. This is the difference between the nominal model and the calibration model. Details of this error may be unknown but various bounds may be available for it.
Building Models
A firstpossible approach to building a plant model is to postulate a specific model structure and to use what is known as a black box approach to modeling. In this approach one varies, either by trial and erroror by an algorithm, the model parameters until the dynamic behavior of model and plant match sufficiently well.
An alternative approach for dealing with the modeling problem is to use physical laws(such as conservation of mass, energy and momentum) to construct the model. In this approach one uses the fact that, in any real system, there are basic phenomenological laws which determine the...