The concept of Model Distortion

A mathematical model of suitably high order can be made to follow any set of recorded transients exactly by varying appropriately the nominally constant parameters as functions of time - distorting the model . Clearly, the better the model the less will be the required distortion. More particularly, if the required distortion comes within acceptable limits (in view of approximations made in the model), then the model may be deemed capable of explaining the recorded transients. This notion accommodates instrument error and signal noise in a pessimistic way, since both make reconciliation between the model and the record more difficult. 

The concept of time-dependent model distortion becomes clearer through considering a typical modelling approximation. For example, steam flow, W, through a valve might be modelled as proportional to the upstream pressure, p, and valve opening, y  

Another way of expressing the idea of model distortion is to regard the recorded plant transients as continuous, indirect measurements of the model s constant parameters. If these new, inferential measurements of the model parameters fall outside the ranges set by previous, more direct measurements then there is an inconsistency. We should reject the model in its current state and seek to improve it. By this formulation, it becomes clear that the model distortion approach consists of mapping the complex dynamic behaviour of recorded plant variables onto the simple 

To translate these ideas into mathematics, let us suppose that we have produced a model of the plant defined by 

We shall call this the nominal model . Comparing equation (24.3) with the standard simulation equation (2.22), it will be seen that the dependence of the vector function, f, on its constant parameters, a, has been made explicit in equation (24.3). 

---

Before considering methods of finding a, let us review how the concept of model distortion has allowed us to move from comparison between model and plant to a comparison between two models, in one of which we allow the nominally constant parameters to be varied. Suppo.se we drive the system to follow the recorded transients exactly. Using the superscript 0 to label the vectors associated with exact matching, the parameter variations will be given by (/), the states by X"(/) and the outputs by Y (f). Exact matching implies ... 

---