Grey box' identification methods and tools cater for the situation where prior knowledge of the object is not comprehensive enough for satisfactory modelling and, in addition, purely empirical ('black box') methods do not suffice for the purpose of model making. What typically happens in the first case is that simulation models, if at all feasible, will neglect unexplained phenomena such as significant effects of unmeasured input or internal phenomena not obviously related to known input. Empirical models of noisy objects, on the other hand, tend to be 'data descriptions', i.e. they have poor reproducibility if the experiment is repeated with the same or another input. In many cases these deficiencies do not matter, in particular, reproducibility is not required for the purpose of adaptive control, while the dynamics of the slower phenomena are not important if fast feedback control is feasible. However, there are two important cases where they do matter.
- Predictive control. When the delay from control to measured response is long compared with the frequencies of significant disturbances, e.g. the transport delay is long or the controlled variable is sampled sparsely, efficient control will have to be based on a model with good predictive properties over a long range.
2. Supervision.
When important variables cannot be measured on-line but still must be kept within limits, there must be a reliable relation between the supervised and the measured variables.
Both these cases need reproducible models whose design clearly requires prior information, because that is invariant information, in contrast with experimental data. An attempted definition of the terms is as follows.