Structure in practical model error bounds

In many processes, control is applied to change the dynamic behaviour of the process such that the process performs better in some sense. Modern techniques for control design are, in general, based on a model of the process. If the model uncertainty, i:e. the difference between the model and the true process, can be bounded and the control design can take this bounded uncertainty into account, the resulting control is said to be robust. This thesis is concerned with the problem of finding bounds on the model uncertainty from experimental data and prior knowledge for application in robust control design. Practical application of model uncertainty bounds obtained by current techniques for uncertainty bounding is hampered by the fact that these bounds often turn out to be unrealistically large. It is analysed which effects (should) contribute to a model uncertainty bound. These effects can be divided into three categories: (a) models used for robust control are takeri to be linear, time-invariant and of low order, while the underlying process is not; (b) experimental data of a process gives only an incomplete and uncertain account of the process behaviour due to finite data length, finite sampling frequency and unknown external factors as noise and disturbances; ( c) some knowledge that is available of the process can be expressed only approximately or not at all in the model and/or the uncertainty bounds. This leads to conservatism. The practical motivation for application of robust control is mainly to cope with the infiuence of category (a). Current model uncertainty bounds take typically the infiuence of categories (b) and (c) into account. To study the interplay between different factors involved in a model uncertainty bounding procedure, a general frarnework has been developed in this thesis. Contrary to other frameworks in which identification procedures are "embedded," this framework takes great care not to put unrealistic restrictions on the process and/or its noise. Some of the properties that all uncertainty bounding algorithms (should) have in common are investigated. Furthermore the relation that should exist between noise, disturbances and simplifications such as tîme-invariance and linearity on the one hand and model uncertainty bounds on the other is clarified. Based on the observations made above, an algorithm is proposed that splits model uncertainty for MIMO systems in so-called structured and unstructured parts. The structured part is bounded in a detailed way and is intended to capture the changes in process dynamics that occur if the process is operated in several operating points. In the unstructured part, all other sources of model uncertainty are lumped together and are bounded in a much less detailed way. If the structured part describes the dominating factors in the uncertainty of