Sensitivity of controller performance indices to model-plant mismatch: An application to paper machine control

The performance of a model-based controller depends inextricably on the quality of the corresponding model. The performance of such a controller is optimal with respect to the model. Therefore any model-plant mismatch can be expected to result in poor performance. The objective of this work is to study the sensitivity of commonly used performance indices to model-plant mismatch. A sensitivity measure is defined and a frequency domain expression for quantifying the sensitivity is derived. It is shown that the sensitivity of the performance indices varies for different types of model mismatch, e.g., gain mismatch, etc. Furthermore, model mismatch has different effects on the performance of the system when it is operating in steady state or in a transitional mode. These differences can reveal the type of plant-model mismatch. The results are illustrated on industrial paper machine data.