Ensuring integral controllability for robust multivariable control. (2nd September 2016) - Panjwani, Shyam; Nikolaou, Michael
Highlights: Integral controllability (IC) has long been known to be desirable for a model to be used in robust multivariable controller design. A mathematical framework, previously developed by the authors, facilitates design of experiments (DOE) for identification of IC-compliant multivariable models. Numerical studies in this paper demonstrate that possible conservatism in that DOE framework is low, but increasing with system size. It is also shown that avoiding IC-compliant DOE through possible replacement of a standard least-squares model by another that might satisfy IC, is generally infeasible. Therefore, research efforts to tame the complexity of DOE for IC-compliant models are well warranted. Abstract: Integral controllability (IC) is a desired property of multivariable models used in robust controller design. IC requires satisfaction of eigenvalue-based inequalities involving the real process and identified model. Design of experiments for identification of models that satisfy these inequalities is cumbersome. To address this issue, Darby and Nikolaou (2009) developed a general mathematical framework, that relies on a much simpler inequality as its starting point. However that inequality is only sufficient, which could potentially be conservative. This paper examines this concern through a numerical simulation study and analysis on a number of systems. The results suggest that conservatism is fairly low but increasing as the identified system size increases. In addition, a rigorous argument is used to establish that it is generally impossible to build an IC-compliant model once a least-squares model is not, thus emphasizing the importance of design of experiments for IC-compliant model identification.