Ensuring integral controllability for robust multivariable control

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.