Multivariable system identification for integral controllability

Integral controllability is necessary and sufficient for a multivariable model to be usable in a decoupling controller with integral action that can be arbitrarily detuned without jeopardizing closed-loop robust stability. The design of experiments for identification of integral controllable models is challenging, because it must satisfy cumbersome eigenvalue inequalities involving a coupling between the real system and its model. To address this challenge, an optimization-based mathematical framework is developed that characterizes efficient identification experiments ensuring integral controllability. The proposed framework recovers well known experiment designs but also produces new ones of both theoretical and practical interest. Such designs are expressed either analytically or as a result of numerical optimization and are demonstrated in a number of examples. These designs can be easily implemented in industrial practice. By combining additional objectives or constraints of interest, the proposed framework can further serve as a basis for new experiment designs in future work.