Conservativeness and stability properties in the optimal design of dynamical systems under uncertainty

In this paper, we study the interdependence between the design of a (process) system and the design of the corresponding controller. This relationship is the subject of a “conservativeness” tradeoff between achieving robust stability and nominal performance in the face of uncertainty in operating conditions. We propose a novel strategy for specifying and fulfilling individual dynamic performance criteria for the dynamics of the process and the associated control system, while maintaining the (bounded input-bounded output- BIBO) stability of the closed-loop system. To this end, we implement a switched control law at the design stage, along with additional constraints that enforce BIBO stability. By establishing a link between the switching conditions and the bandwidth of the closed-loop system, we are able to meet a pre-specified level of process conservativeness (e.g., in terms of size or cost) in process design. Second, we extend our previous results concerning identification-based optimization (IBO) to formulate an efficient algorithm for carrying out the optimization calculations under uncertainty without the need to generate computationally costly scenario sets. We illustrate these ideas with a case study concerning the design of an energy-integrated process.