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

Abstract

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.

Stochastic Back-Off Approach for Integration of Design and Control Under Uncertainty

“…Pseudorandom multilevel signals were employed in that work to capture uncertainty in dynamical systems. In a follow-up work, that identification method was employed to develop a formulation that addresses the optimal design of dynamic systems under uncertainty by establishing a link between a switching control law and the bandwidth of the closed-loop system, which allows the specification of a user-defined level of process conservativeness in the design . Koller et al develop a new framework to address the optimal design, control and scheduling of multiproduct systems under uncertainty.…”

“…In a follow-up work, that identification method was employed to develop a formulation that addresses the optimal design of dynamic systems under uncertainty by establishing a link between a switching control law and the bandwidth of the closed-loop system, which allows the specification of a user-defined level of process conservativeness in the design. 45 Koller et al 46 develop a new framework to address the optimal design, control and scheduling of multiproduct systems under uncertainty. In that work, backoff terms were estimated to compensate for the effect of input-output controllability indexes included as objectives or constraints within the optimization formulation Nguyen et al 3 Luyben and Floudas 4 Alhammadi and Romagnoli 5 Papadopoulos et al 6 simultaneous assessment of controllability with respect to the solvent and process economic and controllability properties Mansouri et al 7,8 a decomposition-based solution approach to integrated design and control through a systematic hierarchical approach for reactive distillation processes dynamic optimization approach Kookos and Perkins 9,10 a sequence of combined configurations of design and control solved using a bounding scheme to successively reduce the size of the search region Mohideen et al 11 a dynamic optimization framework to estimate the disturbance profiles that produce the worst-case scenario Diangelakis and Pistikopoulos 12,13 a single prototype software system (PAROC framework) which allows for the representation, modeling, and solution of integrated design, scheduling and control problems via multiparametric programming Nie et al 14 discrete time formulation optimization approach for the integration of production scheduling and dynamic process operation using generalized benders decomposition (GBD) algorithm to solve the resulting large nonconvex mixed-integer nonlinear program robust approach Ricardez-Sandoval et al 15−17 identification of worst-case scenarios using structured singular value analysis Koller and Ricardez-Sandoval 18 a direct integration of design, control, and scheduling under disturbance and uncertainty while explicitly accounting for scheduling decisions in the analysis by the use of variablesized finite elements in the model discretization Sanchez-Sanchez and Ricardez-Sandoval 19 a model-based control strategy, i.e., model predictive control (MPC), in which the feasibility and stability analyses are formulated as convex problems using robust control tools Gutieŕrez-Limoń et al 20 a reactive heuristic strategy to cope with the simultaneous optimization of short-term planning, scheduling, and control problems under uncertainty back-off approach Bahri et al 21,22 a joint optimization-flexibility aimed to search for the optimality of the system considering flexibility feasibility of the design in a back-off approach Figueroa et al 23 Mehta and Ricardez-Sandoval 24 PSE-based back...…”