Robust distributed control of plantwide processes based on dissipativity

Abstract

This paper presents a novel robust distributed control approach for plantwide processes based on dissipativity. The model of individual process unit (subsystem) is uncertain but within a polytopic region. By adopting the systems behavioral approach, the dissipativity property of process units with model uncertainties can be directly determined from that of the models on the vertices of the polytopic region. The plantwide robust stability and performance conditions are represented in terms of the dissipativity condition of the plantwide system, which is the linear combination of the dissipativity of the individual process units and the controllers subject to process/controller network topology. Then the required dissipativity properties for individual controllers are obtained by solving a set of linear matrix inequalities. Controllers are synthesized individually based on their respective supply rates through J-factorization. The dissipativity properties (both the storage function and supply rate) in quadratic differential forms are used to capture detailed dynamic features of processes, which significantly reduces the conservatism in dissipativity based control analysis and synthesis. This work develops a single dissipativity-based framework to deal with both process model uncertainties and interactions within the process network, leading to a scalable and flexible robust distributed control approach that works with arbitrary process and controller network topologies. A case study is presented to illustrate the proposed method.