(687g) Distributed MPC Design for Nonlinear Two-Time-Scale Process Networks

Chemical processes and plants are characterized by nonlinear behavior and
strong coupling of physico-chemical phenomena
occurring at different time-scales. Tradionally, singular perturbation
theory is used as a framework for modeling, analysis, order reduction and controller
design for nonlinear two-time-scale processes [1]. Rapid advance of wireless communication has inspired augmentation of
traditional point-to-point and wired local control systems with networked control
systems. Model predictive control (MPC) is an appropriate framework to deal with the design
and coordination of networked control systems because of its ability to
account for process/controller interactions in the calculation of the control actions.
MPC is an online optimization-based approach, which takes advantage of a system model to
compute a future manipulated input trajectory by minimizing a typically quadratic cost
function involving penalties on the system state and control action. Typically MPC is studied
within a centralized architecture; however, when the number of manipulated inputs
increases, it may not be computationally efficient to obtain control inputs in a
centralized manner. To reduce the dimensionality of centralized MPC as well as computational
complexity, different manipulated inputs may be obtained through a number of distributed MPCs in a
coordinated manner. Depending on the application and certain specifications, sequential or
iterative distributed schemes are employed to obtain manipulated inputs [2]. Furthermore, accounting for
two-time-scale process network behavior may lead to further simplifications on the distributed
MPC structure.

In this work, we focus on distributed MPC of nonlinear singularly perturbed
systems in standard form where the separation between the fast and slow state variables is explicit; such models arise
naturally in  the context  of chemical process networks. Specifically,
a composite control system comprised of distributed ‘‘fast’’ MPCs
acting to regulate the fast dynamics and distributed ‘‘slow’’ MPCs acting
to regulate the slow dynamics is designed. The composite
distributed MPC system uses multirate sampling of the plant state
measurements, i.e., fast sampling of the fast state variables
is used in the distributed fast MPC and slow-sampling of the slow state
variables is used in the distributed slow MPC as well as in the fast
MPC. Both fast and slow distributed MPCs take advantage of their
corresponding Lyapunov-based controllers in an iterative or sequential manner to characterize
closed-loop system stability region [3]. Using singular perturbation theory, the stability and
optimality of the closed-loop nonlinear singularly perturbed
system are analyzed. The proposed distributed control scheme
does not require communication between the fast and slow layers, and
thus, it can be classified as decentralized in terms of interaction
between two layer while at each layer it implements a distributed control scheme. A chemical
process network  example which exhibits two-time-scale behavior
is used to demonstrate the structure and implementation of
the distributed fast–slow MPC architecture in a practical setting. Extensive
simulations are carried out to assess the performance
and computational efficiency of the fast–slow MPC system.

[1] P. D. Christofides, P. Daoutidis. "Feedback control of two-time-scale nonlinear systems". International Journal of Control, Vol. 63, Pages 965–994, 1996.

[2] J. Liu, X. Chen, D. Munoz de la Pena, P. D. Christofides . "Sequential and iterative architectures for distributed model predictive control of nonlinear process systems". AIChE Journal, Vol. 56, Pages 2137–2149, 2010.

[3] P. D. Christofides, J. Liu, and D. Munoz de la Pena. "Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications". Advances in Induatrial Control Series. Springer-Verlag, London, England, 2011.