Distributed model predictive control of nonlinear systems subject to asynchronous and delayed measurements☆
Introduction
Process control systems traditionally utilize dedicated, point-to-point wired communication links to measurement sensors and control actuators to regulate process variables at desired values. While this paradigm to process control has been successful, we are currently witnessing an augmentation of the existing, dedicated local control networks, with additional networked (wired and/or wireless) actuator/sensor devices which have become cheap and easy-to-install the last few years. Such an augmentation in sensor information and networked-based availability of data has the potential (Christofides et al., 2007, Neumann, 2007, Ydstie, 2002) to significantly improve: (i) the achievable closed-loop system performance, and (ii) the ability of the plant management systems to prevent or deal with abnormal situations more quickly and effectively. However, augmenting local control networks with additional networked sensors and actuators poses a number of new challenges including the feedback of additional measurements that may be asynchronous and/or delayed. Furthermore, augmenting dedicated, local control networks with additional networked sensors and actuators gives rise to the need to design/redesign and coordinate separate control systems that operate on the process.
Model predictive control (MPC) is a natural control framework to deal with the design of coordinated, distributed control systems because it can account for the actions of other actuators in computing the control action of a given set of actuators in real-time. Motivated by the lack of available methods for the design of networked control systems (NCS) for chemical processes, in a previous work (Liu, Muñoz de la Peña, Ohran, Christofides & Davis, 2008), we introduced a decentralized control architecture for nonlinear systems with continuous and asynchronous measurements. In this architecture, the pre-existing local control system (LCS) uses continuous sensing and actuation and an explicit control law. On the other hand, the NCS uses networked sensors and actuators and has access to additional measurements that are not available to the LCS. The NCS is designed via Lyapunov-based model predictive control (LMPC). Following up on this work, in another recent work (Liu, Muñoz de la Peña & Christofides, 2009), we proposed a distributed model predictive control (MPC) method for the design of networked control systems where both the pre-existing LCS and the NCS are designed via LMPC. This distributed MPC design utilizes continuous feedback, requires one-directional communication between the two distributed controllers, and may reduce the computational burden in the evaluation of the optimal manipulated inputs compared with a fully centralized LMPC. The results obtained in Liu et al. (2009) are based on the assumption that continuous state feedback is available. In the present work, we consider the design of distributed MPC schemes in a more common setting for chemical processes. That is, measurements of the state are not available continuously but asynchronously and with delays. With respect to other available results on distributed MPC design, several distributed MPC methods have been proposed in the literature that deal with the coordination of separate MPC controllers (Camponogara et al., 2002, Dunbar, 2007, Keviczky et al., 2006, Magni and Scattolini, 2006, Raimondo et al., 2007, Rawlings and Stewart, 2007, Richards and How, 2007). All of the above results are based on the assumption of continuous sampling and perfect communication between the sensor and the controller. Previous work on MPC design for systems subject to asynchronous or delayed measurements has primarily focused on centralized MPC design (Liu et al., 2009, Muñoz de la Peña and Christofides, 2008) and has not addressed distributed MPC with the exception of a recent paper (Franco, Magni, Parisini, Polycarpou, & Raimondo, 2008) which addresses the issue of delays in the communication between the distributed controllers.
This work focuses on the distributed MPC of nonlinear systems subject to asynchronous and delayed measurements. In the case of asynchronous feedback, under the assumption that there exists an upper bound on the interval between two successive state measurements, distributed LMPC controllers are designed that utilize one-directional communication and coordinate their actions to ensure that the state of the closed-loop system is ultimately bounded in a region that contains the origin. Subsequently, we focus on distributed MPC of nonlinear systems subject to asynchronous measurements that also involve time-delays. Under the assumption that there exists an upper bound on the maximum measurement delay, a distributed LMPC design is proposed that utilizes bi-directional communication between the distributed controllers and takes the measurement delays explicitly into account to enforce practical stability in the closed-loop system. The proposed distributed MPC designs also possess explicitly characterized sets of initial conditions starting from where they are guaranteed to be feasible and stabilizing. The theoretical results are demonstrated through a chemical process example.
Section snippets
Control problem formulation
We consider nonlinear systems described by the following state-space model where is the state, is the set of inputs of controller 1 (which can be thought of as corresponding to an LCS) and is the set of inputs of controller 2 (which can be thought of as corresponding to an NCS). The inputs and are restricted to be in two nonempty convex sets and containing the origin, respectively. The disturbance is
Distributed LMPC with asynchronous measurements
In this section, we design distributed LMPC for systems subject to asynchronous measurements. In Section 4, we will extend the results to systems subject to delayed measurements.
Distributed LMPC with delayed measurements
In this section, we consider distributed LMPC of systems subject to asynchronous and delayed measurements.
Process and control problem description
The process considered in this example is a three vessel, reactor-separator process consisting of two continuously stirred tank reactors and a flash tank separator. The description and modeling of the process can be found in Liu et al. (2009). The process was numerically simulated using a standard Euler integration method, and bounded process noise was added to all the simulations in this work to simulate disturbances/model uncertainty.
Each of the vessels in the process has an external heat
Jinfeng Liu was born in Wuhan, China, in 1982. He received the B.S. and M.S. degrees in Control Science and Engineering in 2003 and 2006, respectively, from Zhejiang University. He is currently a Ph.D. candidate in Chemical Engineering at the University of California, Los Angeles. His research interests include model predictive control, fault detection and isolation, and fault-tolerant control of nonlinear systems.
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Jinfeng Liu was born in Wuhan, China, in 1982. He received the B.S. and M.S. degrees in Control Science and Engineering in 2003 and 2006, respectively, from Zhejiang University. He is currently a Ph.D. candidate in Chemical Engineering at the University of California, Los Angeles. His research interests include model predictive control, fault detection and isolation, and fault-tolerant control of nonlinear systems.
David Muñoz de la Peña was born in Badajoz, Spain, in 1978. He received the master degree in Telecommunication Engineering in 2001 and the Ph.D. in Control Engineering in 2005 from the University of Seville, Spain. In 2006–2007, he held a postdoctoral position at the Chemical and Biomolecular Engineering Department at the University of California, Los Angeles. Since 2007 he has been with the Escuela Superior de Ingenieros of the University of Seville, where he is currently an Assistant Professor. His main research interests are model predictive control, nonlinear systems and optimization.
Panagiotis D. Christofides was born in Athens, Greece, in 1970. He received the Diploma in Chemical Engineering degree in 1992, from the University of Patras, Greece, the M.S. degrees in Electrical Engineering and Mathematics in 1995 and 1996, respectively, and the Ph.D. degree in Chemical Engineering in 1996, all from the University of Minnesota. Since July 1996 he has been with the University of California, Los Angeles, where he is currently a Professor in the Department of Chemical and Biomolecular Engineering and the Department of Electrical Engineering. A description of his research interests, list of distinctions, and a list of his publications can be found at http://www.chemeng.ucla.edu/pchristo/index.html.
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Financial support from NSF, CNS-0930746, and the European Commission, INFSOICT-223866, is gratefully acknowledged. The material in this paper was partially presented at the IFAC International Symposium on the Advanced Control of Chemical Processes, Istanbul, Turkey, July 12–15, 2009. This paper was recommended for publication in a revised form by Associate Editor Lalo Magni under the direction of Editor Frank Allgöwer.