Distributed dissipative model predictive control for process networks with imperfect communication

Abstract

Results are developed to ensure stability of a dissipative distributed model predictive controller in the case of structured or arbitrary failure of the controller communication network; bounded errors in the communication may similarly be handled. Stability and minimum performance of the process network is ensured by placing a dissipative trajectory constraint on each controller. This allows for the interaction effects between units to be captured in the dissipativity properties of each process, and thus, accounted for by choosing suitable dissipativity constraints for each controller. This approach is enabled by the use of quadratic difference forms as supply rates, which capture detailed dynamic system information. A case study is presented to illustrate the results. V C 2014 American Institute of Chemical Engineers AIChE J, 60: 1682-1699, 2014 Keywords: process control, model predictive control, distributed control IntroductionModel predictive control (MPC) is one of the few advanced control techniques which has achieved wide spread use in the chemical industry, 1,2 due to its ability to handle constraints (both soft and hard), multivariable problems, and generate an optimal control action. Constraints, along with large scale and strong interactions (potentially inducing time-scale separation) are key problems in the control of chemical process networks. 3,4 These interactions between process units are due to material recycle and heat integration, which are common in modern chemical plants as a result of designs based upon steady-state efficiency concerns. These recycle loops can be thought of as positive feedback interconnections from a control point of view, which are well known present challenges in control practice.As such, a scalable approach to MPC for process networks which takes interaction effects into account is desired. Although centralized approaches can handle interaction effects, they suffer from poor scalability due to the computational complexity involved in modeling and design. Conversely, decentralized MPC offers a more scalable approach, although it may lead to poor performance or even instability if interaction effects are not accounted for. 5 Due to these short comings, distributed MPC has received much attention in the literature, as it attempts to realize the benefits of centralized and decentralized approaches, some recent examples include 6,7 and those by Rawlings and coworkers,8,9 and Christofides and coworkers, 10-12 a recent review is also available. 13In our previous work, 14 a dissipativity-based approach to noncooperative distributed MPC for systems with constant interconnection topology was presented. A dissipativity ensuring constraint is imposed on the individual controllers such that the closed loop process network satisfies a desired dissipativity condition. Dynamic supply rates in the form of quadratic difference forms (QdFs) were used to ensure stability and minimum performance bounds on the process network.In this work, the controller network is allowed to change to mode...

Reconfigurable distributed model predictive control

“…Thus, the dissipativity properties (essentially the supply rates) of the controllers change with the process network topology, to allow the controllers to reconfigure. This is fundamentally different to our previous work where the controller dissipativity properties remained constant, and were 'robustified' to handle unknown changes in the controller communication network (due to communication failure or data loss) (Tippett and Bao, 2014). Knowledge of the current configuration of the process is a key difference between the proposed approach and many applications in the control of switched systems, where the current mode of the system is often unknown.…”

“…It should be emphasized that this formulation is fundamentally different to that presented in our previous work (Tippett and Bao, 2014), as the controller supply rates are parameterized by αðtÞ, which captures the changes in the process network topology. Whereas in our previous work a single set of controller supply rates was determined to ensure stability of the closed-loop process network in the case of imperfect controller communication (which may be modelled as changes in the controller communication network).…”

“…It is assumed in this section, unless otherwise stated, that the distributed controllers have knowledge of the parameters α i at any point in time, this is in line with the aim of designing reconfigurable controllers. In the case that the parameters are not known online, the approach presented in Tippett and Bao (2014) may be used to developed robust (i.e. non-reconfigurable) DMPCs.…”

“…Definition 1 (Tippett and Bao (2014)). A MPC is said to trace a dissipative trajectory with time varying supply rate Q ϕ c ðuðtÞ; yðtÞ; αðtÞÞ if, for all time steps k,…”

Distributed control of chemical process networks

“…A potential disadvantage of this is that each closed-loop may then not be stable in isolation, or when the controller communication network fails. To rectify this, an approach to ensure stability in these cases has been presented in [47]. Additional extensions to multirate control have also been developed [48] .…”