Implementation of Centralized MPC on the Quadruple-tank Process with Guaranteeing Stability Roza Ranjbar 1 , Lucien Etienne 1 a , Eric Duviella 1 b and Jos´ e Mar´ ıa Maestre 2 c 1 Institute Mines Telecom Lille Douai, Univ. Lille, F-59000, Lille, France 2 Dept. Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, Sevilla, Spain Keywords: Model Predictive Control, Centralized Control, Control Benchmark, Stability. Abstract: This work presents an implementation of a stabilizing model predictive control applied to a nonlinear system. In this work, the quadruple-tank system has been considered. For this process, a precise control benchmark was available and worked on previously. To ensure the asymptotic stability of this nonlinear system, we made a discretized linearized model and applied a centralized MPC controller with terminal cost constraint. The effectiveness of the proposed strategy is illustrated by simulations. 1 INTRODUCTION Optimal control design of systems subject to con- straint is an important problem of control theory. A powerful way of investigating this problem is to use model predictive controllers (MPCs) which are known to be popular in many fields of applications (Qin and Badgwell, 2003). MPC uses a model of the system dynamics for computing an optimal con- trol action sequence therefore enhancing the compu- tational requirements while achieving optimal perfor- mance (Dua et al., 2006). It solves an open-loop con- strained optimization problem at each time step, then it executes only the first control of this sequence. The same procedure is repeated at next time steps (Seung Cheol Jeong and PooGyeon Park, 2005). One of the major benefits of MPC over the other controllers is that it can manage constraints on states, inputs, and outputs. Thus, it allows a system to op- erate closer to boundaries (Huang et al., 2017). In addition, MPC has the ability of tracking a consistent sequence of set points at the same time that it guaran- tees that the constraints are satisfied at all times (Al- varado et al., 2011). MPC strategies have been considered for linear and nonlinear systems, under a variety of communi- cation schemes such as centralized MPC, decentral- ized MPC, distributed MPC (Segovia et al., 2019; a https://orcid.org/0000-0003-0931-843X b https://orcid.org/0000-0002-1622-0994 c https://orcid.org/0000-0002-6343-5445 Fele et al., 2017). In this paper, we propose a frame- work for analyzing the implementation of a classical centralized MPC to ensure the stability of a popu- lar benchmark example of the quadruple-tank process with nonlinear dynamics (Johansson, 2000). We will also emphasize that an optimally controlled system is not necessarily stable and the stability is not ascer- tained by the use of a finite horizon optimal controller (Kalman et al., 1960; Pannocchia, 2012; Scokaert and Rawlings, 1998). Related works: Previous researches have been done to provide sufficient conditions for the stability of a MPC controller. Since (Mayne et al., 2000) indi- cates that stability is an overriding necessity resulting in varied proposals for a MPC and its formulations. Later on, (Cueli and Bordons, 2008) studied a case (both constrained and unconstrained) for deriving the stability criterion that could be ensured under some specific assumptions. Afterwards, (Maiworm et al., 2015), by using a scenario tree, proved how to ensure a reasonable level of stability in the performance of the MPCs. Contributions: Based on the approach of (Scokaert and Rawlings, 1998) and by using conti- nuity arguments, the main contribution of this paper is to provide sufficient conditions for the stability of a nonlinear system comprised of four-tanks (as a rep- resentative of a water network) controlled with a cen- tralized MPC. Namely, we propose a framework for proving asymptotic stability of a Lipschitz nonlinear system using a discretized linearized model for the MPC controller synthesis. Then we apply this result 56 Ranjbar, R., Etienne, L., Duviella, E. and Maestre, J. Implementation of Centralized MPC on the Quadruple-tank Process with Guaranteeing Stability. DOI: 10.5220/0009827700560062 In Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2020), pages 56-62 ISBN: 978-989-758-442-8 Copyright c  2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved