Distributed Model Predictive Control: Theory And Applications
Distributed Model Predictive Control: Theory and ApplicationsbyAswin N. VenkatA dissertation submitted in partial fulfillmentof the requirements for the degree ofDOCTOR OF PHILOSOPHY(Chemical Engineering)at theUNIVERSITY OF WISCONSIN–MADISON2006
c Copyright by Aswin N. Venkat 2006All Rights Reserved
iFor my family . . .
iiDistributed Model Predictive Control: Theory and ApplicationsAswin N. VenkatUnder the supervision of Professor James B. RawlingsAt the University of Wisconsin–MadisonMost standard model predictive control (MPC) implementations partition the plant into several units and apply MPC individually to these units. It is known that such a completely decentralized control strategy may result in unacceptable control performance, especially if theunits interact strongly. Completely centralized control of large, networked systems is viewedby most practitioners as impractical and unrealistic. In this dissertation, a new framework fordistributed, linear MPC with guaranteed closed-loop stability and performance properties ispresented. A modeling framework that quantifies the interactions among subsystems is employed. One may think that modeling the interactions between subsystems and exchangingtrajectory information among MPCs (communication) is sufficient to improve controller performance. We show that this idea is incorrect and may not provide even closed-loop stability.A cooperative distributed MPC framework, in which the objective functions of the local MPCsare modified to achieve systemwide control objectives is proposed. This approach allows practitioners to tackle large, interacting systems by building on local MPC systems already in place.The iterations generated by the proposed distributed MPC algorithm are systemwide feasible,and the controller based on any intermediate termination of the algorithm is closed-loop sta-
iiible. These two features allow the practitioner to terminate the distributed MPC algorithm atthe end of the sampling interval, even if convergence is not achieved. If iterated to convergence, the distributed MPC algorithm achieves optimal, centralized MPC control.Building on results obtained under state feedback, we tackle next, distributed MPCunder output feedback. Two distributed estimator design strategies are proposed. Each estimator is stable and uses only local measurements to estimate subsystem states. Feasibilityand closed-loop stability for all distributed MPC algorithm iteration numbers are establishedfor the distributed estimator-distributed regulator assembly in the case of decaying estimateerror. A subsystem-based disturbance modeling framework to eliminate steady-state offsetdue to modeling errors and unmeasured disturbances is presented. Conditions to verify suitability of chosen local disturbance models are provided. A distributed target calculation algorithm to compute steady-state targets locally is proposed. All iterates generated by thedistributed target calculation algorithm are feasible steady states. Conditions under whichthe proposed distributed MPC framework, with distributed estimation, distributed target calculation and distributed regulation, achieves offset-free control at steady state are described.Finally, the distributed MPC algorithm is augmented to allow asynchronous optimization andasynchronous feedback. Asynchronous feedback distributed MPC enables the practitioner toachieve performance superior to centralized MPC operated at the slowest sampled rate. Examples from chemical engineering, electrical engineering and civil engineering are examinedand benefits of employing the proposed distributed MPC paradigm are demonstrated.
ivAcknowledgmentsAt the University of Wisconsin, I have had the opportunity to meet some wonderful people.First, I’d like to thank my advisor Jim Rawlings. I cannot put into words what I have learntfrom him. His intellect, attitude to research and career have been a great source of inspiration.I have always been amazed by his ability to distill the most important issues from complexproblems. It has been a great honor to work with him and learn from him.I’ve been fortunate to have had the chance to collaborate with two fine researchersSteve Wright and Ian Hiskens. I thank Steve for being incredibly patient with me from theoutset. Steve’s understanding of optimization is unparalleled, and his quickness in comprehending and critically analyzing material has constantly amazed me. I thank Ian for listeningto my crazy ideas, for teaching me the basics of power systems, and for constantly encouraging me to push the bar higher. I have enjoyed our collaboration immensely. I’d like to thankProfessors Mike Graham, Regina Murphy and Christos Maravelias for taking the time to serveon my thesis committee.I’m grateful to my undergraduate professors Dr. R. D. Gudi and Dr. K. P. Madhavanfor teaching me the basics of process control. Their lectures attracted me to this field initially.Dr. Gudi also made arrangements so that I could work in his group, and encouraged me topursue graduate school. Dr. Vijaysai, Thank you for being such a great coworker and friend.
vOver the years, the Rawlings group has been quite an assorted bunch. I thank EricHaseltine for his friendship and for showing me the ropes when I first joined the group. I amindebted to John Eaton for answering all my Octave and Linux questions, and for providinginvaluable computer support. I miss the lengthy discussions on cricket with Dan Patience.Brian Odelson generously devoted time to answer all my computer questions. Thank you MattTenny for answering my naive control questions. Jenny was always cheerful and willing tolend a helping hand. It was nice to meet Dennis Bonne. Gabriele, I’ve enjoyed the discussionswe’ve had. It has been nice to get to know Paul Larsen, Ethan Mastny and Murali Rajamani.Murali, I hope that your “KK curse” is lifted one day. I wish Brett Stewart the best of luck inhis studies. I’ve enjoyed our discussions, though I regret we did not have more time.Thank you Nishant “Nanga” Bhasin for being a close friend all through undergrad andgrad school. I miss our late night expeditions on Market street, the many trips to Pats andyearly camping trips. I could always count on Ashish Batra for sound advice on a range oftopics. In the past five years, I have also made some lifelong friends in Madison, WI. Cliff, Iwill never forget those late nights in town, the lunch trips to Jordans and those Squash games.I’ll also miss your “home made beer and cider”, and the many excuses we conjured up togo try them. Angela was always a willing partner to Nams and to hockey games. I willkeep my promise and take you to a cricket game sometime. Gova, I could always count onyou for a game of Squash and/or beer. Thank you Paul, Erin, Amy, Maritza, Steve, Rajesh“Pager” and Mike for your friendship. I’d like to also thank the Madison cricket team forsome unforgettable experiences over the last four summers.I owe a lot to my family. Thank you Mum, Dad, Kanchan for your love, and for alwaysbeing there. I thank my family in the states: my grandparents, Pushpa, Bobby and the “kids”-
viNathan and Naveen for their unfailing love and encouragement. Finally, I thank Shilpa Panthfor her love and support through some trying times, especially the last year or so. I am solucky to have met you, and I hope I can be as supportive when you need it.A SWIN N. V ENKATUniversity of Wisconsin–MadisonOctober 2006
viiContentsAbstractiiAcknowledgmentsivList of TablesxvList of FiguresxixChapter 11.1IntroductionOrganization and highlights of this dissertation . . . . . . . . . . . . . . . . . .Chapter 2Literature reviewChapter 3Motivation138173.1Networked chemical processes . . . . . . . . . . . . . . . . . . . . . . . . . . . .183.2Four area power system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22Chapter 4State feedback distributed MPC254.1Interaction modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264.2Notation and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .294.3Systemwide control with MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
viii4.3.1Geometry of Communication-based MPC . . . . . . . . . . . . . . . . . .354.4Distributed, constrained optimization . . . . . . . . . . . . . . . . . . . . . . . .404.5Feasible cooperation-based MPC (FC-MPC) . . . . . . . . . . . . . . . . . . . . .424.6Closed-loop properties of FC-MPC under state feedback . . . . . . . . . . . . .474.6.1Nominal stability for systems with stable decentralized modes . . . . .484.6.2Nominal stability for systems with unstable decentralized modes . . . .50Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .544.7.1Distillation column control . . . . . . . . . . . . . . . . . . . . . . . . . .544.7.2Two reactor chain with flash separator . . . . . . . . . . . . . . . . . . . .584.7.3Unstable three subsystem network . . . . . . . . . . . . . . . . . . . . . .604.8Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .634.9Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .684.9.1Rate of change of input penalty and constraint . . . . . . . . . . . . . . .684.9.2Coupled subsystem input constraints . . . . . . . . . . . . . . . . . . . .724.10 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .764.10.1 Proof for Lemma 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .764.10.2 Proof for Lemma 4.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .784.10.3 Lipschitz continuity of the distributed MPC control law: Stable systems794.10.4 Proof for Theorem 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .814.74.10.5 Lipschitz continuity of the distributed MPC control law: Unstable systems 834.10.6 Proof for Theorem 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 5Output feedback distributed MPC8488
ix5.1Notation and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .885.2State estimation for FC-MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .905.2.1Method 1. Distributed estimation with subsystem-based noise shapingmatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.25.391Method 2. Distributed estimation with interconnected noise shapingmatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95Output feedback FC-MPC for distributed regulation . . . . . . . . . . . . . . . .975.3.1Perturbed stability of systems with stable decentralized modes . . . . .985.3.2Perturbed closed-loop stability for systems with unstable decentralizedmodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1005.4Example: Integrated styrene polymerization plants . . . . . . . . . . . . . . . .1045.5Distillation column control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1055.6Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1065.7Appendix: Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1075.7.1Proof of Lemma 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107Appendix: State estimation for FC-MPC . . . . . . . . . . . . . . . . . . . . . . .1095.8.1Proof for Lemma 5.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1105.8.2Proof for Lemma 5.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1115.8.3Proof for Lemma 5.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111Appendix: Perturbed closed-loop stability . . . . . . . . . . . . . . . . . . . . . .1125.9.1Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1145.9.2Main result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1165.9.3Proof for Theorem 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1215.85.9
x5.9.4Construction of DDi for unstable systems . . . . . . . . . . . . . . . . . .1225.9.5Proof for Theorem 5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123Chapter 6Offset-free control with FC-MPC1266.1Disturbance modeling for FC-MPC . . . . . . . . . . . . . . . . . . . . . . . . . .1276.2Distributed target calculation for FC-MPC . . . . . . . . . . . . . . . . . . . . . .1296.2.1Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1336.3Offset-free control with FC-MPC . . . . . . . . . . . . . . . . . . . . . . . . . . .1336.4Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1366.4.1Two reactor chain with nonadiabatic flash . . . . . . . . . . . . . . . . . .1366.4.2Irrigation Canal Network . . . . . . . . . . . . . . . . . . . . . . . . . . .1416.5Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1456.6Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1486.6.1Proof for Lemma 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1486.6.2Proof for Lemma 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1496.6.3Existence and uniqueness for a convex QP . . . . . . . . . . . . . . . . .1506.6.4Proof for Lemma 6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1516.6.5Proof for Theorem 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1526.6.6Proof for Lemma 6.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1536.6.7Simplified distributed target calculation algorithm for systems with nonintegrating decentralized modes . . . . . . . . . . . . . . . . . . . . . . .Chapter 77.1Distributed MPC with partial cooperationPartial feasible cooperation-based MPC (pFC-MPC) . . . . . . . . . . . . . . . .155157158
xi7.27.37.1.1Geometry of partial cooperation . . . . . . . . . . . . . . . . . . . . . . .1597.1.2Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160Vertical integration with pFC-MPC . . . . . . . . . . . . . . . . . . . . . . . . . .1617.2.1Example: Cascade control of reboiler temperature . . . . . . . . . . . . .163Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168Chapter 8Asynchronous optimization for distributed MPC1698.1Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1718.2Asynchronous optimization for FC-MPC . . . . . . . . . . . . . . . . . . . . . .1728.2.1Asynchronous computation of open-loop policies . . . . . . . . . . . . .1738.2.2Geometry of asynchronous FC-MPC . . . . . . . . . . . . . . . . . . . . .1768.2.3Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1778.2.4Closed-loop properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1858.2.5Example: Two reactor chain with nonadiabatic flash . . . . . . . . . . . .185Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1878.3Chapter 9Distributed constrained LQR1899.1Notation and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1899.2Infinite horizon distributed MPC . . . . . . . . . . . . . . . . . . . . . . . . . . .1919.2.1The benchmark controller : centralized constrained LQR . . . . . . . . .1919.2.2Distributed constrained LQR (DCLQR) . . . . . . . . . . . . . . . . . . .1929.2.3Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1989.2.4Method 1. DCLQR with set constraint . . . . . . . . . . . . . . . . . . . .2009.2.5Method 2. DCLQR without explicit set constraint . . . . . . . . . . . . .204
xii9.2.6Closed-loop properties of DCLQR . . . . . . . . . . . . . . . . . . . . . .2069.3Terminal state constraint FC-MPC . . . . . . . . . . . . . . . . . . . . . . . . . .2089.4Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2119.4.1Distillation column of Ogunnaike and Ray (1994) . . . . . . . . . . . . .2119.4.2Unstable three subsystem network . . . . . . . . . . . . . . . . . . . . . .2139.5Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2159.6Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2199.6.1Proof for Lemma 9.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2199.6.2Proof for Lemma 9.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2209.6.3DCLQR with N increased online (without terminal set constraint) . . .2249.6.4Proof for Lemma 9.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .228Chapter 10 Distributed MPC Strategies with Application to Power System AutomaticGeneration Control22910.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23010.2 MPC frameworks for systemwide control . . . . . . . . . . . . . . . . . . . . . .23210.3 Terminal penalty FC-MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23810.3.1 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23810.3.2 Algorithm and properties . . . . . . . . . . . . . . . . . . . . . . . . . . .23910.3.3 Distributed MPC control law . . . . . . . . . . . . . . . . . . . . . . . . .24010.3.4 Feasibility of FC-MPC optimizations . . . . . . . . . . . . . . . . . . . . .24010.3.5 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24110.3.6 Nominal closed-loop stability . . . . . . . . . . . . . . . . . . . . . . . . .241
xiii10.4 Power system terminology and control area model . . . . . . . . . . . . . . . . .24310.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24510.5.1 Two area power system network . . . . . . . . . . . . . . . . . . . . . . .24510.5.2 Four area power system network . . . . . . . . . . . . . . . . . . . . . . .24710.5.3 Two area power system with FACTS device . . . . . . . . . . . . . . . . .24910.6 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25110.6.1 Penalty and constraints on the rate of change of input . . . . . . . . . . .25110.6.2 Unstable systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25610.6.3 Terminal control FC-MPC . . . . . . . . . . . . . . . . . . . . . . . . . . .25810.7 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26210.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26410.8.1 Model Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264Chapter 11 Asynchronous feedback for distributed MPC27011.1 Models and groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27111.2 FC-MPC optimization for asynchronous feedback . . . . . . . . . . . . . . . . .27511.3 Asynchronous feedback policies in FC-MPC . . . . . . . . . . . . . . . . . . . .28411.3.1 Asynchronous feedback control law . . . . . . . . . . . . . . . . . . . . .28411.3.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28411.3.3 An illustrative case study . . . . . . . . . . . . . . . . . . . . . . . . . . .28711.4 Nominal closed-loop stability with asynchronous feedback policies . . . . . . .29311.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29711.6 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .300
xivChapter 12 Concluding Remarks30412.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30412.2 Directions for Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . .307Appendix A Example parameters and model details311A.1 Four area power system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311A.2 Distillation column control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .312A.3 Two reactor chain with flash separator . . . . . . . . . . . . . . . . . . . . . . . .313A.4 Unstable three subsystem network . . . . . . . . . . . . . . . . . . . . . . . . . .314Vita325
xvList of Tables3.1Two integrated styrene polymerization plants. Input constraints. . . . . . . . .203.2Performance comparison of centralized and decentralized MPC . . . . . . . . .224.1Constraints on inputs L, V and regulator parameters. . . . . . . . . . . . . . . .544.2Closed-loop performance comparison of centralized MPC, decentralized MPC,communication-based MPC and FC-MPC. . . . . . . . . . . . . . . . . . . . . . .4.3Input constraints for Example 4.7.2. The symbol represents a deviation fromthe corresponding steady-state value. . . . . . . . . . . . . . . . . . . . . . . . .4.45759Closed-loop performance comparison of centralized MPC, communication-basedMPC and FC-MPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .594.5Input constraints and regulator parameters. . . . . . . . . . . . . . . . . . . . . .634.6Closed-loop performance comparison of centralized MPC, decentralized MPC,communication-based MPC and FC-MPC. . . . . . . . . . . . . . . . . . . . . . .5.15.263Closed-loop performance comparison of centralized MPC, decentralized MPCand FC-MPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104Two valid expressions for αi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
xvi6.1Input constraints for Example 6.4.1. The symbol represents a deviation fromthe corresponding steady-state value. . . . . . . . . . . . . . . . . . . . . . . . .6.2Disturbance models (decentralized, distributed and centralized MPC frameworks) for Example 6.4.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.3137138Closed-loop performance comparison of centralized MPC, decentralized MPCand FC-MPC. The distributed target calculation algorithm (Algorithm 6.1) isused to determine steady-state subsystem input, state and output target vectorsin the FC-MPC framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.4Gate opening constraints for Example 6.4.2. The symbol denotes a deviationfrom the corresponding steady-state value. . . . . . . . . . . . . . . . . . . . . .6.5140143Closed-loop performance of centralized MPC, decentralized MPC and FC-MPCrejecting the off-take discharge disturbance in reaches 1 8. The distributedtarget calculation algorithm (Algorithm 6.1) is iterated to convergence. . . . . .7.1143Closed-loop performance comparison of cascaded decentralized MPC, pFC-MPCand FC-MPC. Incurred performance loss measured relative to closed-loop performance of FC-MPC (1 iterate). . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.1Setpoint tracking performance of centralized MPC, FC-MPC and asynchronousFC-MPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.1187Distillation column model of Ogunnaike and Ray (1994). Bound constraints oninputs L and V . Regulator parameters for MPCs. . . . . . . . . . . . . . . . . . .9.2166212Closed-loop performance comparison of CLQR, FC-MPC (tp) and FC-MPC (tc). 212
xvii9.3Three subsystems, each with an unstable decentralized pole. Input constraintsand regulator parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.4215Closed-loop performance comparison of CLQR, FC-MPC (tp) and FC-MPC (tsc). 21510.1 Basic power systems terminology. . . . . . . . . . . . . . . . . . . . . . . . . . .24410.2 Model parameters and input constraints for the two area power network model(Example 10.5.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.3 Performance of different control formulations w.r.t. cent-MPC, Λ% 100.Λconfig Λcent Λcent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.4 Performance of different MPC frameworks relative to cent-MPC, Λ% 100.247248Λconfig Λcent Λcent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24910.5 Model parameters and input constraints for the two area power network model.FACTS device operated by area 1. . . . . . . . . . . . . . . . . . . . . . . . . . . .10.6 Performance of different MPC frameworks relative to cent-MPC, Λ% 100.251Λconfig Λcent Λcent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25110.7 Performance of different control formulations relative to centralized constrainedΛconfig ΛcentΛcent. . . . . . . . . . . . . . . . . . . . . . . . .26010.8 Regulator parameters for unstable four area power network. . . . . . . . . . . .261LQR (CLQR), Λ% 100.10.9 Performance of terminal control FC-MPC relative to centralized constrainedLQR (CLQR), Λ% Λconfig ΛcentΛcent 100. . . . . . . . . . . . . . . . . . . . . . . . .26111.1 Steady-state parameters. The operational steady state corresponds to maximumyield of B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .298
xviii11.2 Input constraints. The symbol represents a deviation from the correspondingsteady-state value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29811.3 Closed-loop performance comparison of centralized MPC, FC-MPC and asynchronous feedback FC-MPC (AFFC-MPC). Λcost calculated w.r.t performanceof Cent-MPC (fast). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .299A.1 Model, regulator parameters and input constraints for four area power networkof Figure 3.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311A.2 Distillation column model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .312A.3 First principles model for the plant consisting of two CSTRs and a nonadiabaticflash. Part 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313A.4 First principles model for the plant consisting of two CSTRs and a nonadiabaticflash. Part 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .314A.5 Steady-state parameters for Example 4.7.2. The operational steady state corresponds to maximum yield of B. . . . . . . . . . . . . . . . . . . . . . . . . . . . .314A.6 Nominal plant model for Example 5 (Section 4.7.3). Three subsystems, eachwith an unstable decentralized pole. The symbols yI [y1 0 , y2 0 ]0 , yII [y3 0 , y4 0 ]0 ,yIII y5 , uI [u1 0 , u2 0 ]0 , uII [u3 0 , u4 0 ]0 , uIII u5 . . . . . . . . . . . . . . . . . . .315
xixList of Figures2.1A conceptual picture of MPC. Only uk is injected into the plant at time k. Attime k 1, a new optimal trajectory is computed. . . . . . . . . . . . . . . . . .3.19Interacting styrene polymerization processes. Low grade manufacture in firstplant. High grade manufacture in second plant with recycle of monomer andsolvent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.220Interacting polymerization processes. Temperature control in the two polymerization reactors. (a) Temperature control in reactor 1. (b) Temperature control inreactor 2. (c) Initiator flowrate to reactor 1. (d) Recycle flowrate. . . . . . . . . .213.3Four area power system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .223.4Four area power system. Performance of centralized and communication-basedMPC rejecting a load disturbance in areas 2 and 3. Change in frequency ω2 ,23 and load reference setpoints Ptie-line power flow Ptieref 2 , Pref 3 . . . . . . .4.124A stable Nash equilibrium exists and is near the Pareto optimal solution. Communication based iterates converge to the stable Nash equilibrium. . . . . . . .36
xx4.2A stable Nash equilibrium exists but is not near the Pareto optimal solution.The converged solution, obtained using a communication-based strategy, is farfrom optimal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.3A stable Nash equilibrium does not exist. Communication-based iterates do notconverge to the Nash equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . .4.43737Setpoint tracking performance of centralized MPC, communication-based MPCand FC-MPC. Tray temperatures of the distillation column (Ogunnaike and Ray(1994)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.555Setpoint tracking performance of centralized MPC, communication-based MPCand FC-MPC. Input profile (V and L) for the distillation column (Ogunnaikeand Ray (1994)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.6Two reactor chain followed by nonadiabatic flash. Vapor phase exiting the flashis predominantly A. Exit flows are a function of the level in the reactor/flash. .4.75659Performance of cent-MPC, comm-MPC and FC-MPC when the level setpointfor CSTR-2 is increased by 42%. Setpoint tracking performance of levels Hr andHm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.861Performance of cent-MPC, comm-MPC and FC-MPC when the level setpoint forCSTR-2 is increased by 42%. Setpoint tracking performance of input flowratesF0 and Fm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.962Performance of centralized MPC and FC-MPC for the setpoint change describedin Example 4.7.3. Setpoint tracking performance of outputs y1 and y4 . . . . . . .644.10 Performance of centralized MPC and FC-MPC for the setpoint change describedin Example 4.7.3. Inputs u2 and u4 . . . . . . . . . . . . . . . . . . . . . . . . . . .65
xxi4.11 Behavior of the FC-MPC cost function with iteration number at time 6. Convergence to the optimal, centralized cost is achieved after 10 iterates. . . . . . . .664.12 Example demonstrating nonoptimality of Algorithm 4.1 in the presence of coupled decision variable constraints. . . . . . . . . . . .
the proposed distributed MPC framework, with distributed estimation, distributed target cal- culation and distributed regulation, achieves offset-free control at steady state are described. Finally, the distributed MPC algorithm is augmented to allow asynchronous optimization and
Distributed Database Design Distributed Directory/Catalogue Mgmt Distributed Query Processing and Optimization Distributed Transaction Mgmt -Distributed Concurreny Control -Distributed Deadlock Mgmt -Distributed Recovery Mgmt influences query processing directory management distributed DB design reliability (log) concurrency control (lock)
Distributed control with the Limited-Communication Distributed MPC method (LC-DMPC) IEEE 13 Node Test Feeder consisting of building nodes . Presentation from Rohit Chintala and Christopher Bay at the 20202 Workshop on Autonomous Energy Systems on Scale Distributed Model Predictive Control for Building and Renewable Energy Systems. .
predictive analytics and predictive models. Predictive analytics encompasses a variety of statistical techniques from predictive modelling, machine learning, and data mining that analyze current and historical facts to make predictions about future or otherwise unknown events. When most lay people discuss predictive analytics, they are usually .
limits requires a control tool such as MPC, which will better handle the varying set of active constraints. 1.1 GPC (Generalized Predictive Control) Controller The GPC (generalized predictive control) algorithm is a long-range predictive controller using the input-output internal model from Eq. (1) to have knowledge of the process in question [2].
and applied to distributed MPC. As distributed MPC systems also depend on an accurate process model, the development and implemen-tation of RNN models in distributed MPCs is an important area yet to be explored. In the present work, we introduce distributed control frameworks that employ a LSTM network, which is a particular type of RNN. The .
2.3 Model Predictive Control Model predictive control (MPC) [2] is an advanced control technique in which the controller takes control actions by optimizing an objective function that defines the objective of controlling the system. To enable the predictive capabilities of the control system, an explicit model that characterizes the system
Model Predictive Control Model Predictive Control (MPC) Uses models explicitly to predict future plant behaviour Constraints on inputs, outputs, and states are respected Control sequence is determined by solving an (often convex) optimization problem each sample Combined with state estimation
Unit 39: Adventure Tourism 378 Unit 40: Special Interest Tourism 386 Unit 41: Tourist Resort Management 393 Unit 42: Cruise Management 401 Unit 43: International Tourism Planning and Policy 408 Unit 44: Organisational Behaviour 415 Unit 45: Sales Management 421 Unit 46: Pitching and Negotiation Skills 427 Unit 47: Strategic Human Resource Management 433 Unit 48: Launching a New Venture 440 .
