This document must be cited according to its fjnal version which is - PDF document

This document must be cited according to its fjnal version which is published in a conference as: V.Grelet, P. Dufour, M. Nadri, V.Lemort, T. Reiche, "Explicit multi model predictive control of a waste heat Rankine based system for heavy duty trucks", 54rd IEEE Conference on Decision and Control (CDC), Osaka, Japan, pp. 179-184, december 15-18, 2015. You downloaded this document from the CNRS open archives server, on the webpages of Pascal Dufour: http://hal.archives-ouvertes.fr/DUFOUR-PASCAL-C-3926-2008

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Controller development Simulation results Conclusion and next steps Contacts and discussion Appendix EXPLICIT MULTI-MODEL PREDICTIVE CONTROL OF A WASTE HEAT RANKINE BASED SYSTEM FOR HEAVY DUTY TRUCKS Vincent GRELET 1 , 2 , 3 , Pascal DUFOUR 2 , Madiha NADRI 2 , Vincent LEMORT 3 and Thomas REICHE 1 1Volvo Group Trucks Technology Advanced Technology and Research, 1 avenue Henri Germain, 69800 Saint Priest, France 2Universit´ e de Lyon, Lyon F-69003, Universit´ e Lyon 1, CNRS UMR 5007, Laboratory of Process Control and Chemical Engineering (LAGEP), Villeurbanne 69100, France 3LABOTHAP, University of Liege, Campus du Sart Tilman Bat. B49 B4000 Liege, Belgium 54 th IEEE Conference on Decision and Control (CDC 2015) 15-18 December, Osaka, Japan 1/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Controller development Simulation results Conclusion and next steps Contacts and discussion Appendix Table of contents Context and motivations 1 Rankine cycle based heat recovery system 2 Rankine process Studied system and controller objective Nonlinear evaporator detailed model 3 Controller development 4 Identification Piecewise linear approach MMPC strategy Simulation results 5 Conclusion and next steps 6 2/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Controller development Simulation results Conclusion and next steps Contacts and discussion Appendix Context and motivations In nowadays heavy duty engines, a major part of the chemical energy contained in the fuel is released to the ambient through heat. 3/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Controller development Simulation results Conclusion and next steps Contacts and discussion Appendix Context and motivations In nowadays heavy duty engines, a major part of the chemical energy contained in the fuel is released to the ambient through heat. Waste heat recovery based on the Rankine cycle is a promising technique to increase fuel efficiency. 3/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Controller development Simulation results Conclusion and next steps Contacts and discussion Appendix Context and motivations In nowadays heavy duty engines, a major part of the chemical energy contained in the fuel is released to the ambient through heat. Waste heat recovery based on the Rankine cycle is a promising technique to increase fuel efficiency. Dynamic models needed for concept optimization, fuel economy evaluation and control algorithm development. 3/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Controller development Rankine process Simulation results Studied system and controller objective Conclusion and next steps Contacts and discussion Appendix Rankine process T Liquid compression (1 → 2) from condensing to evaporating pressure by ˙ 3c means of the pump power W in . ˙ Q in Preheating (2 → 3 a ), vaporization (3 a → 3 b ) and superheating (3 b → 3 c ) 3a 3b ˙ W out by means of the input heat power ˙ Q in . 4 Vapor expansion (3 c → 4) from 12 ˙ W in evaporating to condensing pressure ˙ ˙ Q out creating power W out on the expander s shaft. Condensation (4 → 1) releasing heat Figure: Temperature-entropy diagram of the Rankine ˙ Q out in the heat sink. cycle 4/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Controller development Rankine process Simulation results Studied system and controller objective Conclusion and next steps Contacts and discussion Appendix Studied system and controller objective Recover heat from both EGR and exhaust in a serial configuration. Working fluid: water ethanol mixture. Focus on the control of the working fluid superheat at the expansion machine inlet. Even more critical when using a kinetic expander. Control issue: Reduce the deviation of the superheat around its set point to have safe and efficient operation. 5/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Controller development Simulation results Conclusion and next steps Contacts and discussion Appendix Nonlinear evaporator detailed model Model representation x i = f i ( x i , u ) , ˙ (1) � ˙ u T = � � , x T ˙ � = m f i ˙ h f i T w inti T g i T w exti (2) m f 0 P f 0 h f 0 m g L T g L i hfi − 1 ∂ρ fi − 1 ∂ρ fi − 1   � � 1 m fi − 1 ˙ + α fi A exchintf T fi − T winti ρ fi − 1 ∂ hfi − 1 ρ fi − 1 ∂ hfi − 1 − ˙ m f i   hfi ∂ρ fi   1 −   ρ fi ∂ hfi   � � � �   m fi − 1 h fi − 1 − ˙ ˙ m fi h fi − α fi A exchintf T fi − T winti     ρ fi V f    � � � �  f i ( x i , u ) = α fi A exchintf T fi − T winti + α g A exchintg T gi − T winti     ρ wint V wint     � �� � � � T ∗ � �   m g c pg ( T gi ) ˙ T gi − 1 − T gi − α g A exchintg gi − T winti − A exchextg T gi − T wexti     ρ gi V g c pg ( T gi )     � � � � α amb A exchextamb T amb − T wexti + α g A exchextg T gi − T wexti   ρ wext V wext 6/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Identification Controller development Piecewise linear approach Simulation results MMPC strategy Conclusion and next steps Contacts and discussion Appendix Identification Dynamic relation between u (working fluid mass flow) and y (working fluid superheat) can be described around an operating point by a first order plus time delay (FOPTD) model: y ( s ) G 1 + τ s e − Ls , u ( s ) = (3) High variation in FOPTD parameters shows high nonlinearity. Linear time invariant controller will hardly achieve the control objective with good performance under transient driving cycle. 7/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Identification Controller development Piecewise linear approach Simulation results MMPC strategy Conclusion and next steps Contacts and discussion Appendix Piecewise linear approach Multi linear model approach consists into identifying a bank of N linear models and combine them by means of a weighting scheme. Global model output is (at time t k ): N � y k = y i , k W i , k (4) i =1 Key design issues are : 1/ the selection of the good model(s) in the bank. 2/ linear models mixing. Modeling error of the i th model at the current time t k is defined by: ǫ i , k = y p , k − y i , k . (5) 8/21 Grelet et al., CDC 2015 paper TuA06.1

Context and motivations Rankine cycle based heat recovery system Nonlinear evaporator detailed model Identification Controller development Piecewise linear approach Simulation results MMPC strategy Conclusion and next steps Contacts and discussion Appendix Weighting scheme New proposed scheme ǫ 2 i , k ǫ i , k ˜ = (8) Bayesian recursive scheme N � ǫ 2 m , k exp( − 1 2 ǫ i , k K ǫ T i , k p i , k − 1 ) m =1 p i , k = (6) N j = N (exp( − 1 2 ǫ m , k K ǫ T � m , k p m , k − 1 ) � X i , k = (1 − ˜ ǫ i , k ) ǫ j , k ˜ (9) m =1 pi , k j � = i , j =1  for p i , k > δ  N  X i , k � W i , k = pm , k (7) ˜ = (10) X i , k m =1 N  0 for p i , k < δ  � X m , k m =1 where K is a vector and δ a scalar. 1 ˜ W i , k = X i , k (11) 1 + Ts where T is a scalar. 9/21 Grelet et al., CDC 2015 paper TuA06.1