Research Papers

Dynamical Graph Models of Aircraft Electrical, Thermal, and Turbomachinery Components

[+] Author and Article Information
Matthew A. Williams

Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: mwillms4@illinois.edu

Justin P. Koeln

Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: koeln2@illinois.edu

Herschel C. Pangborn

Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: pangbor2@illinois.edu

Andrew G. Allenye

Ralph & Catherine Fisher Professor
Fellow ASME
Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: alleyne@illinois.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 21, 2016; final manuscript received October 18, 2017; published online December 19, 2017. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 140(4), 041013 (Dec 19, 2017) (17 pages) Paper No: DS-16-1607; doi: 10.1115/1.4038341 History: Received December 21, 2016; Revised October 18, 2017

The current trend of electrification in modern aircraft has driven a need to design and control onboard power systems that are capable of meeting strict performance requirements while maximizing overall system efficiency. Model-based control provides the opportunity to meet the increased demands on system performance, but the development of a suitable model can be a difficult and time-consuming task. Due to the strong coupling between systems, control-oriented models should capture the underlying physical behavior regardless of energy domain or time-scale. This paper seeks to simplify the process of identifying a suitable control-oriented model by defining a scalable and broadly applicable approach to generating graph-based models of thermal, electrical, and turbomachinery aircraft components and systems. Subsequently, the process of assembling component graphs into a dynamical system graph that integrates multiple energy domains is shown. A sample electrical and thermal management system is used to demonstrate the capability of a graph model at matching the complex dynamics exhibited by nonlinear and empirically based simulation models.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Liptak, B. G. , 1995, Process Control, 3rd ed., Chilton, Radnor, PA. [PubMed] [PubMed]
Guerrero, J. M. , Chandorkar, M. , Lee, T. L. , and Loh, P. C. , 2013, “ Advanced Control Architectures for Intelligent Microgrids—Part I: Decentralized and Hierarchical Control,” IEEE Trans. Ind. Electron., 60(4), pp. 1254–1262. [CrossRef]
Negenborn, R. R. , Sahin, A. , Lukszo, Z. , Schutter, B. D. , and Morari, M. , 2009, “ A Non-Iterative Cascaded Predictive Control Approach for Control of Irrigation Canals,” IEEE International Conference on Systems, Man and Cybernetics (ICSMC), San Antonio, TX, Oct. 11–14, pp. 3552–3557.
Christofides, P. D. , Scattolini, R. , Muñoz de la Peña, D. , and Liu, J. , 2013, “ Distributed Model Predictive Control: A Tutorial Review and Future Research Directions,” Comput. Chem. Eng., 51, pp. 21–41. [CrossRef]
Deppen, T. O. , 2013, “Optimal Energy Use in Mobile Applications With Storage,” Ph.D. thesis, University of Illinois, Urbana, IL. https://www.ideals.illinois.edu/handle/2142/44290
Jain, N. , Koeln, J. P. , Sundaram, S. , and Alleyne, A. G. , 2014, “ Partially Decentralized Control of Large-Scale Variable-Refrigerant-Flow Systems in Buildings,” J. Process Control, 24(6), pp. 798–819. [CrossRef]
Rasmussen, B. P. , and Alleyne, A. G. , 2006, “Dynamic Modeling and Advanced Control of Air Conditioning and Refrigeration Systems,” Ph.D. dissertation, University of Illinois at Urbana-Champaign, Champaign, IL. https://www.ideals.illinois.edu/handle/2142/12355
McCarthy, P. , Niedbalski, N. , McCarthy, K. , Walters, E. , Cory, J. , and Patnaik, S. , 2016, “ A First Principles Based Approach for Dynamic Modeling of Turbomachinery,” SAE Int. J. Aerosp., 9(1), pp. 45–61. [CrossRef]
Williams, M. , Sridharan. S. , Banerjee, S. , Mak, C. , Pauga, C. , Krein, P. , Alleyne, A. , Jacobi, A. , and D'Urso, S. , 2015, “PowerFlow: A Toolbox for Modeling and Simulation of Aircraft Systems,” SAE Paper No. 2015-01-2417.
Garcia, C. E. , Prett, D. M. , and Morari, M. , 1989, “ Model Predictive Control: Theory and Practice—A Survey,” Automatica, 25(3), pp. 335–348. [CrossRef]
Moore, K. L. , Vincent, T. L. , Lashhab, F. , and Liu, C. , 2011, “ Dynamic Consensus Networks With Application to the Analysis of Building Thermal Processes,” IFAC Proc. Vol., 44(1), pp. 3078–3083. [CrossRef]
Preisig, H. A. , 2009, “ A Graph-Theory-Based Approach to the Analysis of Large-Scale Plants,” Comput. Chem. Eng., 33(3), pp. 598–604. [CrossRef]
Koeln, J. P. , Williams, M. A. , and Alleyne, A. G. , 2015, “ Hierarchical Control of Multi-Domain Power Flow in Mobile Systems—Part I: Framework Development and Demonstration,” ASME Paper No. DSCC2015-9908.
Williams, M. A. , Koeln, J. P. , and Alleyne, A. G. , 2015, “ Hierarchical Control of Multi-Domain Power Flow in Mobile Systems—Part II: Aircraft Application,” ASME Paper No. DSCC2015-9904.
West, D. B. , 2001, Introduction to Graph Theory, Prentice Hall, Upper Saddle River, NJ.
Incropera, F. P. , DeWitt, D. P. , Bergman, T. L. , and Lavine, A. S. , 2006, Fundamentals of Heat and Mass Transfer, 6th ed., Wiley, Hoboken, NJ.
Eremia, M. , and Bulac, C. , 2013, Handbook of Electrical Power System Dynamics: Modeling, Stability, and Control, IEEE Press, Piscataway, NJ. [CrossRef]
Sauer, P. , and Pai, M. A. , 1998, Power System Dynamics and Stability, Prentice Hall, Upper Saddle River, NJ.
Cao, Y., Williams, M. A. , Kearbey, B. J. , Smith, A. T. , Krein, P. T. , and Alleyne, A. G. , 2016, “ 20x-Real Time Modeling and Simulation of More Electric Aircraft Thermally Integrated Electrical Power Systems,” International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC), Toulouse, France, Nov. 2–4, pp. 1–6.
Ashford, R. , 2004, “ Verification and Validation of the F/A-22 Raptor Environmental Control System/Thermal Management System Software,” SAE Paper No. 2004-01-2573.
Santos, A. P. P. , Andrade, C. R. , and Zaparoli, E. L. , 2014, “ A Thermodynamic Study of Air Cycle Machine for Aeronautical Applications,” Int. J. Thermodyn., 17(3), pp. 117–126. [CrossRef]
Vargas, J. V. C. , and Bejan, A. , 2001, “ Integrative Thermodynamic Optimization of the Environmental Control System of an Aircraft,” Int. J. Heat Mass Transfer, 44(20), pp. 3907–3917. [CrossRef]
Conceição, S. T. , Zaparoli, E. L. , and Turcio, W. H. L. , 2007, “ Thermodynamic Study of Aircraft Air Conditioning Air Cycle Machine: 3-Wheel × 4-Wheel,” SAE Paper No. 2007-01-2579.
Tu, Y. , and Lin, G. P. , 2011, “ Dynamic Simulation of Aircraft Environmental Control System Based on Flowmaster,” J. Aircr., 48(6), pp. 2031–2041. [CrossRef]
Zhao, H. , Hou, Y. , Zhu, Y. , Chen, L. , and Chen, S. , 2009, “ Experimental Study on the Performance of an Aircraft Environmental Control System,” Appl. Therm. Eng., 29(16), pp. 3284–3288. [CrossRef]
Childs, T. , Jones, A. B. , and Chen, R. , 2015, “ Development of a Full Scale Experimental and Simulation Tool for Environmental Control System Optimisation and Fault Detection,” AIAA Paper No. 2015-1196.
Matullch, D. S. , 1989, “ High-Temperature Bootstrap Compared With F15 Growth Air Cycle Air Conditioning System,” SAE Paper No. 891436.


Grahic Jump Location
Fig. 1

Notional system graph with two input powers and two power sinks

Grahic Jump Location
Fig. 2

Comparison of counter- (a) and parallel-flow (b) heat exchanger temperature profiles for hot (subscript h) and cold (subscript c) flows

Grahic Jump Location
Fig. 3

Graph model of a heat exchanger

Grahic Jump Location
Fig. 4

Comparison of parallel-flow heat exchanger graph model and experimental data for (a) wall temperature, (b) temperature difference between the inlet and outlet of each side, and (c) power flow through the heat exchanger

Grahic Jump Location
Fig. 5

Infrared image showing the temperature gradient across the liquid–liquid heat exchanger

Grahic Jump Location
Fig. 6

Graph model of a cold plate

Grahic Jump Location
Fig. 7

Comparison of cold plate graph model and experimental data for (a) wall temperature and (b) fluid exit temperature

Grahic Jump Location
Fig. 8

Infrared image showing a 15 °C gradient across the cold plate

Grahic Jump Location
Fig. 9

Graph model of a tank with ambient heat loss

Grahic Jump Location
Fig. 10

Comparison of tank graph model and experimental data for tank temperature

Grahic Jump Location
Fig. 11

Graph model for electrical generator

Grahic Jump Location
Fig. 12

Graph model for electrical bus

Grahic Jump Location
Fig. 13

Graph model for constant power, current, and impedance loads

Grahic Jump Location
Fig. 14

Electrical system architecture for graph and simulation comparison

Grahic Jump Location
Fig. 15

Graph of the electrical system in Fig. 14

Grahic Jump Location
Fig. 16

Open loop inputs for (a) generator rotational shaft speed, (b) constant power AC and DC loads, and (c) constant current AC and DC loads

Grahic Jump Location
Fig. 17

Comparison of graph model and nonlinear simulation (a) generator voltage, (b) 270 V and 115 V bus voltages, (c) transient generator voltage, and (d) loads affecting bus voltage, for inputs from Fig. 17

Grahic Jump Location
Fig. 18

Schematic of a closed-loop ACM with a power turbine

Grahic Jump Location
Fig. 20

Flight envelope points where data is collected by Matullch [27]

Grahic Jump Location
Fig. 21

COP by the graph model compared to Matullch [27]

Grahic Jump Location
Fig. 22

Temperatures of the graph model compared to Matullch [27]

Grahic Jump Location
Fig. 23

ACM graph with secondary fuel and bypass air heat exchangers

Grahic Jump Location
Fig. 24

(a) Heat rejected to the bypass air, (b) heat absorbed from the fuel by the ACM, and (c) and (d) detail showing matching transient behavior by the graph model

Grahic Jump Location
Fig. 25

ACM shaft speed comparison with matching transient behavior (insert)

Grahic Jump Location
Fig. 26

(a) Power produced by the power turbine (top) and expansion turbine (bot), (b) power consumed by the compressor, and (c) and (d) detail showing matching transient behavior by the graph model

Grahic Jump Location
Fig. 27

Sample aircraft electrical, thermal, and air cycle system schematic

Grahic Jump Location
Fig. 28

Dynamic graph model of aircraft power systems in Fig. 27

Grahic Jump Location
Fig. 29

Validation of graph (a) avionics wall temperature, (b) generator and engine temperatures, (c) radar temperature, (d) fuel tank #2 temperature, (e) fuel tank #1 temperature, (f) generator voltage, (g) 270 V bus voltage, and (h) 115 V bus voltage

Grahic Jump Location
Fig. 30

Validation of graph power flow for (a) fuel heat rejection along e43, (b) ACM heat rejection along e58, and (c) ram air heat rejection along e19




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In