0
Research Papers

Nested Plant/Controller Codesign Using G-Optimal Design and Continuous Time Adaptation Laws: Theoretical Framework and Application to an Airborne Wind Energy System

[+] Author and Article Information
Joe Deese

Department of Mechanical Engineering,
University of North Carolina at Charlotte,
Charlotte, NC 28223
e-mail: jdeese23@uncc.edu

Chris Vermillion

Department of Mechanical Engineering,
University of North Carolina at Charlotte,
Charlotte, NC 28223
e-mail: cvermill@uncc.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 18, 2018; final manuscript received June 30, 2018; published online August 1, 2018. Assoc. Editor: Mohammad A. Ayoubi.

J. Dyn. Sys., Meas., Control 140(12), 121013 (Aug 01, 2018) (13 pages) Paper No: DS-18-1033; doi: 10.1115/1.4040759 History: Received January 18, 2018; Revised June 30, 2018

This paper presents a nested codesign (combined plant and controller design) formulation that uses optimal design of experiments (DoE) techniques at the upper level to globally explore the plant design space, with continuous-time control parameter adaptation laws used at the lower level. The global design space exploration made possible through optimal DoE techniques makes the proposed methodology appealing for complex, nonconvex optimization problems for which legacy approaches are not effective. Furthermore, the use of continuous-time adaptation laws for control parameter optimization allows for the extension of the proposed optimization framework to the experimental realm, where control parameters can be optimized during experiments. At each full iteration, optimal DoE are used to generate a batch of plant designs within a prescribed design space. Each plant design is tested in either a simulation or experiment, during which an adaptation law is used for control parameter optimization. Two techniques are proposed for control parameter optimization at each iteration: extremum seeking (ES) and continuous-time DoE. The design space is reduced at the end of each full iteration, based on a response surface characterization and quality of fit estimate. The effectiveness of the approach is demonstrated for an airborne wind energy (AWE) system, where the plant parameters are the center of mass location and stabilizer area, and the control parameter is the trim pitch angle.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Fathy, H. K. , Papalambros, P. Y. , Ulsoy, A. G. , and Hrovat, D. , 2003, “ Nested Plant/Controller Optimization With Application to Combined Passive/Active Automotive Suspensions,” American Control Conference, Denver, CO, June 4–6, pp. 3375–3380.
Fathy, H. K. , Papalambros, P. Y. , and Ulsoy, A. G. , 2003, “ Integrated Plant, Observer, and Controller Optimization With Application to Combined Passive/Active Automotive Suspensions,” ASME Paper No. IMECE2003-42014.
Allison, J. T. , Guo, T. , and Han, Z. , 2014, “ Co-Design of an Active Suspension Using Simultaneous Dynamic Optimization,” ASME J. Mech. Des., 136(8), p. 081003.
Fathy, H. K. , Bortoff, S. , Copeland, S. , Papalambros, P. Y. , and Ulsoy, A. G. , 2002, “ Nested Optimization of an Elevator and Its Gain-Scheduled LQG Controller,” ASME Paper No. IMECE2002-39273.
Alexander, M. J. , Allison, J. T. , and Papalambros, P. Y. , 2012, “ Decomposition-Based Design Optimization of Electric Vehicle Powertrains Using Proper Orthogonal Decomposition,” Int. J. Powertrains, 1(1), pp. 77–92.
Deese, J. , Muyimbwa, T. , Deodhar, N. , Vermillion, C. , and Tkacik, P. , 2015, “ Lab-Scale Characterization of a Lighter-Than-Air Wind Energy System—Closing the Loop,” AIAA Paper No. 2015-3350.
Deodhar, N. , Vermillion, C. , and Tkacik, P. , 2015, “ A Case Study in Experimentally-Infused Plant and Controller Optimization for Airborne Wind Energy Systems,” American Control Conference (ACC), Chicago, IL, July 1–3, pp. 2371–2376.
Fathy, H. K. , Reyer, J. A. , Papalambros, P. Y. , and Ulsov, A. G. , 2001, “ On the Coupling Between the Plant and Controller Optimization Problems,” American Control Conference, Arlington, VA, June 25–27, pp. 1864–1869.
Peters, D. , Papalambros, P. Y. , and Ulsoy, A. , 2013, “ Control Proxy Functions for Sequential Design and Control Optimization,” Mechatronics, 23(4), pp. 409–418. [CrossRef]
Youcef-Toumi, K. , 1996, “ Modeling, Design, and Control Integration: A Necessary Step in Mechatronics,” IEEE/ASME Trans. Mechatronics, 1(1), pp. 29–38. [CrossRef]
Reyer, J. , and Papalambros, P. , 1999, “ Optimal Design and Control of an Electric Dc Motor,” ASME Paper No. DETC99/DAC-8599. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.26.4666&rep=rep1&type=pdf
Athan, T. , and Papalambros, P. , 1996, “ A Note on Weighted Criteria Methods for Compromise Solutions in Multi-Objective Optimization,” Eng. Optim., 27(2), pp. 155–176. [CrossRef]
Das, I. , and Dennis, J. , 1997, “ A Closer Look at Drawback of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problems,” Struct. Optim., 14(1), pp. 63–69. [CrossRef]
Allison, J. T. , and Nazari, S. , 2010, “ Combined Plant and Controller Design Using Decomposition-Based Design Optimization and the Minimum Principle,” ASME Paper No. DETC2010-28887.
Archer, C. , 2014, “ Airborne Wind Energy: Optimal Locations and Variability,” Int. J. Renewable Energy, 64, pp. 180–186. [CrossRef]
Vermillion, C. , 2013, “ Altitude and Crosswind Motion Control for Optimal Power-Point Tracking in Tethered Wind Energy Systems With Airborne Power Generation,” ASME Paper No. DSCC2013-3796.
Bafandeh, A. , and Vermillion, C. , 2016, “ Real-Time Altitude Optimization of Airborne Wind Energy Systems Using Lyapunov-Based Switched ES Control,” American Control Conference (ACC), Boston, MA, July 6–8, pp. 4990–4995.
Zgraggen, A. U. , Fagiano, L. , and Morari, M. , 2013, “ On Real-Time Optimization of Airborne Wind Energy Generators,” IEEE Conference on Decision and Control, Florence, Italy, Dec. 10–13, pp. 385–390.
Fagiano, L. , Zgraggen, A. U. , Khammash, M. , and Morari, M. , 2013, “ Automatic Control of Tethered Wings for Airborne Wind Energy: Design and Experimental Results,” European Control Conference (ECC), Zurich, Switzerland, July 17–19, pp. 992–997.
Fagiano, L. , Zgraggen, A. , Morari, M. , and Khammash, M. , 2014, “ Automatic Crosswind Flight of Tethered Wings for Airborne Wind Energy: Modeling, Control Design, and Experimental Results,” IEEE Trans. Control Syst. Technol., 22(4), pp. 1433–1447. [CrossRef]
Fagiano, L. , Zgraggen, A. , Morari, M. , and Khammash, M. , 2015, “ Real-Time Optimization and Adaptation of the Crosswind Flight of Tethered Wings for Airborne Wind Energy,” IEEE Trans. Control Syst. Technol., 23(2), pp. 434–448. [CrossRef]
Cobb, M. , Vermillion, C. , and Fathy, H. , 2016, “ Lab-Scale Experimental Crosswind Flight Control System Prototyping for an Airborne Wind Energy System,” ASME Paper No. DSCC2016-9737.
NikpoorParizi, P. , and Vermillion, C. , 2016, “ Combined Plant and Controller Performance Analysis and Optimization for an Energy-Harvesting Tethered Wing,” American Control Conference (ACC), Boston, MA, July 6–8.
Deodhar, N. , Deese, J. , and Vermillion, C. , 2018, “ Experimentally Infused Plant and Controller Optimization Using Iterative Design of Experiments—Theoretical Framework and Airborne Wind Energy Case Study,” ASME J. Dyn. Syst. Meas. Control, 140(1), p. 011004.
Deese, J. , and Vermillion, C. , 2017, “ Nested Plant/Controller Co-Design Using g-Optimal Design and Extremum Seeking: Theoretical Framework and Application to an Airborne Wind Energy System,” World Congress of the International Federation of Automatic Control, Toulouse, France, July 9–14.
Altaeros Energies, 2010, “ The Next Transformation in Rural Infrastructure Efficiency,” accessed Jan. 10, 2018, http://www.altaerosenergies.com/
Baheri, A. , Deese, J. , and Vermillion, C. , 2017, “ Combined Plant and Controller Design Using Bayesian Optimization: A Case Study in Airborne Wind Energy Systems,” ASME Paper No. DSCC2017-5242.
Ariyur, K. , and Krstic, M. , 2003, Real-Time Optimization by Extremum-Seeking Control, Wiley, Hoboken, NJ.
Ariyur, K. , and Krstic, M. , 2002, “ Analysis and Design of Multivariable Extremum Seeking,” American Control Conference, Anchorage, AK, May 8–10, pp. 2903–2908.
Jin, R. , Chen, W. , and Sudjianto, A. , 2002, “ On Sequential Sampling for Global Metamodeling in Engineering Design,” ASME Paper No. DETC2002/DAC-34092.
Jones, D. , Schonlau, M. , and Welch, W. , 1998, “ Efficient Global Optimization of Expensive Black-Box Functions,” J. Global Optim., 13(4), pp. 455–492. [CrossRef]
Shannon, C. , 1948, “ A Mathematical Theory of Communication,” Bell Syst. Tech. J., 27(3), pp. 379–423. [CrossRef]
Haykin, S. , 2003, Kalman Filtering and Neural Networks, Wiley, New York.
Vermillion, C. , Glass, B. , and Szalai, B. , 2014, “ Development and Full-Scale Experimental Validation of a Rapid Prototyping Environment for Plant and Control Design of Airborne Wind Energy Systems,” ASME Paper No. DSCC2014-5907.
Deodhar, N. , Bafandeh, A. , Deese, J. , Smith, B. , Muyimbwa, T. , Vermillion, C. , and Tkacik, P. , 2017, “ Laboratory-Scale Flight Characterization of a Multitethered Aerostat for Wind Energy Generation,” AIAA J., 55(6), pp. 1823–1832. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Buoyant airborne turbine of Altaeros Energies [26]

Grahic Jump Location
Fig. 2

General process diagram for nested plant and controller optimization

Grahic Jump Location
Fig. 3

Multiparameter ES block diagram displaying the update for a single element of the control vector. In general, i=1,2,3,…,L and L is the number of elements in the control design vector. For odd i, ωi+1=ωi, βi=0, and βi+1=0.

Grahic Jump Location
Fig. 4

General block diagram of entropy-based DoE

Grahic Jump Location
Fig. 5

Visualization of normalized entropy evolution over 10 s. The top plot shows the design points that have been visited as a function of time. The bottom plots show the values of entropy at the over the design space.

Grahic Jump Location
Fig. 6

Axis system for the BAT dynamic model. This diagram illustrates generalized coordinates (left and bottom middle), Euler angles (top middle), and tether attachment points (right).

Grahic Jump Location
Fig. 7

Plant design parameters for the Altaeros BAT

Grahic Jump Location
Fig. 8

Block diagram of closed-loop flight controller for the BAT. Here, zsp is a constant altitude setpoint. The control parameter to be optimized (θsp) is highlighted.

Grahic Jump Location
Fig. 9

Convergence of the ES algorithm for a sample plant design (xcm=45.4% and KA = 1)

Grahic Jump Location
Fig. 10

Response surface characterization at first (top left), second (top right), third (bottom left), and fourth (bottom right) iterations with candidate design points overlaid, when ES for the adaptation law in the nested codesign strategy

Grahic Jump Location
Fig. 11

Convergence for entropy-based DoE algorithm for a sample plant design (xcm=45.4% and KA = 1)

Grahic Jump Location
Fig. 12

Response surface characterization at first (top left), second (top right), third (bottom left), and fourth (bottom right) iterations with candidate design points overlaid when entropy-based DoE for the adaptation law in the nested codesign strategy

Grahic Jump Location
Fig. 13

Comparison of performance index components in a sample time interval between the optimal design and a suboptimal design from the design space, while using ES as the adaption law (see Table 6 for specific design configurations)

Grahic Jump Location
Fig. 14

Comparison of performance index components in a sample time interval between the optimal design and a suboptimal design from the design space, while using entropy-based DoE as the adaption law (see Table 6 for specific design configurations)

Tables

Errata

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