Research Papers: Design Automation

Nested and Simultaneous Solution Strategies for General Combined Plant and Control Design Problems

[+] Author and Article Information
Daniel R. Herber

Industrial & Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: herber1@illinois.edu

James T. Allison

Industrial & Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: jtalliso@illinois.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 23, 2018; final manuscript received June 24, 2018; published online October 10, 2018. Assoc. Editor: Harrison M. Kim.

J. Mech. Des 141(1), 011402 (Oct 10, 2018) (11 pages) Paper No: MD-18-1066; doi: 10.1115/1.4040705 History: Received January 23, 2018; Revised June 24, 2018

In this paper, general combined plant and control design or co-design problems are examined. The previous work in co-design theory imposed restrictions on the type of problems that could be posed. This paper lifts many of those restrictions. The problem formulations and optimality conditions for both the simultaneous and nested solution strategies are given. Due to a number of challenges associated with the optimality conditions, practical solution considerations are discussed with a focus on the motivating reasons for using direct transcription (DT) in co-design. This paper highlights some of the key concepts in general co-design including general coupling, the differences between the feasible regions for each strategy, general boundary conditions, inequality path constraints, system-level objectives, and the complexity of the closed-form solutions. Three co-design test problems are provided. A number of research directions are proposed to further co-design theory including tailored solution methods for reducing total computational expense, better comparisons between the two solution strategies, and more realistic test problems.

Copyright © 2019 by ASME
Topics: Design
Your Session has timed out. Please sign back in to continue.


Allison, J. T. , 2013, “ Plant-Limited Co-Design of an Energy-Efficient Counterbalanced Robotic Manipulator,” ASME J. Mech. Des., 135(10), p. 101003. [CrossRef]
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.
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. [CrossRef]
Deshmukh, A. P. , and Allison, J. T. , 2016, “ Multidisciplinary Dynamic Optimization of Horizontal Axis Wind Turbine Design,” Struct. Multidiscip. Optim., 53(1), pp. 15–27. [CrossRef]
Yan, H.-S. , and Yan, G.-J. , 2009, “ Integrated Control and Mechanism Design for the Variable Input-Speed Servo Four-Bar Linkages,” Mechatronics, 19(2), pp. 274–285. [CrossRef]
Fathy, H. , Reyer, J. , Papalambros, P. , and Ulsov, A. , 2001, “ On the Coupling Between the Plant and Controller Optimization Problems,” American Control Conference, Arlington, VA, June 25–27, pp. 1864–1869.
Allison, J. T. , and Herber, D. R. , 2014, “ Multidisciplinary Design Optimization of Dynamic Engineering Systems,” AIAA J., 52(4), pp. 691–710. [CrossRef]
Martins, J. R. R. A. , and Lambe, A. B. , 2013, “ Multidisciplinary Design Optimization: A Survey of Architectures,” AIAA J., 51(9), pp. 2049–2075. [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.
Kusiak, A. , and Larson, N. , 1995, “ Decomposition and Representation Methods in Mechanical Design,” ASME J. Mech. Des., 117(B), pp. 17–24. [CrossRef]
Herber, D. R. , 2014, “ Dynamic System Design Optimization of Wave Energy Converters Utilizing Direct Transcription,” M.S. thesis, University of Illinois at Urbana-Champaign, Urbana, IL.
Frischknecht, B. D. , Peters, D. L. , and Papalambros, P. Y. , 2011, “ Pareto Set Analysis: Local Measures of Objective Coupling in Multiobjective Design Optimization,” Struct. Multidiscip. Optim., 43(5), pp. 617–630. [CrossRef]
Reyer, J. A. , Fathy, H. K. , Papalambros, P. Y. , and Ulsoy, A. G. , 2001, “ Comparison of Combined Embodiment Design and Control Optimization Strategies Using Optimality Conditions,” ASME Paper No. DETC2001/DAC-21119.
Hale, A. L. , Lisowski, R. J. , and Dahl, W. E. , 1985, “ Optimal Simultaneous Structural and Control Design of Maneuvering Flexible Spacecraft,” AIAA J. Guid., Control, Dyn., 8(1), pp. 86–93. [CrossRef]
Eastep, F. , Khot, N. , and Grandhi, R. , 1987, “ Improving the Active Vibrational Control of Large Space Structures Through Structural Modifications,” Acta Astronaut., 15(6–7), pp. 383–389. [CrossRef]
Sunar, M. , and Rao, S. S. , 1993, “ Simultaneous Passive and Active Control Design of Structures Using Multiobjective Optimization Strategies,” Comput. Struct., 48(5), pp. 913–924. [CrossRef]
Peters, D. L. , Papalambros, P. Y. , and Ulsoy, A. G. , 2011, “ Control Proxy Functions for Sequential Design and Control Optimization,” ASME J. Mech. Des., 133(9), p. 091007. [CrossRef]
Peters, D. L. , Papalambros, P. Y. , and Ulsoy, A. G. , 2009, “ On Measures of Coupling Between the Artifact and Controller Optimal Design Problems,” ASME Paper No. DETC2009-86868.
Wang, Y.-S. , and Wang, Y. , 2015, “ A Gradient-Based Approach for Optimal Plant Controller Co-Design,” American Control Conference (ACC) Chicago, IL, July 1–3, pp. 3249–3254.
Herber, D. R. , and Allison, J. T. , 2013, “ Wave Energy Extraction Maximization in Irregular Ocean Waves Using Pseudospectral Methods,” ASME Paper No. DETC2013-12600.
Maraniello, S. , and Palacios, R. , 2016, “ Optimal Vibration Control and Co-Design of Very Flexible Actuated Structures,” J. Sound Vib., 377, pp. 1–21. [CrossRef]
Chilan, C. M. , Herber, D. R. , Nakka, Y. K. , Chung, S.-J. , Allison, J. T. , Aldrich, J. B. , and Alvarez-Salazar, O. S. , 2017, “ Co-Design of Strain-Actuated Solar Arrays for Spacecraft Precision Pointing and Jitter Reduction,” AIAA J., 55(9), pp. 3180–3195. [CrossRef]
Betts, J. T. , 2010, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Biegler, L. T. , 2010, Nonlinear Programming, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Rao, A. V. , 2010, “ A Survey of Numerical Methods for Optimal Control,” Adv. Astronautical Sci., 135(1), pp. 497–528.
Colson, B. , Marcotte, P. , and Savard, G. , 2007, “ An Overview of Bilevel Optimization,” Ann. Oper. Res., 153(1), pp. 235–256. [CrossRef]
Vicente, L. N. , and Calamai, P. H. , 1994, “ Bilevel and Multilevel Programming: A Bibliography Review,” J. Global Optim., 5(3), pp. 291–306. [CrossRef]
Tanino, T. , and Ogawa, T. , 1984, “ An Algorithm for Solving Two-Level Convex Optimization Problems,” Int. J. Syst. Sci., 15(2), pp. 163–174. [CrossRef]
Liberzon, D. , 2012, Calculus of Variations and Optimal Control Theory, Princeton University Press, Princeton, NJ.
Belvin, W. K. , and Park, K. C. , 1990, “ Structural Tailoring and Feedback Control Synthesis: An Interdisciplinary Approach,” AIAA J. Guid., Control, Dyn., 13(3), pp. 424–429. [CrossRef]
Rao, S. S. , 1988, “ Combined Structural and Control Optimization of Flexible Structures,” Eng. Optim., 13(1), pp. 1–16. [CrossRef]
Spong, M. W. , Hutchinson, S. , and Vidyasagar, M. , 2005, Robot Modeling and Control, 1st ed., Wiley, New York.
Chachuat, B. , 2007, Nonlinear and Dynamic Optimization: From Theory to Practice, Automatic Control Laboratory, Lausanne, Switzerland.
Bryson , A. E., Jr. , and Ho, Y.-C. , 1975, Applied Optimal Control, CRC Press, Washington, DC.
Papalambros, P. Y. , and Wilde, D. J. , 2017, Principles of Optimal Design, 3rd ed., Cambridge University Press, Cambridge, UK.
Pontryagin, L. S. , 1962, The Mathematical Theory of Optimal Processes, Interscience, New York.
Doležal, J. , 1981, “ On Optimal Control Problems With General Boundary Conditions,” J. Optim. Theory Appl., 35(1), pp. 143–148. [CrossRef]
Weisstein, E. W. , 2016, “ Total Derivative. From MathWorld–A Wolfram Web Resource,” MathWorld–A Wolfram Web Resource, accessed date July 9, 2018, http://mathworld.wolfram.com/TotalDerivative.html
Garg, D. , 2011, “ Advances in Global Pseudospectral Methods for Optimal Control,” Ph.D. dissertation, University of Florida, Gainesville, FL.
Herber, D. R. , 2015, “ Basic Implementation of Multiple-Interval Pseudospectral Methods to Solve Optimal Control Problems,” Engineering System Design Lab, Urbana, IL, Technical Report No. UIUC-ESDL-2015-01.
Biegler, L. T. , 2007, “ An Overview of Simultaneous Strategies for Dynamic Optimization,” Chem. Eng. Process.: Process Intensif., 46(11), pp. 1043–1053. [CrossRef]
Herber, D. R. , 2017, “ Advances in Combined Architecture, Plant, and Control Design,” Ph.D. dissertation, University of Illinois at Urbana-Champaign, Urbana, IL.
Xu, H. , and Carrillo, L. R. G. , 2017, “ Near Optimal Control and Network Co-Design for Uncertain Networked Control System With Constraints,” American Control Conference, Seattle, WA, May 24–26, pp. 2339–2344.
Kelly, M. P. , 2015, Transcription Methods for Trajectory Optimization, Tutorial, Cornell University, Ithaca, New York.
Onoda, J. , and Haftka, R. T. , 1987, “ An Approach to Structure/Control Simultaneous Optimization for Large Flexible Spacecraft,” AIAA J., 25(8), pp. 1133–1138. [CrossRef]
Herber, D. R. , “ Co-Design Examples Repository,” accessed July 9, 2018, https://github.com/danielrherber/co-design-examples-repository
Herber, D. R. , and Allison, J. T. , 2017, “ Unified Scaling of Dynamic Optimization Design Formulations,” ASME Paper No. DETC2017-67676.
Liu, T. , Azarm, S. , and Chopra, N. , 2017, “ On Decentralized Optimization for a Class of Multisubsystem Co-design Problems,” ASME J. Mech. Des., 139(12), p. 121404. [CrossRef]
Bertsimas, D. , Brown, D. B. , and Caramanis, C. , 2011, “ Theory and Applications of Robust Optimization,” SIAM Rev., 53(3), pp. 464–501. [CrossRef]
Zhou, K. , Doyle, J. C. , and Glover, K. , 1996, Robust and Optimal Control, Prentice Hall, Englewood Cliffs, NJ.


Grahic Jump Location
Fig. 1

Two co-design solution strategies where indicates an optimization problem: (a) simultaneous strategy and (b) nested strategy

Grahic Jump Location
Fig. 2

Scalar plant, scalar control problem (TP1) results with q = 10, r = 1, wc = 1, and wp=0.3: (a) Ψ(b,K) and (b) ψ(b)

Grahic Jump Location
Fig. 3

Co-design transfer problem (TP2) results for various values of the problem parameters and different values of k marked: (a) results demonstrating a large number of local solutions with tf = 2, x0=0, and v0=−1; (b) results demonstrating single global minimum with tf = 1, x0=1, and v0=2; and (c) results demonstrating degenerate plant solution with tf = 2, x0=5, and v0=−5

Grahic Jump Location
Fig. 4

Simple SASA test problem (TP3) results with J = 1, tf = 2, and umax=1: (a) k = 0, (b) k*=0.8543, and (c) k = 50



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