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Research Papers

Co-Design of an Active Suspension Using Simultaneous Dynamic Optimization

[+] Author and Article Information
James T. Allison

Mem. ASME
Assistant Professor
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: jtalliso@illinois.edu

Tinghao Guo

University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: guo32@illinois.edu

Zhi Han

Mem. ASME
Senior Software Developer
MathWorks, Inc.,
Natick, MA 01760
e-mail: zhi.han@mathworks.com

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 25, 2013; final manuscript received March 23, 2014; published online June 2, 2014. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 136(8), 081003 (Jun 02, 2014) (14 pages) Paper No: MD-13-1099; doi: 10.1115/1.4027335 History: Received February 25, 2013; Revised March 23, 2014

Design of physical systems and associated control systems are coupled tasks; design methods that manage this interaction explicitly can produce system-optimal designs, whereas conventional sequential processes may not. Here, we explore a new technique for combined physical and control system design (co-design) based on a simultaneous dynamic optimization approach known as direct transcription, which transforms infinite-dimensional control design problems into finite-dimensional nonlinear programming problems. While direct transcription problem dimension is often large, sparse problem structures and fine-grained parallelism (among other advantageous properties) can be exploited to yield computationally efficient implementations. Extension of direct transcription to co-design gives rise to new problem structures and new challenges. Here, we illustrate direct transcription for co-design using a new automotive active suspension design example developed specifically for testing co-design methods. This example builds on prior active suspension problems by incorporating a more realistic physical design component that includes independent design variables and a broad set of physical design constraints, while maintaining linearity of the associated differential equations. A simultaneous co-design approach was implemented using direct transcription, and numerical results were compared with conventional sequential optimization. The simultaneous optimization approach achieves better performance than sequential design across a range of design studies. The dynamics of the active system were analyzed with varied level of control authority to investigate how dynamic systems should be designed differently when active control is introduced.

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Figures

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Fig. 1

Illustration of continuity defect ζ1 between time segments 1 and 2 using the multiple shooting method

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Fig. 2

Conceptual solution trajectories through design and state subspaces

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Fig. 3

Analysis structure of (a) DT and (b) DT for co-design

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Fig. 4

DT Jacobian structure: (a) dense and (b) sparse plant constraints

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Fig. 5

Quarter-car vehicle suspension model

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Fig. 6

Helical compression spring with squared ground ends

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Fig. 7

Typical nonlinear damping curve

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Fig. 8

Sectional view of a single-tube telescopic damper

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Fig. 9

Sectional view of the piston compression valve

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Fig. 10

Damper heat transfer model

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Fig. 11

Structure of the plant constraint Jacobian

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Fig. 12

System responses for sequential optimization. (a) Sprung mass response to ramp input. (b) Sprung mass response to rough road input. (c) Control force (ramp input). (d) Control force (rough road input)

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Fig. 13

System responses for simultaneous optimization. (a) Sprung mass response to ramp input. (b) Sprung mass response to rough road input. (c) Control force (ramp input). (d) Control force (rough road input)

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Fig. 14

Pareto sets illustrating the tradeoff between maximum control force and system objective function value (both sequential and simultaneous solution approaches)

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