Introduction Control Co-Design Incorporating System Architecture Summary

Integrated Dynamic System Designthrough the Dimensions of Plant,Control, and System Architecture

g Daniel R. Herber� Colorado State University

Department of Systems EngineeringR daniel.herber@colostate.edu

December 1, 2020

1

Introduction Control Co-Design Incorporating System Architecture Summary

Outline

1. Introduction

2. Control Co-DesignControl Co-design OverviewCase Study : Active Vehicle SuspensionCCD Open Questions

3. Incorporating System ArchitectureSystem Architectures as GraphsCase Study : Vehicle Suspension ArchitecturesCase Study : Aircraft Thermal Management SystemsSysML and Model-Based Systems Engineering Approaches

4. Summary

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1

Introduction

Introduction Control Co-Design Incorporating System Architecture Summary

¸ Introductory Example

sampleplacementpath

samplereturn path

Figure: Task description.

(a) Link length. (b) Cross-section.

Figure: Plant design.↷↷

end effecter

links

jointsground

actuators

(a)

↷ ↷

(b)

Figure: Different architectures.

joint 1joint 2

torq

ue

timeFigure: Joint control trajectories.

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Integrated Design Methods

• Integrated design methods systematically bring togetherdisciplines often considered separately• Adding dynamics can complicate the picture• Many critical design decisions in this area can be broadly

characterized as either architecture, plant, or control decisions• Using fully integrated design methods facilitates the discovery

of novel solutions, identification of system performance limits,and can reduce engineering effort

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2

Control Co-Design

Introduction Control Co-Design Incorporating System Architecture Summary

¸ What is Control Co-Design (CCD)?• Class of integrated engineering system design methods

that:• Consider the explicit relationship between physical and control

system design decisions• Answer the question:

“How should the physical aspects of an actively controlledengineering system be designed such that passive and activeproperties interact synergistically for system-optimalperformance?”

• Account explicitly for both physics coupling and designcoupling• Support discovery of non-obvious physical and control system

design solutions that enable new levels of performance andfunctionality• Subset of Multidisciplinary Design Optimization (MDO)

methods where at least one discipline is control-system design1

1 Allison and Herber 2014

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Design Optimization Across Two Disciplines• Consider a general bi-discipline

optimization problem with two sets ofdisciplinary design variables: x and y

minx,y

fx(x) + fy(y) + fxy(x, y)

subject to: gx(x) ≤ 0, gy(y) ≤ 0gxy(x, y) ≤ 0

• System optimality requiressimultaneous optimization of x and y• Sequential design does not produce

system-optimal designs if cross termsexist1 and is still largely used in practice• Several formulations are

mathematically equivalent tosimultaneous design2

1 Fathy et al. 2001; Allison, Guo, and Han 2014 2 Fathyet al. 2001

Sequential design

Iterated sequential design

Simultaneous design

Nested design

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Common Solution Techniques• Apply existing control design paradigms with additional freedom

in the plant design• Frequently discipline-specific techniques cannot be fully

integrated (i.e., simultaneous design is challenging)• Requires predictive models that are appropriate for CCD

studies2 (different that models used for control design alone)• For some systems, assumed control form may perform poorly for

new physical systems• Utilize optimal open-loop control techniques

• Appropriate for early-stage design studies for determiningsystem-level insights4

• Can identify system-level performance limits and desired dynamicbehaviors with fewer assumptions

• Methods based on direct optimal control (direct transcription)are well established3

2 Allison and Herber 2014 4 Deshmukh, Herber, and Allison 2015; Herber and Allison2017 3 Herber 2017; Allison, Guo, and Han 2014; Chilan et al. 2017

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Case Study : Active Vehicle Suspension• Recent work exploring the two most

common CCD coordination strategies:simultaneous and nested using open-loopoptimal control• Quarter-car suspension case study1

• Consists of two masses (sprung mass ms/4and unsprung mass mus/4)• The suspension between the masses

consists of a force actuator u(t), a linearspring ks(xp), and a linear damper cs(xp)

• The spring design involves the wirediameter d, helix diameter D, pitch p, andnumber of active coils Na

• Damper design involves the valve diameterDo, working piston diameter Dp, anddamper stroke Ds

Active Vehicle Suspension

1 Allison, Guo, and Han 2014; Clarizia 20198

Introduction Control Co-Design Incorporating System Architecture Summary

¸ Active Vehicle Suspension Problem• There are four states in the system:

ξ(t) =[zus − z0 zus zs − zus zs

]T (1)

• The differential equation is:

ξ(t) = A(xp)ξ(t) + Bu(t) + Ez0(t) (2)

A =

0 1 0 0

−kt(xp)mus/4

−[cs(xp)+ct]mus/4

ks(xp)mus/4

cs(xp)mus/4

0 −1 0 10 cs(xp)

ms/4

−ks(xp)ms/4

−cs(xp)ms/4

, B =

0−1

mus/4

01

ms/4

, E =

−1

ctmus/4

00

• Objective is a combination of quadratic penalties on handling (zus − z0),

passenger comfort zs, and control effort u:

o =

∫ tf

t0

[w1ξ

21 + w2[ξ4(t, ξ, u, xp)]

2 + w3u2]

dt (3)

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Active Vehicle Suspension Problem• Considering the weighted combination of two design load cases:

minξ,u,xp

10−2o(ξramp, uramp, xp) + o(ξrough, urough, xp) (4)

• The spring constant ks is computed by:

ks(xp) =d4G

8D3Na

[1 + d2

2D2

] (5)

• Spring manufacturability constraint:

go,1(xp) = 4− D/d ≤ 0 (6)

• Rattlespace constraint:

gi,1(xp, ξ) = maxt|ξ3(t)| − L0 + Ls + 0.02 + δg ≤ 0 (7)

• And many more details . . .10

Introduction Control Co-Design Incorporating System Architecture Summary

¸ Active Vehicle Suspension Dependency Matrix• Dependency matrix for understanding the problem structure

for both the nested and simultaneous strategiesξ xc xp

ξ1 ξ2 ξ3 ξ4 u d D p NaDoDpDsObjective, o(·)Dynamics, f(·)

Initial States, hi,1(·)Rattlespace, gi,1(·)

Spring Linearity, gi,2(·)Soderberg Fatigue Criterion, gi,3(·)

Zimmerli Limit, gi,4(·)Damper Max. Pressure, gi,5(·)

Damper Max. Velocity, gi,6(·)Damper Max. Spool Valve Lift, gi,7(·)

Spring Manufacturability, go,1(·)Spring Antitangling, go,2(·)

Spring Buckling, go,3(·)Spring Min. Pocket Length, go,4(·)Spring Min. Pocket Width, go,5(·)Spring Max. Shear Stress, go,6(·)

Damper Size, go,7(·)Damper Max. Motion Range, go,8(·)Damper Min. Motion Range, go,9(·)

X

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Active Vehicle Suspension Results

Figure: Optimal states for ramp and rough road cases.

Figure: Optimal controls.

• But how can we efficientlyarrive at this solution?

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Active Vehicle Suspension Implementation Results• Explored several implementation variations to gain insights

into best practices• Variations on things like the number of points, solver tolerances,

and derivative methods

(a) Different nt. (b) Different derivative methods.

Figure: Run time vs. relative objective function error for various solutionimplementations.

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ CCD Open Questions

ä• Deeper study and development of strategies to include

closed-loop control in CCD1, balancing design flexibility andimplementability/stability/robustness• Account for uncertainty in the presence of design coupling2

(some specific differences compared to existing RBDO or robustor stochastic control)• Incorporate expensive and multifidelity plant models in

CCD3

• Extension to large-scale systems5 (distributed optimization)

1 Deshmukh, Herber, and Allison 2015; Nash and Jain 2020 2 Cui, Allison, and Wang2020; Azad and Alexander-Ramos 2020 3 Jonkman et al. 2021 5 Liu, Azarm, andChopra 2020; Behtash and Alexander-Ramos 2020

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3

Incorporating SystemArchitecture

Introduction Control Co-Design Incorporating System Architecture Summary

¸ System Architectures as Graphs

• A variety of different engineering systemscan be represented by labeled graphs1

• Many systems can be represented bygraphs such as vehicle suspensions,thermal management networks, hybridpowertrains, mechanisms, biologicalnetworks, electrical circuits, and many otherdiscrete system decisions2

• Finding candidate architectures requiresthe generation of new, useful graphs• Finding the best architectures requires

evaluation and ranking

1 Herber, Guo, and Allison 2017 2 Herber 2020

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3

4

52

6 70

IR

RR

C

CL

L

L

O

Figure: Circuit schematic.

I R L

L

L

R

R

N4 N3C

C G

O

Figure: Circuit as a graph.

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Architecture Synthesis Methods and Challenges• Often discrete, constrained design decisions

• Naıve selection of decision variables may result in many infeasiblearchitectures

• Approaches include enumeration, Monte Carlo tree search,genetic algorithms, machine learning, and gradient-based (forcertain problems)

• Need to balance solution complexity, constraints, andcomputational cost

• Developed efficient graph enumeration algorithms forrepresenting a class of graphs commonly used in systemarchitecture design1

• For engineering systems represented by graphs, we require anexecutable architecture for evaluation

• Obtaining the executable model in a desirable form foroptimization (or even control co-design) can be challenging

• More software tools are becoming available

1 Herber, Guo, and Allison 2017; Herber 2020

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Case Study : Vehicle Suspension Architectures

Figure: Component catalog. Figure: Canonical. Figure: Alternative.

• We seek to identify suspension architecture candidates thatshould be investigated further; a downselecting process• Includes architecture, plant, and control design decisions1

• A state-space dynamic model needs to be constructed for eacharchitecture (graph) for performance evaluation• Each CCD problem is a different dynamic optimization problem

highly dependent on the architecture1 Herber and Allison 2019

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ A Trilevel Solution Approach• The proposed solution approach treats each design domain

modularly to leverage existing theory and tools

candidate architecture

candidate plant optimal controloptimal dynamics

optimal architecture

optimal plant

problem definitioncomponent catalog

network structure constraints

⟲

⟲

nested co-design

Level

Level

Level

• Provides relatively efficient solutions and addresses a numberof other considerations

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Vehicle Suspension Architecture Results• 4,351 candidate suspensions that needed to be evaluated

Figure: Alternative architecture results.

Figure: Performance vs. rank. Figure: Performance vs. complexity.

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Case Study : Aircraft Thermal ManagementSystems

• Conventional thermal managementsystem (TMS) architectures havestruggled to meet the needs of nextgeneration aircraft• Variety of different components

including inter-loop heat exchangers,turbines, compressors, general heatloads, etc.

• Many plant design decisions for thedifferent components as well

• Automated creation of a Modelicamodel from the graph representation1

1 Herber, Allison, et al. 2020

Bleed airsource

Turbine

Fan

Ram airsource

Ram airsink

Bleed airsink

Heatexchanger

Compressor

Heatexchanger

Figure: Two wheel bootstrap.

Figure: Graph representation.

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Introduction Control Co-Design Incorporating System Architecture Summary

¸ Aircraft Thermal Management Systems Results• Multiple objectives related to cooling potential, weight,

volume, and imposed fuel penalty are explored• 32,612 graphs feasible with respect to the graph constraints• 2,097 architectures with successful simulations (multiple

parameters explored for each simulation)

Figure: Pareto-optimal architecture instances (different colors indicatedifferent architectures, 163 in total). 21

Introduction Control Co-Design Incorporating System Architecture Summary

¸ SysML and Model-Based Systems Engineering

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4

Summary

Introduction Control Co-Design Incorporating System Architecture Summary

¸ Summary

• Many critical design decisions in dynamic engineering systemscan be broadly characterized as either architecture, plant, orcontrol decisions• There are still many challenges associated with integrated

design methods• Generating suitable models for CCD and architecture design• Exploring new architectures through graph-theoretic techniques• Balancing the computational cost associated with increasingly

lofty design scope• Translating the assumptions made in early-stage design studies

(such as optimal open-loop control) to realizable design solutions

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Questions?Integrated Dynamic System Design through the

Dimensions of Plant, Control, and SystemArchitecture

g Daniel R. Herber� Colorado State University

R daniel.herber@colostate.edu® www.engr.colostate.edu/∼drherber

� github.com/danielrherber

Appendix References

¸ References

J. T. Allison and D. R. Herber (2014). “Multidisciplinary design optimiza-tion of dynamic engineering systems”. AIAA Journal 52.4. DOI: 10.2514/1.J052182J. T. Allison, T. Guo, and Z. Han (2014). “Co-Design of an Active Sus-

pension Using Simultaneous Dynamic Optimization”. Journal of Mechani-cal Design 136.8. DOI: 10.1115/1.4027335S. Azad and M. J. Alexander-Ramos (2020). “A Single-loop Reliability-

based MDSDO Formulation for Combined Design and Control Optimiza-tion of Stochastic Dynamic Systems”. Journal of Mechanical Design.DOI: 10.1115/1.4047870M. Behtash and M. J. Alexander-Ramos (2020). “A Decomposition-

Based Optimization Algorithm for Combined Plant and Control Design ofInterconnected Dynamic Systems”. Journal of Mechanical Design 142.6.DOI: 10.1115/1.4046240C. M. Chilan et al. (2017). “Co-design of strain-actuated solar arrays for

spacecraft precision pointing and jitter reduction”. AIAA Journal 55.9.DOI: 10.2514/1.J055748

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Appendix References

¸ References (continued)

G. Clarizia (2019). “Co-design optimization of a tethered multi dronesystem”. M.S. Thesis. Politecnico di MilanoT. Cui, J. T. Allison, and P. Wang (2020). “Reliability-based Co-Design of

State-Constrained Stochastic Dynamical Systems”. AIAA Scitech Forum.DOI: 10.2514/6.2020-0413N. Deodhar, J. Deese, and C. Vermillion (2017). “Experimentally Infused

Plant and Controller Optimization Using Iterative Design of Experiments—Theoretical Framework and Airborne Wind Energy Case Study”. Journalof Dynamic Systems, Measurement, and Control 140.1. DOI: 10.1115/1.4037014A. P. Deshmukh, D. R. Herber, and J. T. Allison (2015). “Bridging the gap

between open-loop and closed-loop control in co-design: A framework forcomplete optimal plant and control architecture design”. 2015 AmericanControl Conference. DOI: 10.1109/ACC.2015.7172104H. K. Fathy et al. (2001). “On the coupling between the plant and con-

troller optimization problems”. American Control Conference. DOI: 10 .1109/acc.2001.946008

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Appendix References

¸ References (continued)D. R. Herber (2017). “Advances in combined architecture, plant, and

control design”. Ph.D. Dissertation. University of Illinois at Urbana-Champaign.URL: http://hdl.handle.net/2142/99394— (2020). “Enhancements to the perfect matching approach for graph

enumeration-based engineering challenges”. ASME 2020 InternationalDesign Engineering Technical Conferences. DETC2020-22774D. R. Herber and J. T. Allison (2017). “Unified scaling of dynamic op-

timization design formulations”. ASME 2017 International Design En-gineering Technical Conferences. DETC2017-67676. DOI: 10 . 1115 /DETC2017-67676— (2019). “A problem class with combined architecture, plant, and con-

trol design applied to vehicle suspensions”. ASME Journal of MechanicalDesign 141.10. DOI: 10.1115/1.4043312D. R. Herber, J. T. Allison, et al. (2020). “Architecture generation and

performance evaluation of aircraft thermal management systems throughgraph-based techniques”. AIAA 2020 Science and Technology Forumand Exposition. AIAA 2020-0159. DOI: 10.2514/6.2020-0159

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Appendix References

¸ References (continued)

D. R. Herber, T. Guo, and J. T. Allison (2017). “Enumeration of archi-tectures with perfect matchings”. ASME Journal of Mechanical Design139.5. DOI: 10.1115/1.4036132J. Jonkman et al. (2021). “Functional requirements for the WEIS toolset

to enable controls co-design of floating offshore wind turbines”. (to ap-pear) International Offshore Wind Technical Conference. IOWTC2020-3533T. Liu, S. Azarm, and N. Chopra (2020). “Decentralized Multisubsystem

Co-Design Optimization Using Direct Collocation and Decomposition-Based Methods”. Journal of Mechanical Design 142.9. DOI: 10.1115/1.4046438A. L. Nash and N. Jain (2020). “Hierarchical Control Co-design Using a

Model Fidelity-Based Decomposition Framework”. Journal of MechanicalDesign. DOI: 10.1115/1.4047691

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