1.
Multidisciplinary Dynamic System
Design Optimization (MDSDO)
•
MDSDO is an emerging new area of
MDO that addresses the unique
properties of dynamic systems.
Established MDO formulations have
been applied to dynamic system design,
but do not address directly or capitalize
on the unique nature of dynamic
systems.
•
Important Research Fronts for
MDSDO:
A. Balanced Co-Design
B. Passive Dynamics
C. Direct Transcription
D. Dynamic System Topology
Optimization
E. Surrogate Modeling of Dynamic
Systems
zs
ms /4
ks
cs
zus
mus /4
kt
v
ct
z0
Example Application Areas: Active automotive suspension
design, wave energy converters, wind turbines
Engineering System Design Lab
Important Characteristics of MDSDO:
• Formulations are Intrinsically
Dynamic
• Multidisciplinary and Integrated
• Systems-Oriented
• Capitalize on Passive Dynamics
• Support Parallel Computation
Refs: J7-J10, C12-C19, C21, C22, TH1, TR1
2

2.
Co-Design: Integrated Physical and Control System Design
Conventional methods for active engineering
system design utilize sequential design
processes. First the physical system (plant) is
designed, and then control engineers develop the
control system based on this control design:
min
xp
s.t. gp (⇠(t), xp )  0
˙
⇠(t) f (xp , ⇠(t), t) = 0
3
Mech.
design
Elements of Co-Design Research
• Most co-design researchers approach codesign from a controls-centric perspective. At
the ESDL, we take the opposite approach. We
seek to learn how to solve the co-design
problem when considering physical design
in a more comprehensive way.
• We develop of new numerical strategies,
such as the extension of direct transcription to
co-design, that solve co-design problems
efficiently.
Mech.
Subspace
Plant Design Optimization
Sequential design does not capitalize on coupling
between plant and control design. At the ESDL, we
develop and investigate design methods that
integrate control and mechanical design problems
and produce system-optimal designs efficiently.
Integrated physical and control system design is
often called co-design.
Engineering System Design Lab
(⇠(t), xp )
x p⇤
min
u(t)
(⇠(t), u(t), xp⇤ )
s.t. gp (⇠(t), xp⇤ )  0
˙
⇠(t) f (⇠(t), u(t), xp⇤ , t) = 0
Control Design Optimization
Control
design
Control
Subspace
Above: Conventional design methods explore only one
design domain at a time. While iterating this sequential
approach can in some cases converge on the right solution, it
is inefficient. Co-design allows designers to explore both
domains simultaneously; we can trace a more direct path
toward the system optimum.
Refs: J7-J10, C12-C18, C21-C23

3.
Direct Transcription (DT)
•
•
•
•
•
Numerical method for optimal control that has
emerged as a very important strategy for
solving realistic co-design problems.
In DT we discretize the state and control
trajectories in time:
min
u(t),⇠(t)
Z
tF
L(u(t), ⇠(t), t)dt
0
˙
subject to: ⇠(t) = fd (u(t), ⇠(t), t)
(⇠(t), u(t)) ! (⌅, U)
Infinite-dimensional, continuous problem
and then we convert the state equations to
algebraic equations using collocation.
In DT we solve simultaneously for the optimal
control trajectories and the corresponding
state trajectories (AAO/SAND).
Related to pseudospectral methods
Midpoint Quadrature,
Trapezoidal Collocation
Finite-dimensional, discrete problem
Advantages:
•
Most important reason for using DT with
co-design: it accommodates nonlinear
inequality constraints, which are present in
realistic co-design problems.
•
While DT results in a large-dimension NLP, it
is sparse and can be solved efficiently using
parallel computing.
•
DT can solve singular optimal control
problems.
min
U,⌅
nt 1
X
L(ui , ⇠i , ti )hi
i=1
subject to: ⇣(U, ⌅) =
hi
(fd i + fd i+1 )
2
+ ⇠i+1 ⇠i = 0
i = 1, 2, . . . , nt
1
Refs: J8, J10, C13, C16 – C19, C22, C23
Engineering System Design Lab
4

4.
Wave Energy Converter (WEC) Design
•
•
•
Ocean waves have the highest energy
density among renewable energy sources
We are studying co-design (integrated
optimal control and physical design) of
heaving buoy WECs.
Energy extraction for heaving buoy WECs
is given by:
E=
•
•
•
•
•
Z
T
P (t)dt =
0
Z
z
z0
T
z(t)FP T O (t)dt
˙
0
Active control of the power take-off force
(FPTO) increases energy production.
Direct Transcription used for optimal
control.
We have studied WEC design in the
presence of irregular ocean waves.
We are investigating a variety of PTO
architectures, including linear and rotary
electric machines as well as hydraulic
systems.
Future work will involve other WEC types,
physical testing, and co-design using
high-fidelity multiphysics modeling.
¼
FP T O
PTO
How do we design the FPTO trajectory?
What PTOs and control systems will
produce the optimal force trajectory?
Refs: C16, C22
Engineering System Design Lab
5

5.
Co-Design of an Active Suspension
•
•
•
Objective function:
zs
The physical design of early active
suspension designs were based on
previous passive designs.
The physical aspects of active systems
should be designed differently than
passive systems.
Co-design enables us to design the best
overall system.
ms /4
mus /4
•
•
Engineering System Design Lab
ct
Damper Design
Spring and damper geometry
Stress, fatigue, packaging, and thermal constraints
Our study revealed the importance of
incorporating nonlinear inequality
constraints in co-design problems,
motivating the use of direct transcription
(DT) for optimal control.
Simultaneous co-design with DT was the
most efficient and reliable design
optimization strategy.
v
z0
Previous co-design studies of active
suspensions used simplified plant
models. Here we developed a detailed
plant model that includes:
–
–
cs
zus
kt
•
Dynamic Model:
ks
Spring Design
Rod
D
d
Extension Chamber
Piston Compression Valve
Pressure tube
Fs
Piston Extension Valve
Working Piston
Foot Valve
L0
Compression Chamber
Foot Chamber
Floating Piston
p
Ls
Gas Chamber
Refs: J10, C13
6

6.
Active Automotive Suspension Testbed
•
•
Suspension with reconfigurable linkage:
Validating co-design methods requires a
physical testbed that permits both control
and physical system changes.
We are developing a reconfigurable
suspension testbed where the following
properties can be modified:
–
–
–
–
Linkage geometry
Spring stiffness
Damping rate (using magnetorheological damping)
Feedback control design
•
Testbed reconfigurations are fully
automated
•
This testbed will also be used in several
courses including:
–
–
–
•
GE 100 (Introduction to ISE)
GE 410 (Component Design)
GE 413 (Engineering Design Optimization)
In GE 410 students design their own
suspension system, including detailed
linkage, spring, and shaft design. At the
end of the course they will validate their
designs on the testbed.
Engineering System Design Lab
Refs: J10, C13
7

7.
Design of Genetic Regulatory Networks
•
Synthetic biology is an area that focuses on
construction of functional biological devices and
systems.
•
Existing design methods in synthetic biology are
limited in their ability to manage large-scale and
complex biological systems;
We need new design principles and methods to break
this complexity barrier and develop synthetic
biological systems of practical importance.
FA
FB
•
•
•
Previous numerical design studies based on
enumeration were limited to three-node networks.
We are exploring several techniques for making
possible the topological design of much larger
networks, including Mathematical Programs with
Complementarity Constraints (MPCCs), and
Generative Algorithms.
Our design methods manage both topological and
continuous design variables.
System dynamics are modeled using MichaelisMenten equations (ODEs), and are optimized using
Direct Transcription (DT).
A
B
C
I2
Input
•
Input
Example: Adaptive Network Design
I1
Output
O peak
(Opeak  O1 ) / O1
sensitivity 
(I2  I1 ) / I1
O2
Output
O1
precision 
(O2  O1 ) / O1
( I 2  I1 ) / I1
1
Refs: C19
Engineering System Design Lab
8

8.
Simultaneous Structural and Control Design Optimization
Co-Design of Wind Turbines
problem considers the structural and control design simultaneously.
y, a combined weighted objective function is considered as following.
Simultaneous
Plant
and
Control
Design:
Z tf
• Considering
pslant
aw2 control
d⌧opt (t))2 dt
min
w1 m (x) + nd
(⌧ (t) esign
x=[xp ,⌧ (t)]T
Blade flap-wise
bending mode
together
produces
system-­‐op7mal
wind
s.t.
xp 0
turbine
designs.
ky k1 y max  0
(3.16)
• Direct
TranscripAon
was
utsed
to
tsolve
the
k⇣k1 ⇣max  0
simultaneous
co-­‐design
problem,
accounAng
Pm (vrated ) Prated 0
for
many
plant
constraints
including
x = Ax + Bu
˙
Elements
of
Wind
Turbine
Co-­‐Design
structural
dynamics.
, w1 > 0 and w2 > 0 are the weights on structural design and control design
involves
independent
geometric
design
Plant
Extension
to
Farm-­‐Level
Co-­‐design
n objective function respectively.
variables.
Control
design
includes
open-­‐loop
opAmal
• AccounAng
for
dynamic
wake
effects
allows
control
of
rotor
torque
based
on
actual
wind
data.
us
to
opAmize
system-­‐level
performance
Model Analysis
instead
of
individual
turbine
performance.
• Simultaneous
Refs: C18, C23
notonicity Analysis opAmal
placement,
turbine
The continuous problem 3.16, after this direct transcription becomes:
design,
and
distributed
control.
0
R
Rh
Ht
der the simultaneous structural and control problem:
Z tf
min
w1 ms (x) + w2
(⌧ (t) ⌧opt (t))2 dt
x=[xp ,⌧ (t)]T
0
s.t.
xp
0
kyt k1 yt max  0
k⇣k1 ⇣max  0
Pm (vrated ) Prated 0
x = Ax + Bu
˙
13
Engineering System Design Lab
Tower aft-tofore bending
mode
Tower side-toside bending
mode
min
w1 ms (x) + w2
x=[x p , x s , x c ]T
(xc (i) ⌧o p t (i))2
i =1
s.t.
(4.1)
nX
t +1
max xs (1, i)) yt m
max xs (2, i)) ⇣m
a x
a x
xp 0
 0; for i = 1 . . . nt + 1
 0; for i = 1 . . . nt + 1
Pm (vr a t e d ) Pr a t e d 0
dt
(x(i + 1) + x(i)) = 0; for i = 1 . . . nt
˙
˙
2
(5.1)
tf t0
where, dt = n t is the step size of simulation. Since there are 7 states
9 in the considered system and 1 control input along with 5 structural dex(i + 1) x(i)

9.
˙
x
been made in the area of black-box surrogate modeling, includx (t) ⇡ j (x (t), xp ) + Bu(t)
ing the use of a family of surrogate models where the best (or
weighted average) surrogate model is used as required [31], and
x
x
where j (x (t), xp ) ⇡ f(x (t), xp ). The co-design problem based
extension of surrogate modeling to multi-objective optimization
this surrogate model is:
problems where high accuracy is maintained in regions near the
Z
Pareto front [32].
x
min J = L(x (t), xp , u(t))dt
While in many cases surrogate modeling has been applied
xp ,u(t)
In some dynamic system design problems, the time derivative function for the
to a single engineering discipline at a time [32] (e.g. structural
state space equations is the computational bottleneck.
x
s.t.
g(x (t), xp )  0
design [33], multibody dynamic systems [34], design based on
•
This occurs often in hierarchical, multi-scale models, especially
x
h(x (t), xp ) = 0
aerodynamics and aero-acoustics [17], etc.), it can be extended
models involving multiple analysis domains, such as aeroelasticity.
˙
to multidisciplinary problems [35]. Co-design problems are mulx(t) ⇡ j(x (t), xp ) + Bu(t)
x
New method: iteratively construct a surrogate model of the derivative
tidisciplinary design optimization problems that involve the coufunction instead of the entire dynamic response.
pled physical and control system design disciplines [36]. This
•
Conventional surrogate modeling cannot capitalize on the dynamic The design method proposed here consists of an inner loop t
introducesproperties. complexity to the surrogate modeling probadditional
system
solves Prob. (3), and an outer loop that iteratively enhances
lem, as accuracy must be provided not only in the design space
surrogate model. The method consists of the following five ste
•
Approximating only the derivative function preserves the fundamental
innature of dynamic of the optimum designis still used. in the
the neighborhood system as simulation point, but also
1. Define the sampling domain in state space and design sp
state space in the neighborhood of the state trajectory that corSignificant computational savings:
responds to the optimum design point. The latter requirement
2. Sample test points in the combined state and design spac
•
in
is An order of magnitude improvement in about accuracy in a
more difficult because we are concerned computation time observed3. Build and validate the state derivative surrogate model
cy only in regions of studies. interest (e.g., near the
j (·):
initial case strategic
region near an entire path as opposed to a single point. This arti4.
[29, 30]. A significant number of developments surrogate modeling (DFSM): Solve the co-design problem
Unique challenges for derivative function have
cle introduces one possible approach for tackling this challenge
˙
(Sample surrogate model
x
in the• areaMust ensure surrogate model accuracy across design/state/control 5. x (t) ⇡accuracyxp ) + Bu(t) ofrequirements, repeat st
of black-box surrogate modeling, includCheck j (x (t), and convergence state derivative
(2)
associated with co-design problems.
for a simple second-order dynamic system)
spaces simultaneously. where the best (or
1–4 until requirements are satisfied
e of a family Consider a general co-design optimization problem formulaof surrogate models
Design of Dynamic Systems with Surrogate
Models of Derivative Functions
•
Convergence
verage) surrogateinvolvesis used ascurrently unknown. of physical sys-(x (t), x ) ⇡ f(x (t), x ). process is illustrated in Fig. 1, and describ
tion that modelproperties required [31], and
the simultaneous optimization
x
where j x
p This iterative The co-design problem based on
p
Refs: C23, TH1
of surrogate modeling tosystem designs: optimization
tem and control multi-objective
in detail
this surrogate model is:in the following subsections.
where high accuracy is maintained in regions near the
Original Formulation:
With surrogate derivative function:
Z
tF
Z
t [32].
2.1 Constructing thepSampling Plan
x
min J = L(x (t), x , u(t))dt
x
min
in many cases surrogate,u(t) J = has (t), xp , u(t))dt
modeling L(x been applied
xp ,u(t) process starts with a definition of the modeling doma
xp
The
0
engineering discipline at a time [32] (e.g. structural
i.e., the regions within the state and design spaces where the s
x
s.t.
g(x (t), xp )  0
(1)
(3)
x
s.t.
], multibody dynamic systemsg(x (t), design0based on
[34], xp ) 
rogate model will be constructed, and the regions from wh
x
h(x (t), xp ) = 0
x
ics and aero-acoustics [17], etc.),(t),can = 0extended
h(x it xp ) be
samples will be obtained. Here the modeling domain is defin
˙
ciplinary problems [35]. Co-design= f(x (t), x are mul˙
using simple bounds (t),the)state and design spaces that are e
x
x (t) ⇡ j (x on xp + Bu(t)
x
x (t) problemsp ) + Bu(t).
ry design optimization problems that involve the coumates of the maximum and minimum values that the plant des
and state variables will attain. Sample points are chosen fr
cal and control is a cost functiondisciplines [36]. overall system design
system design that
This
Here J
The 10
design method proposed here domain using Latin Hypercube Sampl
consists of an inner loop that
Engineering System Design represents the
Lab
within the modeling
additional complexity to the surrogate modeling prob-

10.
Plant Limited Co-Design (PLCD)
Many engineering systems are too complex or expensive to consider clean-sheet
design of a completely new system. If an existing system no longer meets current
needs, a common approach is to redesign limited elements of the system.
System redesign is a
commonly encountered
challenge in industry.
PLCD Design Strategy:
Sensitivity analysis is used to
identify what design changes
would have the greatest impact
on system performance.
Co-design is then used to
produce a limited redesign that
meets new system
requirements.
Example PLCD Problem: Counterbalanced
Robotic Manipulator Design.
1:
IdenAfy
Candidate
Plant
ModificaAons
Identify a limited number of system elements to redesign
while still meeting new system requirements.
2:
Develop
System
Model
3:
Formulate
and
Solve
PLCD
Problem
4:
Verify
and
Repeat
if
Needed
Clean-sheet co-design produces a
manipulator that exploits passive
dynamics to produce near-zero
energy consumption, but is very
expensive to implement.
Refs: J7, J9, C14, C15
PLCD produces a limited redesign
with energy consumption almost as
low as the co-design result, but with
much lower implementation cost.
Engineering System Design Lab
11

11.
Generative Algorithms for Design Optimization
Topological design of non-continuum systems is an extremely complex problem, particularly when continuous variables
must be optimized to evaluate how good each topological design really is.
We use generative algorithms to abstract system topology designs for efficient design space exploration.
•
Instead of optimizing system elements directly, we generate system designs using iterative rules.
•
We then optimize with respect to generative algorithm rules, reducing design problem dimension and complexity,
and supporting exploration of designs across a wide range of dimensions.
Example: L-Systems for Structural Truss Design
•
Lindenmayer parallel rewriting system used to perform cellular-division to produce truss designs.
•
Continuous truss design variables are optimized in an inner loop using sequential linear programming.
•
Stability constraints are embedded within the generative algorithm, guaranteeing that any truss generated is
structurally stable.












12












Engineering System Design Lab


Modified cellular division
process for truss generation:
Sample generated
trusses:








12.
Origami-Based Generative Design
•
•
•
Many generative algorithms are inspired by biological processes (e.g., cellular division,
venation).
In this study we instead observe the creative process of an origami artist, and infer new rules
for generative algorithms based on artistic exploration.
These new generative algorithms can be applied to the design of folded engineering systems.
Example:
• Simple operations can be identified based on the folding of the four basic origami bases
(shown below). These operation have been used successfully in the development of a new
generative algorithm.
Kite Base
Engineering System Design Lab
Fish Base
Bird Base
13
13
Frog Base

13.
GE 100 Trebuchet Project
•
•
•
•
•
Engineering System Design Lab
Members of the ESDL worked together to design and build 30
reconfigurable trebuchet kits that have been used in GE 100 since Fall
2012. All ISE freshmen take GE 100.
This project provides with a hands-on design experience, and helps them
learn firsthand the value of modeling and simulation in design.
GE 100 students learn basic Design of Experiments (DOE), and then
tested their trebuchet designs on the Bardeen Engineering Quad.
After learning about the physics of trebuchets and refining their designs
using a SimMechanicsTM model, GE 100 students tested their trebuchets
again with substantially better results.
The trebuchet kits have been used in outreach efforts, including UIUC
Engineering Open House and local K-12 outreach activities.
14