modelingandsim

8/11/2019 ModelingAndSim

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Introduction to Modeling and Simulation

John A. Christian Aerospace Engineering and Engineering Mechanics

The University of Texas at Austin

Suggested Readings:NEW SMAD, Chapter 14

ASE 166M Spacecraft Systems Laboratory


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The purpose of this class

Learn how to model spacecraft subsystem performance

Draw on experience and knowledge learned in previousclasses

Leads to a few questions What kind of spacecraft are there? What are the common spacecraft subsystems? What do I need to know about modeling and simulation?

What are the basics of spacecraft subsystem sizing?

ASE 166M Spacecraft Systems Laboratory 2


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Classes of Spacecraft & Mission Types

Crewed Spacecraft

Crew transportation (Space Shuttle, Orion, Soyuz) Space stations (ISS, MIR) Surface systems (habitat, etc)

Robotic Spacecraft

Near Earth Earth observing (weather, surveillance, Earth science) Communications (TDRSS) Scientific (Hubble)

Planetary

Flyby (New Horizons, Voyager, Cassini) Orbiter (MRO, MESSENGER) Lander (Phoenix, MERs, MSL) Probe (Huygens)



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Spacecraft Subsystems

Common Subsystems

Propulsion Attitude Determination & Control System (ADCS) Communications Command & Data Handling (C&DH) Power Structures Thermal Control System (TCS)

Other Subsystems (depending on spacecraft application) Thermal Protection System (TPS) Landing Systems Environmental Control and Life Support System (ECLSS)


We will coverthese subsystemsthis semester


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Parametric Modeling

This semester we will be developing conceptual design ( pre-phase A )level tools. If you need more fidelity, youll have to call in the subsystemexperts.

Many of the models we develop will be parametric. A parametric modelis usually a series of mathematic relationships that relate a metric ofsystem performance (e.g. mass, power, cost) to some set of designvariables or parameters .

Parametric models are useful during spacecraft design because: they usually give you enough insight to make initial design decisions

they dont require as much information as more sophisticated design toolsand analyses

they easily allow for trade studies between multiple subsystems withcompeting interests (this is your final project!)



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All models are wrong


All models are wrong, but some models are useful .

--George Box

In 1618-1621 Kepler suggested the following modelfor the motion of the Planets about the Sun:

1. The orbit of each planet is in an ellipse with the sun at

one focus2. The heliocentric radius vector of each planet sweepsover equal area in equal time

3. The square of the orbital period is proportional to thecube of the ellipse semimajor axishttp://www.thejubileeacademy.org/articles/2006_

solar_system_image.html

Later, Newton would suggest a more accurate model: 3 /1

3/

i P

n

P ii i P

i P P P P r

mmGm rrF

Which model is better?


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All models are wrong


All models are wrong, but some models are useful .

--George Box

m F Newton suggested the following model: rrF mm

dt d

But this is nothing more than a mathematical abstraction of theobserved behavior of a physical system. In fact, many years laterEinstein demonstrated that Newtons model is wrong.

Einstein suggested this model:

This model has been shown to be more accurate than Newtonsmodel.

But is the model perfect? More importantly, does it matterif the model is perfect?

22

0

1 cv

mdt d

mdt d r

rF


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Wait, are you saying everything I know is wrong?


Yes.

But heres the beauty of engineering:You dont have to be exactly right, you just have to be close enough.

The solution to almost any problem may be made arbitrarily complex. Dontdevelop a complicated model when a simple one will get the job done. Morecomplicated models take more resources to develop, more resources tovalidate/verify, and more resources to run.

This brings up a central point in modeling and simulation.


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Deep thoughts on model fidelity

Assumption : Almost all models involve some form of simplifyingassumptions or approximations to make the problem solvable. Theimportant question is what errors are you introducing by simplifying theproblem.

Error : Are these errors important and do they effect the results? Knowingwhat assumptions to make (and when to make them) is what separates

you from your computer.

Range : Be aware of the range of validity of your model. Again, alwaysask yourself: When do the simplifying assumptions used to make theproblem tractable break down?

Results : Engineers are frequently asked to perform analysis usingexisting codes and models. Be a smart user. How much do you trust theresults? Always know the range of validity of the model. Always researchthe model assumptions and know the models limitations.



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More deep thoughts on model fidelity

Significant Figures : Be cautious of the number of significant digits you report inyour results. Think of it this way, the number of digits you use represents thedegree to which you believe the outcome of your model.

There are at least two main reasons to limit the number of digits you report:1. Your input variables are only known to a certain level of precision2. The approximations made by model introduce errors. Do not report results to

a precision that implies a higher-fidelity model than what you actually used.

Fidelity : Be cautious of disparate fidelity between models used in the sameanalysis. The fidelity of the analysis will be limited by your least accurate model.Can you lower the fidelity of some of your models (thus reducing modeling effort)without impacting the overall fidelity of the output results?


The idea is to be approximately right, rather than exactly wrong . --John Tukey


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An Example


Compute the range, r, of a projectile fired from acannon with an initialvelocity, v 0 , of 11 m/s at aninclination, , of 18 degrees.

Most of you would probably take the following approach: Assume a flat Earth and that gravity is constant, g 0, and acts down. Neglect drag.

Under these assumptions, you could derive the following equations for projectile motion:

a y = -g 0vy = -g 0*t + v 0*sin() y = -0.5*g 0*t2 + v 0*sin( )*t + y 0

g0

a x = 0vx = v 0*cos( ) x = v 0*cos( )*t + x 0

Experience suggests that some of you might also say that g 0 = 9.80665 m/s 2. You may go on tosay that the projectile would impact the ground at x = 11.22792 m.

2 m

But this level of accuracy is notconsistent with the assumptions

made in your model!!!

Instead, you should say something like g 0 = 9.81 m/s 2 and x impact = 11.2 m.


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Simulation

Simulation is the act of subjecting your model to

environments and inputs that are in some wayrepresentative of what the real system will experience

Common types of simulation include: Computer based simulations Field tests



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Multidisciplinary Simulation

What if I want to create an integrated simulation using models frommany different disciplines (e.g. trajectory, power, propulsion, thermal,cost, risk, etc.)?

There are at least three ways to accomplish this task:1. Monolithic Code: rewrite all models as individual subroutines (frequently with

approximations such as look-up tables, etc.) and integrate subroutines into asingle code

2. Manually Integrated Models: each model is executed by a local expert and theresults are integrated manually through meetings, telephone calls, emails, etc.

3. Tightly Integrated Models: shell scripts or wrappers are added around existing(legacy) models. These wrapped models are electronically integrated forautomated execution and data exchange


ManuallyIntegrated

Models

faster, single user

MonolithicCode

TightlyIntegrated

Models

expert involvement,more fidelity


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Why is Integrated Design Important?


Image Ref: NASA Chief Engineers Office.


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UserInputs

MissionProfile(?V)

Comm.

Mass andSizing

Power

Propulsion

Geometry

GN&C(ADCS)

Thermal

N2 Diagrams

N2 Diagrams are also called Design Structure Matrices (DSMs)

DSMs are used to gain an understanding of how information ispassed between different subsystems (or functions) within asystem

Feedback

Feed-forward


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N2 Diagrams


Modeloutput toupstreamoutput todownstream

input fromdownstream

input fromupstream

D

A

E

C

B

The presence of a dot signifies thatinformation is passed from one model

to another at the indicated intersection

D

E

Feedback requires iteration. The tworelevant models must iterate until the

outputs and inputs match.

In this case, for example, on the first pass through the N 2 diagram you must guess the inputs from E to D(because you have not yet run model E). After you run D, you use the outputs to run E. You will see that theoutputs of E probably do not match your guess. Therefore you rerun D using the updated values of theoutputs from E. The new outputs of D will require you to rerun E, and so on. You must continue to iterate untilthe process converges.

Order of model execution

The design is said to be closed whenall iterations have converged and all

the inputs/outputs to all the model are

consistent with each other.


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Fixed-Point Iteration

Iteration is frequently performed through fixed-pointiteration (FPI). Iterations in MS Excel are performedusing this method. This is also sometimes called themethod of successive substitution.

It is important to know how this technique works becausethis method is not universally applicable and this maycause MS Excel to crash for some problems.


D

E

A fixed -point is defined as follows:

Using this definition of a fixed point,a FPI routine may be set up:

** x g x

x

y y = x

y = g ( x)

x* nn x g x 1


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Fixed-Point Iteration


x

y y = x y = g ( x)

x0 x1 x2 x

y y = x y = g ( x)

x0 x1 x2 x3

stable fixed pointunstable fixed point

A FPI routine should be stable if - 1 < g(x *) < 1

Consider the following two examples

y0

y1


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Fixed-Point Iteration Example


Consider the following problem:

xn+1 = log 10 (xn+2)x0 = 4.0

Iter Num x n xn+1 =g(xn)0 4.00000 0.778151 0.77815 0.443762 0.44376 0.388063 0.38806 0.378044 0.37804 0.376225 0.37622 0.375896 0.37589 0.37583

7 0.37583 0.375818 0.37581 0.375819 0.37581 0.37581

This problem converges to within5 significant digits of the fixedpoint after 8 iterations


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N2 Diagrams as FPI


A

B

C

nn x g x 1Recall the simple FPI defined earlier:

Let the variable passed from C to A be x

But we need a guess of x before we can begin theanalysis.

Lets try closing thisfeedback with FPI. Breakthe link and call your initialguess x0

x0

After one complete pass through the DSM, wehave a new value of x that is produced bymodule C, this will be x1

Replace x0

with x1

andrepeat the FPI process untilthe value for x converges towithin a specified tolerance

g ( x0) x1


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N2 Diagram Rescheduling

Rescheduling is the process of rearranging the order of execution ofmodels within a simulation

The objective of rescheduling is usually to reduce the simulation runtime


Massand

Sizing

Cust.Req.

Cost

Risk

Traj.

Risk

Cust.Req.

Cost

Massand

Sizing

Traj.


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N2 Example 1 Launch Vehicle Design


T

W u

W b

S

Opt. ,r,T_W 0

Wgross

Ae, Tvac ,Isp vac

Vsplit

Wgross , S ref

MR upper

r,T_W 0

Wgross , S ref ,W prop , W land

Tsl /W e

Wupper

Wdry_booster

MR booster

W_S

Wgross

P p e

N2 Diagram in ModelCenter

You may see the intersectionslabeled to indicate what variablesare being passed between models

Christian, J.A., Final Project: Launch Vehicle Design, AE6374/AdvancedDesign Methods II, Georgia Institute of Technology, Spring 2006.

Christian, J.A., DCarlo, P.A., Otero, R.E., Salmon, J.L.,


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N2 Example 2 Mars EDL Design


Aerodynamics model computespressure distribution and lift/drag

coefficients

Vehicle sizer and optimizer adjustsvehicle geometry to meet mission

needs

Supersonic inflatable aerodynamicdecelerator (IAD) model dynamically

scales to meet mission needs

-6 -4 -2 0 2 -20

20

0.5

1

1.5

2

2.5

Crossrange, kmDownrange, km

A l t i t u

d e ,

k m

Powered descent guidancealgorithm attempts to guide vehicle

to specified landing site

9

7

5a

3

5b

5c 5d

8

6

5e

4

6.5 m 8.4 m

4 m

Christian, J.A., D Carlo, P.A., Otero, R.E., Salmon, J.L.,and Sanders, J.L. An Entry System for Delivering

Massive Payloads to the Martian Surface, AE8803/Planetary Entry, Georgia Institute of

Technology, Spring 2007.


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