Post on 27-Jun-2020
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ME 375 System Modeling and Analysis
Section 1 – Introduction
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Spring 2009School of Mechanical Engineering
Douglas E. AdamsAssociate Professor
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What We Will DoExample: vehicle speed control
θθ
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MODEL: MODEL: Solid mechanics, dynamics, circuits, heat transfer, Solid mechanics, dynamics, circuits, heat transfer, fluid mechanics and measurements with a clear fluid mechanics and measurements with a clear understanding of the understanding of the inputs, outputs and assumptionsinputs, outputs and assumptions
Disturbance(Must model this)
Excitation / input(Must model this)
θθ
MgtfBvvMMgBvtfvM
e
e
−≅+−−=
)(sin)(
&
&
(Must model this)(Must model this)
gfe )(
© 2009 D. E. AdamsME 375 – Introduction
Assumptions
Response / output Who gives us this parameter?We must estimate it.
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What We Will DoExample: vehicle speed control
θθ
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ANALYZE: ANALYZE: Differential equations, Differential equations, Laplace, Laplace, time series, time series, frequency frequency spectra, spectra, MatlabMatlab and common senseand common sense
Speed___ Desired speed___ Actual speed
Steady stateerrorApply disturbance
Steady state response
pEncounter steep grade
Transient response
Time© 2009 D. E. AdamsME 375 – Introduction
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What We Will DoExample: vehicle speed control
θθ
1.3
CONTROL: CONTROL: Feedback, Feedback, feedforwardfeedforward, , P, PD, PI, PID, etcP, PD, PI, PID, etc..control with clear understanding of whatcontrol with clear understanding of whatneeds needs to to be changed be changed and and performance performance metricsmetrics
Gravitational force
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due to inclineActualSpeedSpeed
ModelControl
Law- Ensure stability- Reduce response time- Reduce error
© 2009 D. E. AdamsME 375 – Introduction
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Course OutlineIntroduction
1.4
Components/elements
Connections/interconnects
Mechanical
Thermal
Electrical
Electro- ____Hydraulic
Input/output Vs.state-variable
models
Time & frequencydomain tools of
systems analysis
Feedback andsystem design
© 2009 D. E. AdamsME 375 – Introduction
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Modeling ErrorsWhat can happen when we choose the wrong model?
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© 2009 D. E. AdamsME 375 – Introduction
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Modeling ErrorsExample of failure due to un-modeled aeroelastic oscillations
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Errors in model can be of two types:yp
First type (qualitative errors): Should be nonlinear when it is linear, should be time-varying when it is time invariant.Second type (quantitative errors): Model is correct but parameters (numerical, units, etc.) have random or bias errors.
© 2009 D. E. AdamsME 375 – Introduction
Wings should not fall off of aircraft Temperature variations are critical
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ModelingExample: stop-and-go traffic jam dynamics
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Consider the following generic modeling example with g g g pstop-and-go traffic jam dynamics:
k=1 k=2 k=3 1st order
Element law:
Connection law:
( )k k k k kM v B v f t+ =&
[ ]1 1 1( ) ( ) ( )k k k kf t G d t d t+ + += ⋅ −
© 2009 D. E. AdamsME 375 – Introduction
[ ]1 1
1
( ) ( )
( )k k kG v t v t dt
f t A+ += −
=∫What effect does the
neighboring lane of traffichave on these vehicles?
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Interdisciplinary nature of ME 375Analogous systems
Models are the same regardless of the physical domain of interest
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= = =
CurrentCharge
==
yy& velocityTransl
displ. Transl.==
yy& velocityAng
displ. Ang.==
yy& rateFlow
Volume ==
yy&
We only have to understand one mathematical model, but fourphysical systems!
VoltageCurrent
==
uy
ForcevelocityTransl.
==
uy
TorquevelocityAng.
==
uy
PressurerateFlow
==
uy
Input, u Output, y)(tuyyy =++ &&&
© 2009 D. E. AdamsME 375 – Introduction
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Gas pulsations reduce efficiency, reduce valve life and introduce operating noise. There is a trade-off between performance and
Influence of Gas Pulsations in CompressorMulti-cylinder compressor noise, efficiency and reliability
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p g pnoise – faster valves provide greater capacity but more noise.
Current approaches for designing multi-cylinder compressors are empirical involving many iterations (prototypes) prior to manufacture.
Suction Discharge
Suction valve
manifoldg
manifold Discharge valve
Cylinder wall
Piston
© 2009 D. E. AdamsME 375 – Introduction
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The analytical model consists of several parts- First, the fluid mechanics of the suction manifold are modeled.- Second the thermodynamics of the cylinders are modeled
Flow Chart for Analytical Modeling ApproachExample: Air conditioning compressor
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Second, the thermodynamics of the cylinders are modeled.- Third, the valve dynamics are modeled to estimate the mass flow rates.- Fourth, the first three models are combined.- Fifth, the temperature and muffler along the suction pipe are considered.
OperatingparametersValve Dynamics m&
( )tp ,θ
muffler
evapora
Manifold Thermodynamicstor
© 2009 D. E. AdamsME 375 – Introduction
Similar towater bottleresonance
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Analytical ModelsExample: Air conditioning compressor
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11 22 ∂∂ mpp &&
Constant cross section
)(11 *22
022 θθδ
θ−−=
∂∂
−∂∂
rAm
tp
cp
r
)(1 *22
θθδ∂∂∂∂ mphphph &&
Variable cross section
)(22222 θθδθθθ
−=∂
+∂∂
−∂
−rbt
pc
prr
p
512 Hz 503 Hz 512 Hz
© 2009 D. E. AdamsME 375 – Introduction
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Wake Turbulence on AA587Courtesy: Dr. Nick Lieven, Department of Aerospace Engineering, University of Bristol, UK
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Wind
JAL – 747
9/11Ground Zero
AA – A300
Eddy vortices
JFK Runway
© 2009 D. E. AdamsME 375 – Introduction
Courtesy: Dr. Nick Lieven, Department of Aerospace Engineering, University of Bristol, UK
Runway
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Wake Turbulence on AA587Courtesy: Dr. Nick Lieven, Department of Aerospace Engineering, University of Bristol, UK
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Wind
JAL – 747
JFK Runway
AA – A300
Eddy vortices
Runway
© 2009 D. E. AdamsME 375 – Introduction
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Wake Turbulence on AA587Courtesy: Dr. Nick Lieven, Department of Aerospace Engineering, University of Bristol, UK
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Wind
JAL – 747Eddy vortices
JFK RunwayAA – A300
Eddy vortices
© 2009 D. E. AdamsME 375 – Introduction
Aircraft damageto tail
Air Traffic Control
Prevailing Winds
PilotReaction
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Time and Frequency AnalysisRelationship between time and frequency response characteristics
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We utilize time and frequency domain analysis to estimate the q y yfree/forced and transient/steady state linear responses.
Time: Initial portion is transient, final portion is steady state
Frequency: Initial portion is attributed to steady state, final portion is attributed to transient
spon
se
pons
e
portion is attributed to transient
© 2009 D. E. AdamsME 375 – Introduction
Time
Res
Frequency
Res
p
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Feedback Control The concept of feedback to enhance system performance
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We utilize feedback control approaches to achieve better ppperformance than the system can provide on its own:
- Make certain the response is stable- Increase the speed of response (bandwidth)- Reduce the error in the response of the system- Reduce the error due to external disturbances- Reduce the error due to external disturbances
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ActualDesired
ErrorDeal with
error System
Disturbances
© 2009 D. E. AdamsME 375 – Introduction
Desired error y