1. No category

Someapplicationissues…
Theremainingtopicsofthiscourseistointroducesomekeyideason
howtodesigncontrolsystemsforsomepracticalproblemssuchas
flightcontrolandharddiskdriveservosystems.
Interestedreadersshouldrefertothefollowingmonographformore
detailedmaterials…
Cai,Chen,Lee UnmannedRotorcraftSystems Springer,NewYork,2011
Chen,Lee,Peng,Venkataramanan HardDiskDriveServoSystems(2nd ed.)

Springer,NewYork,2006
LINEAR SYSTEMS &CONTROL ~PAGE 180
BEN M.CHEN,NUSECE
FlightControlSystems
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Overallflightcontrolstructure
A3layerautomaticflightcontrolstructure
Guidance&
Navigation
Outer‐loop
Control
Inner‐loop
Control
 Innerloop(H)controlistoguaranteethestabilityoftheaircraftattitude
 Outerloop(RPT)controlistocontroltheaircraftpositionandvelocity
 Guidanceandnavigation aretogeneratereferencesof flightmissionsforouter‐loop
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Detailedstructureoftheflightcontrolsystem
Winddisturbance
H control
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Inner‐loopcommandgenerator
Theinner‐loopcommandgeneratorisgivenas
r 
whereG isaconstantmatrix
 

G
a

b,r
 r
fornormalapplications…
 
 r
Anonlineardynamicsinversionmightbenecessaryforhighperformancemaneuvers.
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Outer‐loopcontrolstructure
道
Avirtualactuator
withaknownbandwidth
RPT control,whichiscapableoftrackingposition,velocityandacceleration references!
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Frequencyresponseofthevirtualactuator…HeLion &SheLion
XChannel
ZChannel
Frequencyresponseofthevirtualactuator…
UnstableZeros!
YChannel
Frompracticalpointofview,itissafe
toignorethemsolongastheouter‐
loopbandwidthiswithin1rad/sec…
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CompositeNonlinearFeedbackControl
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Keyidea…
1.5
Response with a small damping ratio
fastrise
time
Magnitude
1
no
overshoot
Response with a large damping ratio
0.5
CNFControl
0
0
LINEAR SYSTEMS &CONTROL ~PAGE 188
1
2
3
4
5
Time
6
7
8
9
10
BEN M.CHEN,NUSECE
CNFControl
CNFcontrolconsistsofalinearlawandanonlinearfeedbacklawwithanyswitching
element.UnlikethePTOSandMSCcontrollaws,boththelinearandnonlinear
controllersinCNFareinoperationallthetime.Thelinearpartisdesignedtoyielda
closed‐loopsystemwithasmalldampingratioforaquickresponse.Ontheother
hand,thenonlinearpartisusedtoincreasethedampingratiooftheclosed‐loop
systemasthesystemoutputapproachesthetargetreferencetoreducetheovershoot
causedbythelinearpart.
Aswillbeseenshortly,CNFcontrolhasemergedasaneffectivetoolindesignmany
controlsystemsthatrequirefasterdynamicalresponseandsmallovershootor
undershoot.
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CNFControlFormulation
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PreliminarySetup
We first follow the usual practice to augment an integrator into the system by defining
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Step‐by‐StepDesignProcedureforStateFeedbackCase
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MainResult
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SelectionofNonlinearFeedbackParameters
The closed-loop system comprising the augmented plant and the CNF control
law can be expressed as
It is clear that the closed-loop poles can be changed by the nonlinear function .
Such a mechanism can be interpreted using the classical root locus theory
where
, whose zeros can
be properly pre-selected by choosing an appropriate another design parameter
W (this is related to the so-called zero placement problem).
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Illustrationofclosed‐loopsystempolesvsthenonlinearfunction…
Root Locus
1
0.945
0.974
0.9
0.82
0.66
0.4
0.66
0.4
0.8
0.99
0.6
0.4
0.997
Imaginary Axis
0.2
4
0
3
2
1
-0.2
-0.4
0.997
-0.6
0.99
-0.8
0.974
-1
-5
-4.5
-4
0.945
-3.5
-3
0.9
-2.5
-2
0.82
-1.5
-1
-0.5
道
0
Real Axis
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Thefollowingisoneofthemanychoicesofthenonlinearfunction:
ZongliLin
LINEAR SYSTEMS &CONTROL ~PAGE 197
KemaoPeng
GuoyangCheng
WeiyaoLan
BEN M.CHEN,NUSECE
CNFControlToolkit– TheMainPanel
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TheCNFControlLawtogetherwithanappropriatenotchfilter:
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FinalNote:SystemsAdaptationFrameworkforStockModeling
Whatisthemarketinput?
actualstockprice
externalinput
Plant
(S)
r (n)
markettrends
(slowsub‐system)
Ŝ
InternalModel
(I)
+
‐
pˆ i ( n )
AdaptiveFilter
(A)
LINEAR SYSTEMS &CONTROL ~PAGE 208
identification
error
internal
pˆ i ( n  1) stockprice
pˆ ( n  1)
z 1
ei ( n )
external
force
p (n)
eˆi ( n  1)
z 1
+
e(n)
‐
pˆ (n)
estimated
stockprice
exogenousinfluences(fastsubsystem)
BEN M.CHEN,NUSECE
Turningperiodforecasting
16,000
14,000
FFT
12,000
10,000
8,000
6,000
4,000
2,000
1996
1998
2000
2002
2004
2006
2008
Turning
period
identification
LINEAR SYSTEMS &CONTROL ~PAGE 209
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That’sall,folks!
ThankYou!
BugsBunny
1940–
Lifeisabunchofintegratedchains!B.M.C.
生命无非就是一堆积分串！
有的自始至终，有的有始无终，有的无始有终，有的无始无终
LINEAR SYSTEMS &CONTROL ~PAGE 210
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