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TRANSCRIPT
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PROF. DR. JOÃO EDGAR CHAVESFILHO
DEPARTAMENTO DE ELETRICIDADE
Control Systems Engineering, Fourth Edition by
Norman S. Nise
Copyright © 2004 by John Wiley & Sons. All rights
reserved.
SISTEMAS DE CONTROL
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Objetivos
Control Systems Engineering, Fourth Edition by
Norman S. Nise
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Introdução
Control Systems Engineering, Fourth Edition by
Norman S. Nise
Copyright © 2004 by John Wiley & Sons. All rights
reserved.
Os métodos de resposta em freqüênciadesenvolvidos por Nyquist e Bode (anos 30), sãomais antigos do que o método do lugar dasraízes que foi descoberto por Evans 1948.
Esta técnica tem vantagens distintas nasseguintes situações:
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Figure 10.1 The HP 35670A DynamicSignal Analyzer obtains
frequency responsedata from a physicalsystem. Thedisplayed data can be used toanalyze, design, or determinea mathematical model
for the system.
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Courtesy of Hewlett-Packard.
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O Conceito de Resposta emFreqüência
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Figure 10.2 Sinusoidalfrequencyresponse:
a. system;b. transfer function; c. input andoutputwaveforms
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Figure 10.3 System with
sinusoidal input
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Norman S. Nise
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As equações abaixo formam nossa definição de resposta em
Freqüência
M (ω) e Ф(ω) são a magnitude e a fase da resposta em
Freqüênncia.
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Figure 10.4 Frequency responseplots for G(s) = 1/(s + 2):separate magnitudeand phase
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Figure 10.5 Frequency response
plots for G(s)= 1/(s + 2): polar plot
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Figure 10.6
Bode plots of (s + a):a. magnitude plot;b. phase plot.
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Table 10.1
Asymptotic and actualnormalized and scaledfrequency response datafor (s + a)
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Figure 10.7 Asymptotic and actual normalized and scaledmagnitude response of (s + a)
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Figure 10.8 Asymptotic and actual normalized and scaled phaseresponse of (s + a)
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Figure 10.9Normalized and scaledBode plots for a. G(s) = s;b. G(s) = 1/s;
c. G(s) = (s + a);d. G(s) = 1/(s + a)
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Closed-loopunity
feedbacksystem
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Figure
10.11 Bodelog-magnitudeplot for Example 10.2:a. components;b. composite
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Figure
10.12 Bode phaseplot for Example 10.2:a. components;b. composite
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Figure 10.13Bode asymptotesfor normalizedand scaled G(s) =
a. magnitude;b. phase
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22s
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Table 10.4Data for normalized andscaled log-magnitude andphase plots for (s2 + 2 ns +
n2
).Mag = 20 log(M / n2)
(table continues)
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Norman S. Nise
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reserved.
Freq. / n
Mag
(dB) = 0.1
Phase
(deg) = 0.1
Mag
(dB) = 0.2
Phase
(deg) = 0.2
Mag
(dB) = 0.3
Phase
(deg) = 0.3
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Table 10.4
(continued)
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Norman S. Nise
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Freq. / n
Mag
(dB) = 0.5
Phase
(deg) = 0.5
Mag
(dB) = 0.7
Phase
(deg) = 0.7
Mag
(dB) = 1
Phase
(deg) = 1
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Figure 10.14Normalized and scaled
log-magnitude response for
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Figure 10.15 Scaled phase response for
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Table 10.5Data for normalized andscaled log-magnitude andphase plots for
1/(s2
+ 2 ns + n2
).Mag = 20 log(M / n2)
(table continues)
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Norman S. Nise
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Freq. / n
Mag
(dB) = 0.1
Phase
(deg) = 0.1
Mag
(dB) = 0.2
Phase
(deg) = 0.2
Mag
(dB) = 0.3
Phase
(deg) = 0.3
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Table 10.5 (continued)
Control Systems Engineering, Fourth Edition by
Norman S. Nise
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Freq. / n
Mag
(dB) = 0.5
Phase
(deg) = 0.5
Mag
(dB) = 0.7
Phase
(deg) = 0.7
Mag
(dB) = 1
Phase
(deg) = 1
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Figure 10.16Normalized and scaled log magnituderesponse for
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Figure 10.17 Scaled phase response for
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Figure
10.18Bode magnitudeplot for G(s) =(s + 3)/[(s + 2)(s2 + 2s + 25)]:a. components;b. composite
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Table 10.7
Phase diagram slopes for Example 10.3
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(s + 3)/[(s +2)
(s2 + 2s +25)]:a.
components;
b.compositeControl Systems Engineering, Fourth Edition by
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Figure 10.20 Closed-loop controlsystem
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. Mapping contour A through function
F (s)to contour B
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Figure 10.22 Examples of contour mapping
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Figure 10.23
Vector representationof mapping
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Figure10.24 Contour enclosingright half-plane
to determine stability
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Figure 10.25 Mapping examples:a. contour doesnot encloseclosed-loop poles;b. contour doesencloseclosed-loop poles
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Figure
10.26a. Turbine andgenerator;b. block diagramof speed control systemfor
Example 10.4
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Figure 10.27 Vector evaluation of the Nyquist diagramfor Example 10.4:a. vectors on contour at lowfrequency;b. vectors on contour aroundinfinity;c. Nyquist diagram
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Figure 10.28Detouring around open-loop poles:a. poles on contour;b. detour right;c. detour left
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Figure 10.29a. Contour for Example 10.5;b. Nyquist diagram for Example 10.5
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Figure 10.30Demonstrating
Nyquist stability:a. system;b. contour;c. Nyquist diagram
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Figure 10.31 a. Contour for Example 10.6;b. Nyquist diagram
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Figure 10.32a. Contour and root locus of system thatis stable for small gain and unstable for large gain;b. Nyquist diagram
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Figure 10.33a. Contour and root locus of system that is unstable for small gain and stable for large gain;b. Nyquist diagram
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Figure 10.34 a. Portion of contour to be mapped for Example 10.7;b. Nyquist diagram of mapping of positive imaginary axis
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Figure10.35Nyquist diagramshowing gainand phasemargins
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Figure
10.36 Bodelog-magnitudeand phase diagramsfor the system
of Example 10.9
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10.37 Gain and
phasemargins on
the Bodediagrams
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Figure 10.38 Second-order
closed-loopsystem
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Figure
10.39 Representative log-magnitude plot of Eq. (10.51)
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Figure 10.40Closed-loop frequency percent
overshoot for a two-pole system
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vs
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vs.damping
ratiofor:a. settling
time;b. peak
time;c. rise time
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Figure 10.42Constant M circles
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Figure 10.43 Constant N
circles
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Figure
10.44 Nyquist diagramfor Example 10.11 andconstantM and N circles
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10 45
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10.45 Closed-
loopfrequencyresponsefor Example
10.11
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.Ni h l
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. Nicholschart
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Figure 10.47Nichols chart with frequency response for G(s) = K /[s(s + 1)(s + 2)] superimposed.Values for K = 1 and K = 3.16 are shown.
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Figure 10.48 Phase margin vs.damping ratio
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Figure 10.49Open-loop gain vs. open-loop phase angle for –3 dB closed-loopgain
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Fi 10 0
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Figure 10.50
a. Block diagram(figure continues)
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ed)
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ed) b. Bode
diagrams for systemof Example
10.13
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Bode
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Bodelog-
magnitudeplots for Example
10.14
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Bode log-magnitude plot
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Bode log magnitude plotfor
Skill-Assessment Exercise10.10
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10.54
Effect of
delayuponfrequencyresponse
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Figure
10.55Frequency responseplots for G(s) =K/ [s (s + 1)(s + 10)]with a delay of 1 second and
K = 1:a. magnitude plot;b. phase plot
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Figure 10.56Step response for closed-loop systemwith G(s) =5/[s(s +1)(s + 10)]:a. with a 1 second
delay;b. without delay
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Figure
10.57 Bode plots for subsystem withundeterminedtransfer function
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Figure 10.58 Original Bode plots
minus response of G1(s) =25/(s2 + 2.4s + 25)
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Figure 10.59 Original Bode plotminus responseof G1(s)G2(s) =[25/(s2 + 2.4s +25)]
· [90/(s + 90)]
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Figure
10.60 Bode plots for Skill-AssessmentExercise 10.12
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response
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pplots
for theantennacontrol
system(K = 1)
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Figure P10-1 (p. 675) Control Systems Engineering, Fourth Edition by
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P10 2
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P10.2
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Figure
P10.3
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Figure P10-4 (p. 677) Control Systems Engineering, Fourth Edition by
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Figure P10.5
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Fi P10 6
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Figure P10.6
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P10 7
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P10.7
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P10 8
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P10.8
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Figure P10-9 (p. 681)
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Figure P10.10
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Figure P10.11
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Figure P10 12
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Figure P10.12 Soft Arm position
control systemblock diagram
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Figure P10.13
Floppy disk driveblock diagram
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Figure
P10.14 AdeptOne, a four- or five-axisindustrial robot, is used for assembly, packaging,and other manufacturing tasks.
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© 1994 Adept Technology, Inc.
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Figure
P10.15 a. A cutaway viewof a Nikon 35-mm camerashowing parts of the CCDautomatic focusing
system;b. functional blockdiagram;c. block diagram
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Courtesy of Nikon, Inc.
oc agram oa
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aship’s roll
stabilizingsystem
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Table 10.2Bode magnitude plot: slop contribution from each pole and zero in Example 10.2
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Table 10.3Bode phase plot: slop contribution from each pole and zero in Example 10.2
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Table 10.6Magnitude diagram slopes for Example 10.3
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