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Transcript of Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons....
![Page 1: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/1.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.1 (p. 664)Two different structures for the realization of an accumulator. (a) Feed-forward structure of infinite order. (b) First-order recusive structure.
![Page 2: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/2.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.2 (p. 665)(a) Simple parallel RC circuit driven by current source i(t). (b) Block diagram of the RC circuit, formulated in terms of two variables: the current i1(t) through the capacitor C and the voltage v(t) across c. This figure clearly displays the presence of a feedback loop, even though there is no physical evidence of feedback in the RC circuit itself.
![Page 3: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/3.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.3 (p. 666)Block diagram representations of single-loop feedback system: (a) time-domain representation and (b) s-domain representation.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.4 (p. 667)s-domain representation of a scheme for measuring the return difference F(s), which is defined as the difference between the unit signal applied to the plant and the return signal G(s)H(s).
![Page 5: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/5.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.5 (p. 667)s-domain representation of a scheme for measuring the loop transfer function L(s).
![Page 6: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/6.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.6 (p. 669)Block diagram of single-loop feedback amplifier.
![Page 7: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/7.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.7 (p. 670)Block diagram of a single-loop feedback system that includes a disturbance inside the loop.
![Page 8: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/8.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.8 (p. 671)Feedback system for Problem 9.2.
![Page 9: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/9.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.9 (p. 674)(a) Conventional symbol for operational amplifier. (b) Operational amplifier with input and output voltages.
![Page 10: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/10.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.10 (p. 674)Operational amplifier embedded in a single-loop feedback circuit.
![Page 11: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/11.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.11 (p. 675)Ideal model for the feedback circuit of Fig. 9.10.
![Page 12: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/12.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.12 (p. 676)Reformulation of the feedback circuit of Fig. 9.10 so that it corresponds to the basic feedback system of Fig. 9.3(b).
![Page 13: Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.](https://reader035.fdocuments.us/reader035/viewer/2022081420/56649f1c5503460f94c332f8/html5/thumbnails/13.jpg)
Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.13 (p. 677)Operational amplifier circuit used as an integrator in Example 9.2
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.14 (p. 678)Operational amplifier circuit for Example 9.3.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.15 (p. 679)(a) Block diagram of open-loop control system and (b) configuration for calculation of the error signal e(t).
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.16 (p. 680)Control system with unity feedback.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.17 (p. 681)Reformulation of the feedback control systems of Fig. 9.16.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.18 (p. 681)A pair of equivalent block diagrams used to change fig. 9.16 into the equivalent form shown in Fig. 9.17.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.19 (p. 683)Transient response of first-order system, plotted against the normalized time t/, where is the time constant of the system.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.20 (p. 684)Transient response of the second-order system with T(0) = 1 and n = 1 for three different values of the damping ratio : overdamped ( = 2), critically damped ( = 1), and underdamped ( = 0.1)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.21 (p. 686)Effect of feedback, with increasing K, on the locations of the poles of a first-order system.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.22 (p. 687)Effect of feedback, with increasing K, on the locations of the poles of a second-order system. The loop transfer function has poles at s = 0 and s = –1/.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.23 (p. 691)RC audio oscillataor.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.24 (p. 694)Illustrating the angle criterion of Eq. (9.67) and the magnitude criterion of Eq. (9.68) for the loop transfer function .
)/ - )(1/ - 1 (
)/ - (1 )(
d*sdss
csKsL
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.25 (p. 697)Diagram showing the intersection point (i.e., the centroid of the root locus) of the three asymptotes for the feedback system of Example 9.8.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.26 (p. 698)Root locus of third-order feedback system with loop transfer function
.3) 2)( 1)( (
6 )(
sss
KsL
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.27 (p. 698)Unity-feedback system for Example 9.9.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.28 (p. 700) Root locus of closed-loop control system with loop transfer function
12) 4)( - (
2) (0.5 )(
sss
sKsL
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.29 (p. 701)(a) Contour C traversed in counterclockwise direction in s-plane. (b) and (c) Two-possible ways in which contour C is mapped onto F-plane.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.30 (p. 702)Illustration of the definition of encirclement. As point s1 traverses contour C in the s-plane in the counterclockwise direction, as shown in (a), point A is encircled by contour only once and point B is encircled twice, both in the clockwise direction in the F-plane, as shown in (b).
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.31 (p. 703)Diagram for Problem 9.14.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.32 (p. 704)Nyquist contour.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.33 (p. 705)Nyquist diagrams representing (a) a stable system and (b) an unstable system.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.34 (p. 706)Nyquist diagram for three-stage feedback amplifier with loop frequency response with K = 6.
3) 2)( 1)( (
6 )(
jjj
KjL
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.35 (p. 708)Straight-line approximation to gain component of Bode diagram for open-loop response for K = 6.
3) 2)( 1)( (
6 )(
jjj
KjL
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.36 (p. 708)(a) Exact gain response and (b) phase response for open-loop response for K = 6.
3) 2)( 1)( (
6 )(
jjj
KjL
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.37 (p. 709)Illustration of the definitions of (a) gain margin and gain crossover frequency and (b) phase margin and phase crossover frequency.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.38 (p. 711)Nyquist diagram illustrating the notion of conditional stability.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.39 (p. 712)Block diagram of sampled-data feedback control system, which includes both discrete-time and continuous-time components.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.40 (p. 713)Impulse response of zero-order hold.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.41 (p. 713)Model of sampled-data feedback control system shown in Fig. 9.39.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.42 (p. 715)Illustration of Property 2 of the Laplace transform of a sampled signal. (a) Pole-zero map of A(s). (b) Pole-zero map ofwhere s is the sampling frequency.
),(1
)( sks
jk - sAT
sA
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.43 (p. 716)Block diagram of sampled-data system obtained by reformulating the model of Fig. 9.41
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.44 (p. 720)Root locus of sampled-data system with loop transfer function
)21
1)( - (
21
)( -z z
KzzL
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.45 (p. 723)Root locus diagram illustrating the application of MATLAB command r l o c f i n d.
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure 9.46 (p. 726)Harold Black’s original feedback diagram and equation.
0) (for - 1
Input
Output de
μβ
μ
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.22 (p. 727)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.23 (p. 727)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.24 (p. 727)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.25 (p. 728)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.26 (p. 728)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.42 (p. 729)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.43 (p. 729)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.44 (p. 729)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.46 (p. 730)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.47 (p. 731)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.48 (p. 731)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.49 (p. 731)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.50 (p. 731)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.51 (p. 731)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.53 (p. 732)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.54 (p. 732)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.55 (p. 733)
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Signals and Systems, 2/E by Simon Haykin and Barry Van VeenCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.
Figure P9.56 (p. 733)