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Chapter 13: Digital Control Systems 1 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Chapter 13 Digital Control Systems

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Chapter 13: Digital Control Systems 2 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.1 Conversion of antenna azimuth position control system from: a. analog control to b. digital control

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Chapter 13: Digital Control Systems 3 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.2 a. Placement of the digital computer within the loop; b. detailed block diagram showing placement of A/D and D/A converters

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Chapter 13: Digital Control Systems 4 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.3 Digital-to-analog conver ter

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Chapter 13: Digital Control Systems 5 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.4 Steps in analog- to-digital conversion : a. analog signal; b. analog signal after sample-and- hold; c. conversion of samples to digital numbers

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Chapter 13: Digital Control Systems 6 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.5 Two views of uniform-rate sampling: a. switch opening and closing; b. product of time waveform and sampling waveform

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Chapter 13: Digital Control Systems 7 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.6 Model of sampling with a uniform rectangular pulse train

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Chapter 13: Digital Control Systems 8 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.7 Ideal sampling and the zero-order hold

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Chapter 13: Digital Control Systems 9 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Table 13.1 Partial table of z- and s-transforms

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Chapter 13: Digital Control Systems 10 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Table 13.2 z-transform theorems

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Chapter 13: Digital Control Systems 11 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.8 Sampled-data systems: a. continuous; b. sampled input; c. sampled input and output

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Chapter 13: Digital Control Systems 12 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.9 Sampled-data systems and their z-transforms

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Chapter 13: Digital Control Systems 13 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.10 Steps in block diagram reduction of a sampled-data system

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Chapter 13: Digital Control Systems 14 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.11 Digital system for Skill-Assessment Exercise 13.4

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Chapter 13: Digital Control Systems 15 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.12 Computer-controlled torches cut thick sheets of metal used in construction © BlairSteitz/Photo Researchers.

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Chapter 13: Digital Control Systems 16 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.13 Mapping regions of the s-plane onto the z -plane

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Chapter 13: Digital Control Systems 17 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.14 Finding stability of a missile control system: a. missile; b. conceptual block diagram; c. block diagram; d. block diagram with equivalent single sampler

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Chapter 13: Digital Control Systems 18 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.15 Digital system for Example 13.7

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Chapter 13: Digital Control Systems 19 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Table 13.3 Routh table for Example 13.8

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Chapter 13: Digital Control Systems 20 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.16 Digital system for Skill-Assessment Exercise 13.5

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Chapter 13: Digital Control Systems 21 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.17 a. Digital feedback control system for evaluation of steady-state errors; b. phantom samplers added; c. pushing G(s) and its samplers to the right past the pickoff point; d. z-transform equivalent system

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Chapter 13: Digital Control Systems 22 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.18 Constant damping ratio, normalized settling time, and normalized peak time plots on the z-plane

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Chapter 13: Digital Control Systems 23 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.19 The s-plane sketch of constant percent overshoot line

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Chapter 13: Digital Control Systems 24 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.20 Generic digital feedback control system

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Chapter 13: Digital Control Systems 25 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.21 Digital feedback control for Example 13.10

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Chapter 13: Digital Control Systems 26 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.22 Root locus for the system of Figure 13.21

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Chapter 13: Digital Control Systems 27 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.23 Root locus for the system of Figure 13.21 with constant 0.7 damping ratio curve

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Chapter 13: Digital Control Systems 28 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.24 Sampled step response of the system of Figure 13.21 with K = 0.0627

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Chapter 13: Digital Control Systems 29 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.25 a. Digital control system showing the digital computer performing compensation; b. continuous system used for design; c. transformed digital system

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Chapter 13: Digital Control Systems 30 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.26 Closed-loop response for the compensated system of Example 13.12 showing effect of three different sampling frequencies

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Chapter 13: Digital Control Systems 31 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.27 Block diagram showing computer emulation of a digital compensator

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Chapter 13: Digital Control Systems 32 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.28 Flowchart for a second-order digital compensator

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Chapter 13: Digital Control Systems 33 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.29 Flowchart to implement

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Chapter 13: Digital Control Systems 34 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.30 Antenna control system: a. analog implementation; b. digital implementation

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Chapter 13: Digital Control Systems 35 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.31 Analog antenna azimuth position control system converted to a digital system

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Chapter 13: Digital Control Systems 36 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.32 Root locus superimposed over constant damping ratio curve

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Chapter 13: Digital Control Systems 37 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.33 Sampled step response of the antenna azimuth position control system

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Chapter 13: Digital Control Systems 38 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.34 Simplified block diagram of antenna azimuth control system

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Chapter 13: Digital Control Systems 39 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.35 Closed-loop digital step response for antenna control system with a lead compensator.

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Chapter 13: Digital Control Systems 40 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure 13.36 Flowchart for digital lead compensator

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Chapter 13: Digital Control Systems 41 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.1

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Chapter 13: Digital Control Systems 42 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.2

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Chapter 13: Digital Control Systems 43 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.3

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Chapter 13: Digital Control Systems 44 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.4

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Chapter 13: Digital Control Systems 45 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.5

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Chapter 13: Digital Control Systems 46 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.6

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Chapter 13: Digital Control Systems 47 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.7

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Chapter 13: Digital Control Systems 48 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.8

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Chapter 13: Digital Control Systems 49 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.9 Simplified block diagram for robot swing motion

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Chapter 13: Digital Control Systems 50 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Figure P13.10 Simplified block diagram of a floppy disk drive

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Chapter 13: Digital Control Systems 51 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Table 13.1 Partial table of z- and s-transforms

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Chapter 13: Digital Control Systems 52 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Table 13.2 z-transform theorems

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Chapter 13: Digital Control Systems 53 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Table 13.3 Routh table for Example 13.8

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