chapter 13: digital control systems 1 ©2000, john wiley & sons, inc. nise/control systems...
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©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems1
Chapter 13
Digital Control Systems
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems2
Figure 13.1Conversion of antennaazimuth positioncontrol system from:a. analog control tob. digital control
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems3
Figure 13.2a. Placement of the digital computer within the loop;b. detailed blockdiagram showingplacement of A/D and D/A converters
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems4
Figure 13.3Digital-to-analogconver ter
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems5
Figure 13.4Steps in analog-to-digital conversion:
a. analog signal;b. analog signal after sample-and-hold;c. conversion ofsamples to digitalnumbers
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Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems6
Figure 13.5Two views of uniform-ratesampling:a. switch opening and closing;b. product of timewaveform andsampling waveform
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems7
Figure 13.6Model of sampling with a uniform rectangularpulse train
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Chapter 13: Digital Control Systems8
Figure 13.7Ideal sampling and thezero-order hold
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Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems9
Table 13.1Partial table of z- and s-transforms
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Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems10
Table 13.2z-transform theorems
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems11
Figure 13.8Sampled-datasystems:a. continuous;b. sampled input;c. sampled inputand output
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Chapter 13: Digital Control Systems12
Figure 13.9Sampled-data systems and their z-transforms
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Chapter 13: Digital Control Systems13
Figure 13.10Steps in blockdiagram reductionof a sampled-data system
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems14
Figure 13.11Digital system forSkill-AssessmentExercise 13.4
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems15
Figure 13.12Computer-controlledtorches cut thicksheets of metal usedin construction
© BlairSteitz/Photo Researchers.
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems16
Figure 13.13Mapping regions of the s-plane onto the z-plane
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems17
Figure 13.14Finding stability ofa missile controlsystem:a. missile;b. conceptual blockdiagram;c. block diagram;d. block diagramwith equivalent singlesampler
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems18
Figure 13.15Digital system forExample 13.7
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Chapter 13: Digital Control Systems19
Table 13.3Routh table for Example 13.8
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems20
Figure 13.16Digital system forSkill-AssessmentExercise 13.5
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems21
Figure 13.17a. Digital feedbackcontrol system forevaluation ofsteady-state errors;b. phantom samplersadded;c. pushing G(s) and its samplers to the right past the pickoff point;d. z-transformequivalent system
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems22
Figure 13.18Constant dampingratio, normalizedsettling time, andnormalized peak time plots on the z-plane
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Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems23
Figure 13.19The s-plane sketch of constant percentovershoot line
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Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems24
Figure 13.20Generic digitalfeedback controlsystem
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems25
Figure 13.21Digital feedbackcontrol forExample 13.10
©2000, John Wiley & Sons, Inc.
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Chapter 13: Digital Control Systems26
Figure 13.22Root locusfor the systemof Figure 13.21
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Chapter 13: Digital Control Systems27
Figure 13.23Root locus for the system of Figure 13.21 with constant0.7 damping ratiocurve
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems28
Figure 13.24Sampled stepresponse of thesystem ofFigure 13.21 withK = 0.0627
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems29
Figure 13.25a. Digital controlsystem showingthe digital computerperformingcompensation;b. continuous systemused for design;c. transformed digitalsystem
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems30
Figure 13.26Closed-loop responsefor the compensatedsystem of Example13.12 showing effectof three differentsampling frequencies
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems31
Figure 13.27Block diagramshowing computeremulation of a digitalcompensator
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems32
Figure 13.28Flowchart for a second-orderdigital compensator
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Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems33
Figure 13.29Flowchart toimplement
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems34
Figure 13.30Antenna controlsystem:a. analogimplementation;b. digitalimplementation
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Chapter 13: Digital Control Systems35
Figure 13.31Analog antenna azimuth positioncontrol system converted to a digital system
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Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems36
Figure 13.32Root locussuperimposed over constant damping ratio curve
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Chapter 13: Digital Control Systems37
Figure 13.33Sampled stepresponse of theantenna azimuthposition controlsystem
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Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems38
Figure 13.34Simplified blockdiagram of antennaazimuth controlsystem
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Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems39
Figure 13.35Closed-loop digitalstep response forantenna controlsystem with a leadcompensator.
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Chapter 13: Digital Control Systems40
Figure 13.36Flowchart for digital lead compensator
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Chapter 13: Digital Control Systems41
Figure P13.1
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Chapter 13: Digital Control Systems42
Figure P13.2
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems43
Figure P13.3
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems44
Figure P13.4
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems45
Figure P13.5
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems46
Figure P13.6
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems47
Figure P13.7
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems48
Figure P13.8
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems49
Figure P13.9Simplified blockdiagram for robotswing motion
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems50
Figure P13.10Simplified blockdiagram of a floppydisk drive
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems51
Table 13.1Partial table of z- and s-transforms
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems52
Table 13.2z-transform theorems
©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering, 3/e
Chapter 13: Digital Control Systems53
Table 13.3Routh table for Example 13.8
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