10 Digital Control Systems Sampling, Z-transform, transfer function

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10Digital Control SystemsSampling, Z-transform,
transfer function

• Reg1_slide4
• Chap. 13.1-3,4,(5)
• J.Nybo
• Rev.14.04.04

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From analog to digital system
Figure 13.1Conversion of antennaazimuth
positioncontrol system froma. analog control
tob. digital control
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Block-diagram of digital system
Figure 13.2a. Placement of the digital computer
within the loopb. detailed blockdiagram
showingplacement of A/D and D/A converters
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Digital-to-analogconver ter
Figure 13.3Digital-to-analogconverter
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Steps in analog-to-digital conversion
Figure 13.4Steps in analog-to-digital
conversiona. analog signalb. analog signal
after sample-and-holdc. conversion ofsamples
to digitalnumbers
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Two views of uniform-rate sampling
Figure 13.5Two views of uniform-ratesamplinga.
switch opening and closingb. product of
timewaveform andsampling waveform
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Model of sampling with a uniform rectangular
pulse train

Figure 13.6Model of sampling with a uniform
rectangularpulse train
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Ideal sampling and thezero-order hold
Figure 13.7Ideal sampling and thezero-order hold
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Zero Order Hold
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Z-transform of a sampled signal
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Table 13.1Partial table of z- and s-transforms
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Table 13.2z-transform theorems
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Inverse z-transform

• Partial fraction expansion (partial brøker)
• Power series (polynomiers division)
• Tables

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Pulse Transfer Function
Figure 13.8 Sampled-datasystemsa.
continuousb. sampled inputc. sampled
inputand output
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Sampled-data systems and their z-transforms
Figure 13.9Sampled-data systems and their
z-transforms
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Exercise

• Skill_assesment-Exercise 13.3