Digital Control Systems Recall from 1st lecture … Sense Compute ...
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Digital Control Systems Recall from 1st lecture … Sense Compute ...
1. Digital Control Systems. Recall from 1st lecture … Boeing 777. Sense. Vehicle
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Digital Control Systems Recall from 1st lecture …
Boeing 777
Actuate
Sense
Gas Pedal
Vehicle Speed
Compute Control “Law” 1
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Source: ctheory.net 2
Digital Control Systems
3
Digital to Analog
4
Analog To Digital
Sampler
Conversion to Binary
2 Step Process Does NOT happen instantaneously!
5
Nyquist-Shannon Sampling Theorem Theorem: If a function f(t) contains no frequencies higher than ω cycles/sec, it is completely determined by giving its ordinates at a series of points spaced 1/(2ω) seconds apart.
We must sample AT LEAST 2 x highest frequency
6
Modeling the Sampler
Sampling signal – s(t)
7
Modeling the Sampler (cont’d)
Sampling Waveform Characteristic 8
Modeling the Conversion to Binary (Z.O.H.)
9
The Z-Transform • Transform used to analyze digital systems • Contains information on the sampling • Recall the ideal sampler:
Z-Transform
10
Z-Transforms
11
Properties of the Z-Transform
12
Inverse Z-Transforms Two Methods: • Partial Fraction Expansion • Power Series Method
