Nyquist-Shannon Sampling Theorem. Theorem: If a function f(t) contains no frequencies higher than Ï cycles/sec, it is c
Digital Control Systems Recall from 1st lecture …
Boeing 777
Actuate
Sense
Gas Pedal
Vehicle Speed
Compute Control “Law” 1
Advantages • Reduce costs • Flexibility to design changes • Immunity to noise
Source: Boston Dynamics Source: Segway
Source: ctheory.net 2
Digital Control Systems
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Digital to Analog
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Analog To Digital
Sampler
Conversion to Binary
2 Step Process Does NOT happen instantaneously!
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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
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Modeling the Sampler
Sampling signal – s(t)
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Modeling the Sampler (cont’d)
Sampling Waveform Characteristic 8
Modeling the Conversion to Binary (Z.O.H.)
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The Z-Transform • Transform used to analyze digital systems • Contains information on the sampling • Recall the ideal sampler:
Z-Transform
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Z-Transforms
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Properties of the Z-Transform
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Inverse Z-Transforms Two Methods: • Partial Fraction Expansion • Power Series Method
