department of air-conditioning and refrigeration engineering/ national taipei university of...
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Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
數位控制設計使用MATLAB
李達生
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
Continuous Signal, Discrete Signal and Digital Signal
ttf sin)(
ADC
f(t) =
0000
0001
0010
0011
….
Sampling
1,2,3,... 0,
,sin)(
k
kTkTf
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
Z Transform v.s. Laplace Transform
• For a discrete signal
• Laplace Transform can be written as
0
)()()(k
kTtkTftfs
0
0k0
00
0
)(
)()(
)()(
)(
)]([)(
k
skT
st
k
st
st
ekTf
dtkTtekTf
ekTtkTf
dtetfs
tfsLsFs
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
Z Transform v.s. Laplace Transform
• If we define • The Z transform can be expressed as
• For a sampling time equals to 1 sec, Z transform can be expressed as
sTez
0
)()(k
kzkTfzF
0
][)(k
kzkfzF
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
Z Transform mapping TjTsT eeez
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
Z Transform
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
PID controller in Z domain
• A PID controller can be expressed in Z domain by
• T is the sampling time. i.e. the control performance can be influenced by sampling time
zT
zK
z
zTKK DIP
1
1
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
PID controller in Z domain
zT
zK
z
zTKK DIP
1
1
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
Nyquist sampling frequency
• The sampling frequency should exceed the signal frequency at least two times.
• The frequency is called Nyquist Frequency
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
RLC Circuit Response Design
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
Sampling and Notch Filter
Department of Air-conditioning and Refrigeration Engineering/ National Taipei University of Technology
DC Motor Control