Transcript TMR4240 Marine Control Systems

Filtering
Professor Asgeir J. Sørensen,
Department of Marine Technology,
Norwegian University of Science and Technology,
Otto Nielsens Vei 10, NO-7491 Trondheim, Norway
E-mail: [email protected]
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Outline
• Motivation
• Analog filtering
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Ideal filters
Nonideal low pass filter
Nonideal high pass filter
Bandstop filter - Notch
Motivation
• Filtering of measurement noise. Most
sensor signals are contaminated by some
noise that may have negative impact on
the controller performance. By filtering
we achieve a change in the relative
amplitudes of the frequency components
in a signal or even elimination of some
frequency components.
• Reconstruction of non-measured data.
For many applications important process
states are not measured. Model based
filtering techniques - state estimation can be applied to reconstruct unmeasured
signals and perform filtering before the
signals are used in a feedback control
system.
• Dead reckogning. All kind of equipment
will fail according to some failure rate.
Model based filters replace the measured
signal by a mathematical model
prediction for some period of time.
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SATELLITE
THRUSTER
SETPOINTS
MEASUREMENTS
SIGNAL
PROCESSING
THRUSTER
ALLOCATION
REAL WORLD
VESSEL
OBSERVER
CONTROLLER
COMMAND
THRUSTER
FORCES
VESSEL
SETPOINTS
VESSEL
MOTIONS
Motivation (cont.)
• Shaping Filtering. The power spectral
density of the output of a linear system
satisfies:
u(t )
y (t )
H ( j )
Example Simulation of Ship Roll Motion
S yy  H ( j ) Suu
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Then, the filter can be designed to
Simulate time series of a signal with
a particular power spectral
density by filtering white noise.
Fourier representation (multi sine)
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Filtered white noise (shaping filter)
Conventional filters used in marine
control systems
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Low pass filter suppressing e.g. noise
High pass filter
Band stop filters, e.g. notch filter
Band pass filter
Cascaded low pass and notch filter for wave
filtering
Analog low pass filter - Tolerances
|H(j)|



Passband  Transition 
p
s
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Stopband

Low pass filter - Butterworth filter
n =1 : bs=
gc
s+
gc
x%f +gc x f = gc x
n =2 : b
s=
2
gc
2
2
s + 2 gc s+
gc
x6f + 2 gc x%f +g2c x f =g2c x
n = 3 : b
s=
3
gc
2
s 2+
gc s +
gc s +
gc 
x4f +2gc x6f +2g2c x%
g3c =g3c x
f +
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High pass filter
High pass filter may be designed by substituting
s  1s , and gc  T c
in the equation describing low pass filter, e.g.
b
s=
gc
s+
gc
=
1
+
1
s
gc
The corresponding high pass filter becomes
b hp 
s=
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Tc
1
s
+
Tc
=
sT c
1+
sT c
Band stop filter - Notch filter
`di =1
`ni =0.1
g1 =0. 4
g2 =0. 63
g3 =1.0
r
hn =
i=1
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s2+
2`ni gi s+
g2i
s2+
2`di gi s+
g2i
Examples
Filter examples by Finn Haugen,
KYBSIM
http://techteach.no/kybsim/filters/
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