Principles of Control System DEE3313

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Principles of Control System (DEE3313)

• Bode Plots

KOLEJ UNIVERSITI KEJURUTERAAN TEKNOLOGI
MALAYSIA UTEC
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Frequency Response Method

• Frequency response analysis and design methods
  consider response to sinusoids methods rather
  than steps and ramps.
• Frequency response is readily determined
  experimentally in sinusoidal testing.
• Frequency response is readily obtained from the
  system transfer function (s j?) , where ? is
  the input frequency).
• Link between frequency and time domains is
  indirect. Design criteria help obtain good
  transient time response.

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Frequency Response Method

• The frequency response of a system is
  steady-state response of the system to a
  sinusoidal input signal.
• For linear dynamic systems, the steady state
  output of the system is a sinusoid with the same
  frequency as the input, but with the same
  frequency as the input, but differing in
  amplitude and phase angle (there is a phase shift
  in the output).
• The frequency response can be computed for a
  single frequency, and can be plotted for a single
  frequency, and can be plotted for a range of
  frequencies.

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Decibels

However, when scaled logs of the quantities are
taken, the unit of decibels (dB), is assigned.
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• There are two types of Bode plots
• The Bode straight-line approximation to the
  log- magnitude (LM) plot, LM versus w (with w on
  a log scale)
• The Bode straight-line approximation to the
  phase plot, ?(w) versus w (with w on a log
  scale)

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• Standard form for H(jw)
• Before drawing a Bode plot, it is necessary to
  find H(jw) and put it in standard form.

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Five types of terms in H(jw) 1) K (a
constant) 2) (a zero)
or (a pole) 3) jw (a
zero) or 1/jw (a pole)
4) 5) Any of the terms raised to a
positive integer power.
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• Constant term in H(jw)
• If H(jw) K K/0?
• Then LM 20log(K) and ?(w) 0? , so the LM
  and phase responses are

• Summary A constant in H(jw)
• Adds a constant value to the LM graph (shifts
  the entire graph up or down)
• Has no effect on the phase

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2. A) 1 jw/w1 (a zero) The
straight-line approximations are

• To determine the LM and phase responses,
  consider 3 ranges for w
• 1) w ltlt w1
• 2) w gtgt w1
• 3) w w1

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So the Bode approximations (LM and phase) for 1
jw/w1 are shown below.

• Summary A 1 jw/w1 (zero) term in H(jw)
• Causes an upward break at w w1 in the LM plot.
  There is a 0dB effect before the break and a
  slope of 20dB/dec or 6dB/oct after the break.
• Adds 90? to the phase plot over a 2 decade range
  beginning a decade before w1 and ending a decade
  after w1 .

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B) (a pole) The
straight-line approximations are
To determine the LM and phase responses, consider
3 ranges for w 1) w ltlt w1 2) w gtgt w1 3) w w1
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So the Bode approximations (LM and phase) for
are shown below.

• Summary A 1 jw/w1 (zero) term in H(jw)
• Causes an downward break at w w1 in the LM
  plot. There is a 0dB effect before the break and
  a slope of -20dB/dec or -6dB/oct after the break.
• Adds -90? to the phase plot over a 2 decade
  range beginning a decade before w1 and ending a
  decade after w1 .

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EXAMPLES
Consider the transfer function
a. Plot the Bode magnitude and phase
Solution