Dead Time Compensation

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Chapter 3

• Dead Time Compensation Smith Predictor, A Model
  Based Approach

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1. Effects of Dead-Time (Time Delay)

• Process with large dead time (relative to the
  time constant of the process) are difficult to
  control by pure feedback alone
• Effect of disturbances is not seen by controller
  for a while
• Effect of control action is not seen at the
  output for a while. This causes controller to
  take additional compensation unnecessary
• This results in a loop that has inherently built
  in limitations to control

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Example A Bode Plot Example
htf(1,1 3 3 1,'inputdelay',1)
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Example- continued, case without time delay
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PID Control Results- Case with delay
(Kc1,Ki1,Kd1)
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PID Control Results- Case without delay
(Kc1,Ki1,Kd1)
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2. Causes of Dead-Time

• Transportation lag (long pipelines)
• Sampling downstream of the process
• Slow measuring device GC
• Large number of first-order time constants in
  series (e.g. distillation column)
• Sampling delays introduced by computer control

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3. The Smith Predictor
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Control with Smith Predictor (Kc1,Ki1,Kd1)
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Alternate form
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Example 2 Long time delay
1 G(s)
exp(-3s) ---------------------
s3 3 s2 3 s 1

Mag-3.3dB20log10(AR) AR0.6839 Wu0.5Pu2p/0.
512.5664 Ku1/0.68391.4622 Kc0.8601 TauiPu/26
.2832 TaudPu/81.5708
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Load Disturbance Response
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The Effect of Modeling Error
Errors in td,G both cause the control system to
degrade
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Smith Predictor with Modeling Error
Plante-s/(s33s23s1)
Modele-s/(s3s2s1)
Modele-0.5s/(s3s2s1)
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Analytical Predictor
y(s)
GC(s)
GPe-DS
ySP
Analytical Predictor
y(tD)
Analytical Predictor is a model that projects
what y will be D units into the future (on-line
model identification)
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Processes with inverse response
The output goes to the wrong way first
Example This can occurs in (1) reboiler level
response to change in heat input to the
reboiler. (2) Some tubular reactor exist
temperature To inlet flow rate . Inverse response
is caused by a RHP zero
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Example Inverse response of concentration and
temperature to a chanbe in process flow of 0.15
ft3/min
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Open Loop Response Analysis