Process Control BEE4343

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Process Control (BEE4343)

• Chapter 7 Cascade Control

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From last class

• Chapter 6 Application of Feedback Control
• Equipment Specification
• Accuracy
• Reproducibility
• Cost
• Input Processing
• Validity check
• Conversion for nonlinearity
• Engineering units
• Filtering
• Set point limits
• Application of Feedback Control
• Equipment Specification
• Input Processing
• Feedback Control Algorithm
• Output Processing

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Todays discussion

• Chapter 7 Cascade Control
• Cascade Design
• Controller algorithm and tuning

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Learning Outcomes

• At the end of this chapter, students should be
  able to
• Identify situations for which cascade control is
  a good control enhancement
• Apply the tuning procedure to cascade control

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Simplified control loop drawing, showing
application topics
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Recap on Feedback Control Algorithm
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Recap on Proportional Mode
Sense switch
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Recap on Proportional Mode
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Recap on Proportional Mode
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Recap on Integral Mode
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Recap on Integral Mode
Effect of reset windup ? poor control performance
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Recap on Integral Mode
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Recap on Integral Mode
Anti Reset Wind Up External Feedback
Block diagram of a PI control algorithm with
external feedback
When limitation is not active
When limitation active
constant
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Recap on Derivative Mode

• Effects
• reduce amplification of noise
• retain some of the good control performance
  possible with derivative mode

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Cascade Control

• Introduction on Cascade Control
• Cascade Design criteria
• Cascade performance
• Response to step disturbance
• Controller algorithm and tuning

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Introduction to Cascade Control
Level control of tank without cascade control
Level control of tank with cascade control
WHAT IS THE MAIN DIFFERENCE BETWEEN THESE TWO
SYSTEMS?
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Introduction to Cascade Control

• Conventional control
• Attempts to maintain CV near to its SV in
  response to all disturbances and ensures zero
  steady-state offset for step-like disturbance
• Disadvantage using single loop control
• Slow response
• Cascade control
• Considers the likely disturbance and tailors the
  control system to the disturbance(s) that
  strongly degrades the performance
• Use additional secondary measured process input

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Introduction to Cascade Control
SP2MV1
Stirred tank heat exchanger with single loop
temperature control
Stirred tank heat exchanger with cascade control
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Introduction to Cascade Control

• Stirred-tank heat exchanger with cascade control
  (page 459)
• Output of the exit temperature controller adjusts
  the set point of the flow controller in the
  cascade structure
• Secondary controller set point is equal to
  primary controller output
• Secondary control loop is essentially the MV for
  the primary temperature controller
• Net feedback same for both single-loop
  cascade control
• Heating oil valve is adjusted ultimately by the
  feedback

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• Single loop structure makes no correction for the
  oil pressure disturbance until tank exit
  temperature is upset
• Cascade structure make a much faster correction,
  which provides better control performance
• Better control performance
• As described in paragraph 2 of page 459

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• Dynamic response of stirred tank heat exchanger
  to a disturbance in oil pressure
• With single loop control
• With cascade control

Source Marlin pg 459
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Features of cascade control for this example

• The flow controller is much faster than the
  temperature controller
• Temperature controller with an integral mode
  remains in the design to ensure zero offset for
  all disturbance sources
• Why
• Secondary variable may not totally eliminate the
  effect of the disturbance
• Other disturbance that are not affected by the
  cascade will also occur
• The ability to change the set point must be
  retained

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Commonly used terminology
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Cascade Design Criteria

• Cascade control is desired when
• Single-loop control does not provide satisfactory
  control performance
• A measured secondary variable is available
• A secondary variable must satisfy the following
  criteria
• The secondary variable must indicate the
  occurrence of an important disturbance
• There must be a causal relationship between the
  manipulated and secondary variables
• Is required so that a secondary feedback control
  loop functions properly
• The secondary variable dynamics must be faster
  than the primary variable dynamics.
• Guidelines secondary must be 3 times as fast as
  the primary

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Cascade Performance
Block diagram of a cascade control
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Transfer functions from the block diagram
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Response to Step Disturbance in D2
Given that
Secondary
? relative dynamics between the secondary and
primary
Primary
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Response to Step Disturbance in D2
Disturbance
Instrumentation
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Response to Step Disturbance in D2

• Performance of cascade control for a disturbance
  in the secondary loop
• With ? 10
• With ? 1.0

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Controller algorithm and tuning

• Can use standard feedback control PID algorithms
  for both loops
• Cascade strategy is tuned in sequence manner
• Secondary controller is tuned first
• Secondary affects the dynamics of the primary
• Set the primary loop in manual mode
• Tune using tuning methods that weve learned
  before (Ziegler Nichols, Cohen Coon etc)
• When secondary is satisfactorily tuned, next tune
  the primary controller using any tuning method

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Tuning Methods (recap from Chapter 5)

• Ziegler Nichols First Method (Process Reaction
  Curve)
• Ziegler Nichols Second Method (Ultimate
  Sensitivity Method)
• Cohen Coon Method

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Rule 1 First Method Process Reaction Curve

• Obtain experimentally the response of the plant
  to a unit step input
• This technique only applies if the response
  exhibit an S-shaped curve, otherwise other
  technique has to be used.
• S-shaped may be characterized by two constant
• ? dead time
• t time constant
• The tuning constants can be obtained by referring
  to the table where the two constants obtained
  from the S-shaped curved are to be utilized.

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S-shaped Curve response due to a step input
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Ziegler-Nichols Tuning Rule Based on Step
Response of Plant (First Method)
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Rule 2 Second Method Ultimate Sensitivity
Method

• First set Ti8 and Td0.
• Using the proportional action only, increase Kc
  from 0 to a critical value Kcr, which the output
  first exhibits sustained oscillations.
• If the output does not exhibit sustained
  oscillation for whatever value Kc may take, then
  this method does not apply.
• Thus, the critical gain Kcr and the corresponding
  period Pcr are experimentally determined.
• The tuning constants can be obtained by referring
  to the table where the two parameters which were
  determined before are to be utilized.

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Tune Kc from 0 until reaches Kcr
Pcr is determined when the response reaches
sustained oscillation
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Ziegler-Nichols Tuning Rule Based on Critical
Gain Kcr and Critical Period Pcr (Second Method)
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Cohen Coon Tuning Method

• Under Manual (or open loop) mode, wait until the
  process is at steady state.
• Next, introduce a step change in the input.
• Based on the output, obtain an approximate first
  order process with a time constant t delayed by ?
  units from when the input step was introduced.

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Cohen Coon Tuning Method (cont.)

• The values of t and ? can be obtained by first
  recording the following time instances
• t0 time when input step was initiated
• t2 time when half point occurs
• t3 time when 63.2 point occurs

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t0 time when input step was initiated t2
time when half point occurs t3 time when 63.2
point occurs
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Cohen Coon Tuning Method (cont.)

• From the measurements based on the step test t0,
  t2, t3, A and B, evaluate the following process
  parameters
• t1 (t2 - ln(2) t3)/(1 - ln(2))
• t t3 - t1
• ? t1 - t0
• K B/A

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Cohen Coon Tuning Method (cont.)

• Based on the parameters K, t and ?, the following
  formulas prescribe the controller parameters Kc,
  Ti and Td

where r ? /t
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Cascade Control tuning
Tune the secondary loop first
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Cascade control tuning

Gv(s)
Gc2(s)
Gp2(s)
-
Final element
Controller 2
Secondary process
Gs2(s)
Sensor 2
Using any tuning methods weve learned
previously, determine the tuning constants for
the controller
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Cascade Control tuning
Secondary loop
Tune primary loop after secondary loop has been
tuned satisfactorily
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Cascade control tuning
Gp(s)

G(s)
Gc1(s)
Gp1(s)
-
Secondary loop
Controller 1
Primary process
Gs1(s)
Sensor 1
By taking the secondary loop into account, using
any tuning methods weve learned previously,
determine the tuning constants for the controller
1
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Closure

• What we have learned so far
• Features of cascade control design
• Cascade control tuning

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For next class

• Chapter 8
• Feedforward control