Wathanyoo Khaisongkram David Banjerdpongchai

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Controller Design for a Binary Distillation
Column under Disturbances with Bounds on
Magnitudes and Derivatives Using Zakians
Framework
Wathanyoo Khaisongkram David
Banjerdpongchai Dept. of Electrical Engineering,
Chulalongkorn Univ., Bangkok, THAILAND
2004 Asian Control Conference (ASCC 2004) Grand
Hyatt Melbourne, AUSTRALIA July 21-23, 2004
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Outline

• Introduction

• Model of a Binary Distillation Column

• Zakians Framework

• Design Results

• Conclusions

Controller Design for a Binary Distillation Column
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Introduction

• Binary Distillation Column
• Multi-input multi-output
• Strong nonlinearity
• Strong loop interaction
• Disturbances
• Deviation of feed flow rate

Interesting challenging to many
researchers (Luyben 1990,1992, Morari Zafiriou
1989)
Controller Design for a Binary Distillation Column
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Objective Regulate output y within a
prescribed bound in the presence of
disturbances f
Controller Design for a Binary Distillation Column
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• Controller design problem
• Disturbance model signals with bounds on
• magnitudes and derivatives
• Applicable to MIMO systems
• Controller structure can be specified
• Formulate problem as a set of inequalities
• Utilize numerical search methods

Controller Design for a Binary Distillation Column
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Binary Distillation Column Model
Control system structure L-V (Luyben, 1990)

• Regulated outputs
• Top composition xD
• Bottom composition xB

• Control inputs
• Reflux rate L
• Reboiler rate V

Controller Design for a Binary Distillation Column
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• Configurations
• Number of trays 20
• Feed tray 10th
• General assumptions (Luyben, 1990)
• Constant relative volatility
• Neglect vapor holdup
• Neglect dynamics of condenser reboiler
• Linearize the dynamics at the operating point

Controller Design for a Binary Distillation Column
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Zakians Framework
Design a controller such that y is
maintained inside a certain bound in the
presence of all possible disturbances f
Controller Design for a Binary Distillation Column
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Input Space

• Step signal
• Infinite rate of change
• Piecewise constant

• Random noise
• no bound on magnitude
• no bound on derivative

Controller Design for a Binary Distillation Column
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Input Space
Input with bound on magnitude derivative
Controller Design for a Binary Distillation Column
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• Consistency with real disturbances
• Magnitude restriction is caused by dimension
  of piping system.
• Derivative restriction is caused by mass
• of fluid preceding processes.
• Magnitude derivative randomly vary
• over time.

Controller Design for a Binary Distillation Column
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Design Criteria
Specifications on top bottom compositions Lim
itations on reflux rate and reboiler rate
(From the physical constraints)
Controller Design for a Binary Distillation Column
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Performance Index
Upper bound v1 (v1 gt v) Since F f
f lt 10 (Bounded input) then v1
10 h(t)dt where h(t) impulse response
(from f to v)
Controller Design for a Binary Distillation Column
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Upper bound v2 (v2 gt v) (Zakian,
1979) From v(t,f) s(q)f(t-q)dq then
v2 5 s(t) - sssdt 10sss where
s(t) step response (from f to v) sss
lim s(t)
Upper bound v v minv1 , v2
Controller Design for a Binary Distillation Column
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The Method of Inequalities
The method of inequalities (Zakian Al-Naib
1973) requires the design problem be cast as
Qi(p) lt i i 1, , m where
Qi() performance index (v) i
positive value p design parameter

Numerical solution can be obtained by the moving
boundaries process algorithm.
Controller Design for a Binary Distillation Column
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Controller Structure
Choose the controller K of the form

• The dependent elements are eliminated
• p p1, , p12 design parameters

Controller Design for a Binary Distillation Column
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Design Results

• Controller is obtained after 156 iterations.

Controller Design for a Binary Distillation Column
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Nonlinear Simulation
Using nonlinear model in (Luyben, 1990) and input
f in F
Top Composition
Bottom Composition
Controller Design for a Binary Distillation Column
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Conclusions

• Controller design for a binary distillation
  column with
• specified criteria can be practically
  formulated
• using Zakians Framework.

• Employ the disturbance model with bounds on
• magnitudes and derivatives.

• The simulation results show that the design
  criteria
• can be fulfilled via the 2nd order linear
  controller.

Controller Design for a Binary Distillation Column