W' Khaisongkram, D' Banjerdpongchai, S' Arunsawatwong

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Dynamic Controller Design for a Binary
Distillation Column via the Method of Inequalities
W. Khaisongkram, D. Banjerdpongchai, S.
Arunsawatwong Department of Electrical
Engineering, Chulalongkorn University
2002 Electrical Engineering Conference (EECON
25) November 21, 2002
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Outline

• Introduction

• Mathematical Model of a Binary Distillation
  Column

• Problem Statement

• Design Criteria
• Performance Index

• Solution via the Method of Inequalities

• Controller Structure
• Nonlinear Simulation 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
• Significant disturbances
• Feed flow rate
• Feed composition

Interesting challenging to many
researchers (Luyben 1990,1992, Morari Zafiriou
1989)
Controller Design for a Binary Distillation Column
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• Objective Regulate y within a prescribed
  bound in the presence of disturbances
• Disturbance modeling
• Step input signal
• White (Colored) noise
• Persistent input with bounds on magnitude
  rate of change

Controller Design for a Binary Distillation Column
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• Controller design via the method of inequalities
• Applicable to MIMO systems
• Controller structure can be specified
• Formulate problem as a set of inequalities
• Utilize numerical search methods
• The regulated outputs are maintained
• within the prescribed bounds

Controller Design for a Binary Distillation Column
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Model of a Binary Distillation Column

• Control system structure L-V (Luyben 1990)
• Regulated outputs
• Top composition xD
• Bottom composition xB
• Control inputs
• Reflux rate R
• Reboiler rate V
• Disturbance
• Feed flow rate F

(Assume constant feed composition xF )
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• Parameters
• Number of trays 20
• Feed trays 10th
• More (Perry Chemical Handbook 1984)
• General assumptions
• Constant relative volatility
• Neglect vapor holdup
• Neglect dynamics of condenser reboiler
• More (Luyben 1990)
• Linearize at the equilibrium state set point

Controller Design for a Binary Distillation Column
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Problem Statement
Design a controller such that y is
maintained inside a certain bound in the
presence of all possible inputs f ...
What should be a reasonable input space ??
Controller Design for a Binary Distillation Column
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Input Space

• Step signal
• Infinite rate of change
• Piecewise constant

• White (Colored) noise
• unbounded magnitude
• unbounded rate of change

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Input Space
Input with bound on magnitude rate of change
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• Consistency with real disturbances
• Magnitude restriction is caused by dimension
  of piping system.
• Restriction on rate of change is effected by
  mass of fluid liquid foregoing process.
• Magnitude rate of change randomly and
  persistently change for all 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 limitation)
Controller Design for a Binary Distillation Column
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Performance Index
Upperbound 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)
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Upperbound 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)
Upperbound v v minv1 , v2
Controller Design for a Binary Distillation Column
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Solution via 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

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Design Results

• Solution is obtained after 156 iterations.

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Nonlinear Simulation Results
Using nonlinear model in Luyben 90 and input f
in F
Top Composition
Bottom Composition
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Nonlinear Simulation Results (cont.)
Using nonlinear model in Luyben 90 and input f
in F
Reflux rate
Reboiler Rate
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Conclusions

• control design for a binary distillation column
  with
• specified controller structure can be
  formulated as
• a set of inequalities.

• A new idea of disturbance modeling, which is
  more
• realistic than former models, is proposed.

• The design problem is numerically solved via
  the
• method of inequalities.

• The simulation results show that the controller
  satisfies
• the design criteria.

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QUESTIONS AND ANSWERS
Controller Design for a Binary Distillation Column