Ph.D. Summer school Process and Tools Integration Operability and Control for Process Integration 17. August 2005 Sten Bay J

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Ph.D. Summer schoolProcess and Tools Integration
Operability and Control forProcess
Integration17. August 2005Sten Bay Jørgensen
CAPEC - Department of Chemical Engineering
Technical University of Denmark,DK-2800 Lyngby,
Denmark
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Motivation for Process and Design Integration
No recycle of information flow (arrow)
Integration possible ?

Sequential design of Heat integration Mass
integration Control
Issue 2
Issue 1
Recycle of information flow Integration
possible?
Integrated design of Heat and mass
integration with control
Issue 1
Issue 2
Requirement Measures for dynamic consequences of
integration to be used
early in the design phase for control structuring
and design
3
Dynamics and Control of Integrated Plants

• Process dynamics and control a recap!
• Transfer functions, dynamics and stability
• Process integration structures
• Effects of process integration on dynamics and
  control
• Analysis of linear behaviour
• Implications upon control
• Nonlinear behaviour
• Dynamic consequences of optimal operation
• How to configure control?

4
Schedule for Operability and Control of
integrated plants
Lecture 1 Process dynamics and control recap
1 Lecture 2 Process dynamics and control recap
2 Lecture 3 Control of plants with units in
series Lecture 4 Dynamics of integrated
processes Lecture 5 Control effects of
recycle Lecture 6 Effects of process integration
and optimization
5
Lecture 1 Process Dynamics and Control recap 1

• Chemical Process Dynamics Simplified
• Material Balance Control

6
Chemical Process Dynamics
A
A B
B
A ? B
Reactor
Separator
Heat Exchanger
Standard process dynamics considers single simple
standard units with linear dynamics expressed in
transfer functions
7
Material Balance P-Control exit flow
8
Material Balance P-Control simulation
9
Material Balance PI-Control
10
Material Balance PI-Control simulation
11
Material Balance P-Control inlet flow
12
Material Balance PI-Control simulation
13
Lecture 2 Process Dynamics and Control recap!

• Transfer functions and single loop control
• Internal model based control
• Performance limitations in single loop control
• Control of Production Rate in Chemical Plant
• Front end control (Push)
• On demand control (Pull)

14
Transfer functions

• Local Transfer Function
• zi a zero in left half plane
• gives overshoot
• pj a pole in left half plane
• gives exponential decay
• Initially single variable transferfunctions are
  considered, i.e. all signals are scalars gi(s)
  ni(s)/di(s)
• Transfer functions will also be divided into
  g(s)ga(s)gm(s)
• where gm(s) is the minimum phase part
• and ga(s) is the allpass part,
• which contains all nonminimum
• phase components

15
Single Control Loop
Standard single variable open loop process
y g u gd d
d
gd
Standard single loop control
y
u
g
d
gd

• Significantly reduces sensitivity to
• disturbances at low frequences
• For high gain control the sensitivity to model
  uncertainty is significantly reduced
• Control performance is limited for RHP zeros,
  i.e. Nonminimumphase behaviour

y
r
u
g
gc
-1
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Internal Model Based Control Design
The IMC regulator gives the closed loop
gd
d
y
r
u
g
gcIMC
Thus the nonminimum phase in Ga limits
achievable performance!
-gm
-1
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Control Performance Reducing Dynamics

• Local Transfer Function

• Zero Dynamics
• Real zero in right half plane

• Singularities (due to sensitivity to uncertainty)
• Real pole into right half plane
• Complex pole pair into right half plane

18
Material Balance P-Control
19
Plant Production Rate Front End 1
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Plant Production Rate Front End 2
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Plant Production Rate Front End 3
Simple strategy
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Plant Production Rate - On Demand
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Lecture 3 Control of Plants with units in series

• Units in Series
• Disturbance effects
• Production rate front end
• Production rate on demand
• How to achieve changes in production rate
• Partial control
• Reactor control
• Examples of Production rate control

24
Units in Series - No Recycle

• The plantwide control problem is greatly
  simplified when there is no recycle of mass or
  energy.
• The control system of each unit is configured
  individually to handle load disturbances.

• Separation ExampleVolatility order A gt B gt
  CDirect Sequence The lightest component is
  taken out of the top of the first column.

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Production Rate - Front End
Disturbances propagate in the direction of mass
flow
26
Production Rate - On Demand
Disturbances propagate in the opposite direction
of mass flow
27
Production Plant without recycles
An ideal abstraction since energy and
rawmaterials are not used very efficiently!

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Production Rate

• Changes in production rate can be achieved only
  by changing the conditions in the reactor.
• Some variable that affects the reaction in the
  reactor must vary.

• Liquid Phase Reactors
• Hold-up
• Temperature
• Concentrations

• Gas Phase Reactors
• Pressure
• Temperature
• Concentrations

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Partial Control

• Often for reactors (and other units) the number
  of control objectives exceed the number of
  manipulated variables.
• We must assign manipulated variables to achieve
  the control objectives, which must be important
  for the operation of the plant and leave the rest
  of the variables uncontrolled.

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Plantwide Production Rate Control

• Production rate changes should be achieved by
  modifying the setpoint of a partial control loop
  in the reaction section.
• Separation section will not be significantly
  disturbed.

31
Reactor Control

• Managing energy (temperature control)
• Keeping as constant as possible the composition
  and flow rate of the total reactor feed stream
  (Fresh feed and recycle).

32
Units in Series - Production Rate

• How do we specify and control the plant-wide
  production rate of B, when there is a reactor in
  the plant?
• Reaction kinetics has to be considered!

Sensitivities
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Units in Series - Production Rate

• The production rate is controlled through partial
  control of the reaction rate.V controlledxA
  controlledT controlled (by ass.)
• Production rate may be changed by changing the
  setpoint to the reactor CC or the reactor LC.
• Reactor LC change will not change the composition
  fed to the distillation col.

All three dominant reaction rate variables
controlled gt SMALL variance.
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Units in Series - Production Rate

• One dominant variable, xA, of the reaction rate
  is uncontrolled because reactor composition
  measurement is not possible.
• Reaction rate and production rate may fluctuate.
• Production rate may be changed by changing the
  setpoint to the reactor FC or the reactor LC.
• Rate set at front end.

xA not controlled directly. This leads to larger
variance in the production rate than in the
previous configuration.
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Units in Series - Production Rate

• On-DemandThe production rate is specified by
  setting the FC of the bottom product in the
  distillation column.
• The disturbances propagates in the opposite
  direction of the mass flow.

xA not controlled directly. This leads to larger
variance in the production rate than in the first
configuration.
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Lecture 4 Process Integration and Dynamics

• Process Integration Structures
• Series has been covered
• Parallel
• Recycle
• Example Recycle Plant models
• Disturbance Sensitivity of Recycle plant

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Generic Production Plant
Process integration is mandatory for energy and
rawmaterial efficiency!
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Dynamic consequences of process integration
g4(s)

g1(s)
g2(s)
g3(s)

• Plant as an integration of different unit
  processes
• Relate behaviour of integrated plant to
• behaviour of individual units
• structure of interconnections
• Thereby existing knowledge of unit behaviour
  can be exploited, for the analysis of linear
  behaviour

Hangos (1991) and Jacobsen (1999)
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Interconnection Structures
Recycle
Series
Parallel
g2(s)
g2(s)
g1(s)
g2(s)
g1(s)
g1(s)
Zeroes and poles are the union of those of units
Zeroes are moved Poles are the union of those of
units
Zeroes are the union of those of n1 and poles of
d2 Poles are moved!
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Summary Process Integration Structures

• Series and parallel interconnections
• Realtively simple to deduce overall behaviour
  from unit behaviours (only zeros are affected in
  parallel interconnections).
• Recycle interconnections
• More complicated relation between overall
  behaviour and unit behaviours (poles are moved).

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Simple Recycle Example (1)
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Simple Recycle Example (2)
Laplace Transformation
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Simple Recycle Example (3)
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Simple Recycle Example (4)
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Simple Recycle Example (5)
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Simple Recycle Example (6)
Unit Step Response
Both the time constant and the steady-state gain
has been dramatically changed by the recycle
stream
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Snowball Effect

• Observation Recycle systems has a large tendency
  to exhibit large variations in the magnitude of
  the recycle flow.

• Snowball effect sensitivity of recycle flow
  rates to small disturbances

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Snowball Effect Static analysis

• Snowball effect sensitivity of recycle flow
  rates to small disturbances

Only show composition of reactant A, i.e. x All A
is removed in Distillate, i.e. xB0 and xD1
Total balance
F, xF
D
L
Component balance around reactor
R, xR
V
AgtB
B , xB
Thus if Da Vk/F approaches xF then R can become
very large!
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Control Implications of the Snowball Effect

• Set the production rate at the front end, I.e. by
  setting U.
• If the snowball effect is dominant, K2K gtgt 1,
  small changes in U lead to large changes in X2.
• Large changes in X2 implies that the recycle
  valve goes either fully open or closed.
• As X2 is large, X1 is also large and this may
  overload the separation section.

Production rate can typically NOT be set at the
front end for mass recycle systems.
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Snowball Effect - Example

• Isothermal reactor operation (perfect
  temperature control)
• Produce pure B
• Be able to manipulate the production rate of B
• Select a control structure that will meet these
  objectives

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Snowball Effect - Example

• All flows in recycle loop set by level
  controllers
• A small change in the production rate set
  front-end leads to large changes in the recycle
  loop flow rates.
• No plantwide control of inventory of A.

SMALL flexibility index regarding production rate.
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Snowball Effect - Example

• We cannot manipulate production rate directly by
  manipulating the fresh feed flow
• The setpoint to the reactor LC is used to
  control production rate
• No snowball effect due to FC in recycle loop

System inventory of A is controlled by the
reactor LC. This improves the flexibility index.
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Snowball Effect - Example

• To prevent the snowball effect, the mass recycle
  loop must have a flow controller.
• The plant inventory of A must be controlled. It
  is not sufficient to control the individual unit
  inventories of A.
• In the upper flow sheet any disturbance that
  increase the total inventory of A in the process
  will produce large increases in the flowrates
  around the recycle loop.

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Snowball Effect - Example

• Consider a 20 production rate increase of B.
• In the first control structure the separation
  section must handle the entire load, as xA must
  change with 20. The feed to the distillation
  column changes, as well as the feed rate.
• In the second control structure both reactor
  composition and volume changes. So the separation
  section sees a smaller load disturbance
• Production rate can only be changed by changing
  the conditions in the reactor!

55
Disturbance Sensitivity of single loop control
d
gd
Standard single variable process y g
u gd d

y
u
g
Standard single loop control gd
g gc y
----------d ----------- r 1 g gc
1 g gc Significantly reduces
sensitivity to disturbances at low
frequences What happens with process integration?
d
gd
y
u
g
gc
-1
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Disturbance Sensitivity with process recycle
y
d
gd
g gd/(1 gd grec) S gd
grec

• The Sensitivity function S 1/ (1 gd grec)
  catches the effect of recycle upon
  disturbance sensitivity.
• Instability is induced by recycle if gd grec is
  stable and
• gd grec (i?c) gt 1 and
  f(gd grec (i?c)) n 2p
• where ?c is the critical
  frequency
• Note feedback may be positive or negative
• Control is based upon negative feedback
• Recycle introduces positive feedback

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Feedback effects on Disturbance Sensitivity

• Negative feedback if gd grec (0) lt 0
• Static Sensitivity S(0) lt 1
• Hence disturbance sensitivity is reduced at low
  frequences
• The critical frequency ?c gt 0 Increasing the
  loop gain will yield a pair of complex poles
  crossing the imaginary axis.
• The closed loop response usually is faster

• Positive feedback if gd grec (0) gt 0
• Static Sensitivity S(0) gt 1
• Hence disturbance sensitivity is increased at
  low frequencies
• The critical frequency may be at ?c 0 thus a
  real pole crosses the imaginary axis for gd
  grec (0) gt 1, i.e. static multiplicity. Or at ?c
  n 2p where a complex pair crosses.
• Thus the recycle loop response usually is slower
  if not unstable

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Example Plant
Mixer
Reactor
Separator
DF, yD
F, xFi
xF
Note autocatalytic reaction, e.g.
bioreactor Main disturbance xFi Objective Maint
ain yD constant
L
xR
ARgt2R
V
B R, xB
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Example Plant Unit models
Mixer static

M
Reactor
Separator
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Example Plant Block Diagram

L
yD
GD
xF
xFi
xR
1-k
gr
xB
k
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Example Plant Disturbance Sensitivity
Effect of xFi on yD
yD

gD12
xF
xFi
zF
1-k
gD22
gr
xB
k

• Sensitivity S 1/(1-kgrgD22)
• Static loop gain kgr(0) gD22(0) 1.32 k
  thus positive feedback
• Unstable for k gt 0.76 (R/F gt 3.1)

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Summary on Sensitivity effects of Recycle

• Recycle of material or energy introduces
  positive feedback which
• increases low frequency disturbance sensitivity
• induces slower dynamics or instability
• Thus recycle implies a stronger need for
  control to reduce the effect of disturbances and
  also to stabilize the plant
• How to handle the increased disturbance
  sensitivity?

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Lecture 5 Control of Recycle Plants

• Feedback Control of Recycle Plants
• Control of variable in recycle path
• Control of variable not in recycle path
• Summary of control effects of recycle
• Conclusions on linear dynamics and control of
  Process Integrated Plants

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Feedback Control SISO versus recycle variable
Standard single variable process y g
u gd d Perfect rejection of disturbance
requires u - (gd / g ) d
u
g
y
d
gd
u

• Control of variable in recycle loop
• y (gu gdd)/(1-gdgrec) S(gu gdd)
• Perfect rejection of disturbance requires
• u - (gd / g ) d
• Thus required input unaffected by recycle

g
y
d
gd
grec
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Feedback Control of variable not in recycle 1
Control of variable not in recycle loop
g11
u
y
g21
g12
x
u2
d
g22
grec
Thus the transfer function from u to y is
affected by recycle! But how?
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Feedback Control of variable not in recycle 2
The recycle transfer function

Recycle affetcs the static behaviour such that
1. It will have more poles in the RHP than g11
if g22(0)grec(0) gt1 and ?11(0) ?1 2. It will
have more zeros in the RHP than g11 if
g22(0)grec(0)/?11(0) gt1 and ?11(0) ?1. The above
two conditions are sufficient for moving a real
pole or zero into the RHP. Thus if g11 is stable
and nonminimum phase the above two conditions
imply that the recycle system has RHP poles and
RHP zeros respectively. In Conclusion Closing a
control loop from y to u will most certainly be
affected by the dynamics introduced through
recycle!
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Plantwide Control Structure Design Procedure
(Luyben et al.)

• Establish control objectives
• Determine control degrees of freedom
• Establish energy management system
• Set production rate
• Control production quality and handle safety,
  environmental and operational constraints
• Fix a flow in every recycle loop and control
  inventories
• Check component balances
• Control individual unit operations
• Optimize economics and improve dynamic
  controllability

68
Summary on control effects of recycle

• Control of variables within the recycle loop
• Input required to reject a disturbance is
  unaffected by recycle
• Control of variable not within the recycle loop
• Input required to reject a disturbance is
  affected by recycle
• in fact the effect of control inputs relative
  to disturbance may decrease significantly.
• Recycle may introduce RHP zeros
• If acceptable control is not possible then
  redesign such that recycle loop gain decreases

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Conlusions on linear dynamics and control

• Plant dynamics may be strongly affected by
  recycles
• Recycle usually gives positive feedback
• increases low freqency sensitivity
• renders response slower or causes instability
• Controllability for variables outside the
  recycle loop may be severely reduced by recycle,
  i.e. reduced efffect of control inputs possibly
  combined with RHP zeros
• Recycle may significantly increase model
  uncertainty for units in plant compared to that
  of individual units (not shown).
• Remedy Redesign loop to decrease loop gain.
  Often that means modify reactor design!

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Lecture 6 Effects of Process Integration on
nonlinear behaviour

• The Control Hierachy and degrees of freedom
• Profit Optimizing Control
• Operational Implications
• Example Continuous cultivation of yeast
• Analysis
• Experiment
• Example with Optimal operation of process
  integrated plant
• Ammonia reactor with feed-effluent heat exchange
  

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Profit Optimizing Control

• Productivity in Continuous Process

• Optimality requires Max J

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Gain Changes for Xprod vs. F

• Output Multiplicity
• Dynamic Consequence
• Instability when (dXprod/dF)lt0

• Input Multiplicity
• Dynamic Consequence
• May be a zero in RHP, i.e. unstable zero
  dynamics.

73
Control Performance Reducing Dynamics

• Local Transfer Function

• Zero Dynamics - input multiplicity
• Real zero in right half plane

• Singularities - output multiplicity
• Real pole into right half plane
• Complex pole pair into right half plane

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Process Analysis Operational Implications of
Optimality
Theorems based upon induction

• Complex behaviour may be encountered near an
  optimal operating point
• Optimised process integrated design increases the
  likelihood of complex behaviour

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Continuous Cultivation of Yeast

• Bifurcation analysis reveals
• Hysteresis curve, multiple steady-states at
  maximal biomass productivity!

f
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Adaptive Model Predictive Control
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Response to Etanol Setpoint Changes
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Ethanol Concentration vs. Dilution Rate
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Ammonia Reactors

• Operating point
• Feed temperature
• Feed concentration
• Feed flow rate
• Pressure
• No automatic control of inlet temperature

3-bed quench reactor
simple reactor
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Energy Integrated Ammonia Reactor
I
II
III
IV
V
VI
I

• Subcritical Hopf bifurcation from the upper
  steady state
• Stable limit cycle coexists with the upper stable
  steady state
• Safer to operate in region with no stable limit
  cycle

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Dynamic Simulation

• Operate at ignited steady state and increase
  inlet concentration
• Passing Hopf at 2.3 mole
• Large amplitude oscillations
• Decrease inlet concentration
• Passing cyclic fold at 2.1 mole
• Stable steady state

Inlet Ammonia Mole Fraction
82
Conclusions on nonlinear analysis

• New process design tools should be developed to
  account for possible nonlinear behaviours
• To operate near optimal operating points reliable
  model identification and nonlinear control is
  desirable - a profit margin of 3 has been
  estimated!
• Is a combined process and nonlinear control
  design optimization formulation solvable - to
  exploit the nonlinearity?

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General Plantwide Control Structure Design
Procedure

• Top down analysis
• Define operational objectives
• Manipulated variables and degrees of freedom for
  control
• Select primary controlled variables (given via
  design goal)
• Production rate determine where to set this in
  the plant, often at some interior position
• Investigate possible nonlinear complex
  behavioours near optimal operation
• Bottom up design
• Regulatory control layer
• Stabilization
• Local disturbance rejection
• Supervisory control layer
• Keep controlled outputs at optimal setpoints
• Optimization layer
• identify active constraints and determine optimal
  setpoints
• Validation simulations

Extention of Skogestad (2004)
84
Conclusions on Dynamics and Control of Process
Integrated Plants

• Linear Analysis explains large sensitivity of
  recycle plants especially for control of
  variables not in recycle path.
• Optimizing Operation exploits nonlinearities,
  therefore nonlinear analysis is recommendable.
• Nonlinear Analysis explains specific cases it
  is therefore difficult to generalise. It is
  however important to understand how to avoid
  occurrence of potentially serious problems.

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References and Further Reading

• Luyben, Tyreus, Luyben Plantwide Process
  Control, McGraw-Hill (1998), chap. 1-3
• Jacobsen, E.W. On the dynamics of integrated
  plants non-minimum phase behaviour. Journal of
  Process Control 9 (1999) 439-451
• Skogestad, S. Plantwide control the search for
  the self-optimizing control structure Journal of
  Process Control 10 (2000) 487-507
• Skogestad, S. Control structure design for
  complete chemical plants. Comp. and Chem.
  Engineering 28(2004)219-234.

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Monographs

• Buckley Techniques of Process Control, Wiley
  (1964)
• Shinskey Process Control Systems, McGraw-Hill
  (1988)
• Rijnsdorp Integrated Process Control and
  Automation, Elsevier (1991)
• Luyben, Tyreus, Luyben Plantwide Process
  Control, McGraw-Hill (1999)
• Ng, Stephanopoulos Plant-wide control structures
  and strategies, Academic Press (2000)