TO PLANTWIDE CONTROL

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1







A SYSTEMATIC APPROACH
TO PLANTWIDE CONTROL

Sigurd Skogestad



Department of Chemical Engineering

Norwegian University of Science and Tecnology (NTNU)

Trondheim, Norway




Stockholm, April 2010




7







NTNU,

Trondheim




8







Main references


The following paper summarizes the procedure:


S. Skogestad, ``
Control structure design for complete chemical
plants'',

Computers and Chemical Engineering
,
28

(1
-
2), 219
-
234 (2004).


There are many approaches to plantwide control as discussed in the
following review paper:


T. Larsson and S. Skogestad,
``Plantwide control: A review and a new
design procedure''

Modeling, Identification and Control
,
21
, 209
-
240
(2000).

Download papers: Google ”Skogestad”




9








S. Skogestad
``Plantwide control: the search for the self
-
optimizing control structure'',

J. Proc. Control
, 10, 487
-
507 (2000).


S. Skogestad,
``Self
-
optimizing control: the missing link between steady
-
state optimization and control'',

Comp.Chem.Engng.
, 24, 569
-
575 (2000).



I.J. Halvorsen, M. Serra and S. Skogestad,
``Evaluation of self
-
optimising control structures for an integrated Petlyuk distillation
column'',

Hung. J. of Ind.Chem.
, 28, 11
-
15 (2000).


T. Larsson, K. Hestetun, E. Hovland, and S. Skogestad,
``Self
-
Optimizing Control of a Large
-
Scale Plant: The Tennessee Eastman
Process'',

Ind. Eng. Chem. Res.
, 40 (22), 4889
-
4901 (2001).


K.L. Wu, C.C. Yu, W.L. Luyben and S. Skogestad,
``Reactor/separator processes with recycles
-
2. Design for composition control'',
Comp. Chem. Engng.
, 27 (3), 401
-
421 (2003).


T. Larsson, M.S. Govatsmark, S. Skogestad, and C.C. Yu,
``Control structure selection for reactor, separator and recycle processes'',
Ind. Eng. Chem. Res.
, 42 (6), 1225
-
1234 (2003).


A. Faanes and S. Skogestad,
``Buffer Tank Design for Acceptable Control Performance'',
Ind. Eng. Chem. Res.
, 42 (10), 2198
-
2208
(2003).


I.J. Halvorsen, S. Skogestad, J.C. Morud and V. Alstad,
``Optimal selection of controlled variables'',
Ind. Eng. Chem. Res.
, 42 (14),
3273
-
3284 (2003).


A. Faanes and S. Skogestad,
``pH
-
neutralization: integrated process and control design'',
Computers and Chemical Engineering
, 28
(8), 1475
-
1487 (2004).


S. Skogestad,
``Near
-
optimal operation by self
-
optimizing control: From process control to marathon running and business systems'',
Computers and Chemical Engineering
, 29 (1), 127
-
137 (2004).


E.S. Hori, S. Skogestad and V. Alstad,
``Perfect steady
-
state indirect control'',
Ind.Eng.Chem.Res
, 44 (4), 863
-
867 (2005).


M.S. Govatsmark and S. Skogestad,
``Selection of controlled variables and robust setpoints'',
Ind.Eng.Chem.Res
, 44 (7), 2207
-
2217
(2005).


V. Alstad and S. Skogestad,
``Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables'',
Ind.Eng.Chem.Res
, 46 (3), 846
-
853 (2007).


S. Skogestad,
``The dos and don'ts of distillation columns control'',
Chemical Engineering Research and Design (Trans IChemE, Part
A)
, 85 (A1), 13
-
23 (2007).


E.S. Hori and S. Skogestad,
``Selection of control structure and temperature location for two
-
product distillation columns'',
Chemical
Engineering Research and Design (Trans IChemE, Part A)
, 85 (A3), 293
-
306 (2007).


A.C.B. Araujo, M. Govatsmark and S. Skogestad,
``Application of plantwide control to the HDA process. I Steady
-
state and self
-
optimizing control'',
Control Engineering Practice
, 15, 1222
-
1237 (2007).


A.C.B. Araujo, E.S. Hori and S. Skogestad,
``Application of plantwide control to the HDA process. Part II Regulatory control'',
Ind.Eng.Chem.Res
, 46 (15), 5159
-
5174 (2007).


V. Kariwala, S. Skogestad and J.F. Forbes,
``Reply to ``Further Theoretical results on Relative Gain Array for Norn
-
Bounded
Uncertain systems''''
Ind.Eng.Chem.Res
, 46 (24), 8290 (2007).


V. Lersbamrungsuk, T. Srinophakun, S. Narasimhan and S. Skogestad,
``Control structure design for optimal operation of heat
exchanger networks'',
AIChE J.
, 54 (1), 150
-
162 (2008). DOI 10.1002/aic.11366


T. Lid and S. Skogestad,
``Scaled steady state models for effective on
-
line applications'',
Computers and Chemical Engineering
, 32,
990
-
999 (2008). T. Lid and S. Skogestad,
``Data reconciliation and optimal operation of a catalytic naphtha reformer'',
Journal of
Process Control
, 18, 320
-
331 (2008).


E.M.B. Aske, S. Strand and S. Skogestad,
``Coordinator MPC for maximizing plant throughput'',
Computers and Chemical
Engineering
, 32, 195
-
204 (2008).


A. Araujo and S. Skogestad,
``Control structure design for the ammonia synthesis process'',
Computers and Chemical Engineering
, 32
(12), 2920
-
2932 (2008).


E.S. Hori and S. Skogestad,
``Selection of controlled variables: Maximum gain rule and combination of measurements'',
Ind.Eng.Chem.Res
, 47 (23), 9465
-
9471 (2008).


V. Alstad, S. Skogestad and E.S. Hori,
``Optimal measurement combinations as controlled variables'',
Journal of Process Control
, 19,
138
-
148 (2009)


E.M.B. Aske and S. Skogestad,
``Consistent inventory control'',
Ind.Eng.Chem.Res
, 48 (44), 10892
-
10902 (2009).





11







How we design a control system for a
complete chemical plant?


Where do we start?


What should we control? and why?


etc.


etc.




14








Alan Foss (“Critique of chemical process control theory”, AIChE
Journal,
1973
):


The central issue to be resolved ... is the determination of control system
structure.
Which variables should be measured, which inputs should be
manipulated and which links should be made between the two sets?

There is more than a suspicion that the work of a genius is needed here,
for without it the control configuration problem will likely remain in a
primitive, hazily stated and wholly unmanageable form. The gap is
present indeed, but contrary to the views of many, it is the theoretician
who must close it.



Carl Nett (
1989
):

Minimize control system complexity subject to the achievement of accuracy
specifications in the face of uncertainty.




19







c
s
= y
1s

MPC

PID

y
2s

RTO

u (valves)

Follow path
(+ look after
other variables)

CV=y
1

(+ u)
; MV=
y
2
s

Stabilize + avoid drift

CV=y
2
; MV=
u

Min J (economics);
MV=
y
1s

OBJECTIVE

Dealing with complexity

Main simplification: Hierarchical decomposition

Process control


The controlled variables (CVs)

interconnect the layers

MV = manipulated variable

CV = controlled variable




20







Example: Bicycle riding

Note: design starts from the bottom


Regulatory control
:


First need to learn to stabilize the bicycle


CV = y
2
= tilt of bike


MV = body position



Supervisory control
:



Then need to follow the road.


CV = y
1

= distance from right hand side


MV=y
2
s


Usually a constant setpoint policy is OK, e.g. y
1
s
=
0.5
m



Optimization
:


Which road should you follow?


Temporary (discrete) changes in y
1
s



Hierarchical decomposition

MV = manipulated variable

CV = controlled variable




22







Implementation

of optimal operation


Paradigm
1
:

On
-
line optimizing control

where measurements are
used to update model and states



Paradigm
2
:


Self
-
optimizing” control scheme
found by exploiting
properties of the solution




23







Implementation:
Paradigm 1


Paradigm 1
:
Online
optimizing
control


Measurements are primarily used
to update the model


The optimization problem is
resolved online to compute new
inputs.


Examples:


Conventional MPC,


RTO (real
-
time optimization)


Supply chain optimization (Martin
Rudberg)


This is the “obvious” approach (for
someone who does not know
control)






24







Implementation:
Paradigm
2


Paradigm
2
:

Precomputed solutions based on
off
-
line

optimization


Find properties of the solution suited for simple and robust on
-
line
implementation


Proposed method
: Turn optimization into feedback problem.


Control layer
: Identify good CVs


Find regions of active constraints and
in each region:

1.
Control active constraints

2.
Control “self
-
optimizing ” variables for the remaining unconstrained
degrees of freedom


“inherent optimal operation”


Higher level in hierarchy: Indentify good KPIs



CV = controlled variable

KPI = Key Performance Indicators




25







Outline


Control structure design (plantwide control)


A procedure for control structure design


I

Top Down
(main new part)


Step
1
: Identify degrees of freedom


Step
2
: Identify operational objectives (cost function and constraints)


Step
3
:
What to control ?

(primary CV’s)


Active constraints


Self
-
optimizing variables


Step
4
:
Where set the production rate? (
Inventory control)


II Bottom Up


Step
5
: Regulatory control strategy:
What more to control?

(secondary CV’s)


Step
6
: Supervisory control strategy: Decentralized or multivariable?


Step
7
: Real
-
time optimization: Do we need it?


Case studies




26







Step 1. Degrees of freedom (DOFs) for
operation




To find all operational (
dynamic
) degrees of freedom:


Count valves! (N
valves
)


“Valves” also includes adjustable compressor power, etc.


Anything we can manipulate!





27







Steady
-
state

degrees of freedom (DOFs)

IMPORTANT!

DETERMINES THE NUMBER OF VARIABLES TO CONTROL!


No. of primary CVs = No. of steady
-
state DOFs

CV = controlled variable (
c
)

N
ss

=

N
valves



N
0ss



N
specs



N
0ss

= variables with no steady
-
state effect






28









N
valves

=
6

,
N
0
y

=
2
,

N
specs

=
2
, N
DOF,SS

=
6
-
2
-
2
=
2

Distillation column with given feed and pressure

N
0
y

:
no. controlled variables (liquid levels) with no steady
-
state effect

NEED TO IDENTIFY
2
CV’s

-

Typical: Top and btm composition

1

2

3

4

5

6




31







Step
2
. Define optimal operation (economics)


What are we going to use our degrees of freedom
u

(MVs
) for?


Define scalar cost function J(
u
,x,d)


u
: degrees of freedom (usually steady
-
state)


d: disturbances


x: states (internal variables)

Typical cost function:




Optimize operation with respect to u for given d (usually steady
-
state):



min
u

J(
u
,x,d)

subject to:


Model equations:


f(
u
,x,d) =
0


Operational constraints:

g(
u
,x,d) <
0


J = cost feed + cost energy


value products




33







Optimal operation



1.
Given feed

Amount of products is then usually indirectly given and J = cost energy.
Optimal operation is then usually
unconstrained:



2.
Feed free

Products usually much more valuable than feed + energy costs small.


Optimal operation is then usually
constrained:



minimize J = cost feed + cost energy


value products

“maximize efficiency (energy)”

“maximize production”

Two main cases (modes) depending on marked conditions:

Control: Operate at bottleneck


(“obvious what to control”)

Control: Operate at optimal
trade
-
off (not obvious what to
control to achieve this)




35







Implementation of optimal operation


Optimal operation for given d
*
:



min
u

J(u,x,d)

subject to:


Model equations:


f(u,x,d) = 0


Operational constraints:

g(u,x,d) < 0




u
opt
(d
*
)

Problem:

Usally cannot keep
u
opt

constant because disturbances d change

How should we adjust the degrees of freedom
(u)?




36







Implementation (in practice): Local feedback
control!

“Self
-
optimizing
control:” Constant
setpoints for c gives
acceptable loss

y

Feedforward

Optimizing control

Local feedback:

Control c (CV)

d




38







Step
3
. What should we control (
c
)?


(primary controlled variables
y
1
=c
)













Introductory example: Runner

Issue:

What should we
control?




39








Cost to be minimized, J=T


One degree of freedom (u=power)


What should we control?



Optimal operation
-

Runner

Optimal operation of runner




40







Sprinter (
100
m)


1
. Optimal operation of Sprinter, J=T


Active constraint control:


Maximum speed (”no thinking required”)



Optimal operation
-

Runner




41








2
. Optimal operation of Marathon runner, J=T


Unconstrained optimum!


Any ”
self
-
optimizing”

variable c (to control at
constant setpoint)?


c
1
= distance to leader of race


c
2
= speed


c
3
= heart rate


c
4

= level of lactate in muscles


Optimal operation
-

Runner

Marathon (
40
km)




42








Conclusion Marathon runner



c = heart rate

select one measurement



Simple and robust implementation



Disturbances are indirectly handled by keeping a constant heart rate



May
have infrequent adjustment of setpoint (heart rate)

Optimal operation
-

Runner




47







Active constraints can vary!

Example: Optimal operation distillation


Cost to be minimized


J =
-

P where P= p
D

D + p
B

B


p
F

F


p
V

V


2
Steady
-
state DOFs (must find
2
CVs)


Product purity constraints distillation:


Purity spec. valuable product (
y
1
):
Always active



“avoid give
-
away of valuable product”.


Purity spec. “cheap” product (
y
2
): May
not

be active


may want to overpurify to avoid loss of valuable product


Many possibilities for active constraint sets (may vary from day to day!)

1.
Two active purity constraints

(
CV
1
= y
1
& CV
2
=
y
2
)


Happens when energy is relatively expensive


2.
One active purity constraint
.
CV
1
= y
1


Energy quite cheap:
Unconstrained.

Overpurify cheap product.





CV
2
=? (self
-
optimizing, e.g.
y
2
)


Energy really cheap: Overpurify until reach
MAX load

(active input constraint)



CV
2
= max input (max. energy)




48







a)
If constraint can be violated dynamically (only average matters)


Required Back
-
off

=
“bias” (steady
-
state measurement error for
c
)



b)
If constraint
cannot

be violated dynamically (“hard constraint”)


Required Back
-
off

=
“bias”

+
maximum dynamic control error

J
opt

Back
-
off

Loss

c


c
constraint

c

J

1
. CONTROL ACTIVE CONSTRAINTS!


Active
input

constraints: Just set at MAX or MIN


Active
output

constraints: Need
back
-
off

Want tight control of hard output constraints to reduce the
back
-
off

“Squeeze and shift”




49








Example. Optimal operation = max. throughput.


Want tight bottleneck control to reduce backoff!

Time

Back
-
off

= Lost
production


Rule for control of hard output constraints: “Squeeze and shift”!


Reduce variance (“Squeeze”) and “shift” setpoint
c
s

to reduce backoff




51







2
. UNCONSTRAINED VARIABLES:

-

WHAT MORE SHOULD WE CONTROL?

-

WHAT ARE GOOD “SELF
-
OPTIMIZING” VARIABLES?



Intuition:

“Dominant variables” (Shinnar)



Is there any systematic procedure?



A. Sensitive variables: “Max. gain rule” (Gain= Minimum singular
value)


B. “Brute force” loss evaluation


C. Optimal linear combination of measurements, c = Hy




52







Optimal operation

Cost J

Controlled variable c

c
opt

J
opt

Unconstrained optimum




53







Optimal operation

Cost J

Controlled variable c

c
opt

J
opt

Two problems:


1
. Optimum moves because of
disturbances d: c
opt
(d)


2
. Implementation error, c = c
opt

+
n

d

n

Unconstrained optimum




54







Candidate controlled variables c


for self
-
optimizing control

Intuitive


1.
The

optimal

value

of

c

should

be

insensitive

to

disturbances

(avoid

problem

1
)


2
.

Optimum

should

be

flat

(avoid

problem

2



implementation

error)
.


Equivalently
:

Value

of

c

should

be

sensitive

to

degrees

of

freedom

u
.



“Want

large

gain”,

|G|


Or

more

generally
:

Maximize

minimum

singular

value,




Unconstrained optimum

BAD

Good

Good




56







Recycle plant: Optimal operation

m
T

1
remaining unconstrained degree of freedom




57







Control of recycle plant:

Conventional structure (“Two
-
point”:
x
D
)

LC

XC

LC

XC

LC

x
B

x
D

Control active constraints
(M
r
=max and x
B
=
0.015
)

+
x
D




58








Luyben rule


Luyben rule (to avoid snowballing):

“Fix a stream in the recycle loop” (
F

or
D
)




59








Luyben rule: D constant


Luyben rule (to avoid snowballing):

“Fix a stream in the recycle loop” (
F

or
D
)

LC

LC

LC

XC




60







A
. Maximum gain rule: Steady
-
state gain

Luyben rule:

Not promising

economically

Conventional:

Looks good




62







Outline


Control structure design (plantwide control)


A procedure for control structure design


I

Top Down


Step
1
: Degrees of freedom


Step
2
: Operational objectives (optimal operation)


Step
3
: What to control ? (self
-
optimzing control)


Step
4
: Where set production rate?


II Bottom Up


Step
5
: Regulatory control: What more to control ?


Step
6
: Supervisory control


Step
7
: Real
-
time optimization


Case studies




63







Step
4
. Where set production rate?


Very important!


Determines structure of remaining inventory (level) control system


Set production rate at (dynamic) bottleneck


Link between
Top
-
down

and
Bottom
-
up

parts




64







Consistency of inventory control


Consistency

(required property):


An inventory control system is said to be
consistent

if the
steady
-
state mass balances

(total, components and
phases)
are satisfied

for any part of the process, including
the individual units and the overall plant.



Local
-
consistency (
desired property):



A consistent inventory control system is said to be
local
-
consistent
if for each unit the

local

inventory control
loops by themselves

are sufficient to achieve steady
-
state
mass balance consistency for that unit.







66







CONSISTENT?




67







Production rate set at inlet :

Inventory control in direction of flow*


* Required to get “local
-
consistent” inventory control




68







Production rate set at outlet:

Inventory control opposite flow





69







Production rate set inside process





72







Where set the production rate?



Very important decision that determines the structure of the rest of the
control system!



May also have important economic implications





73







Often optimal: Set production rate at
bottleneck!


"A bottleneck is a unit where we reach a constraints which makes
further increase in throughput infeasible"


If feed is cheap and available: Optimal to set production rate at
bottleneck



If the flow for some time is not at its maximum through the
bottleneck, then this loss can never be recovered.





74







Reactor
-
recycle process:


Want to maximize feedrate: reach
bottleneck

in column

Bottleneck: max. vapor


rate in column




75







Reactor
-
recycle process with max. feedrate


Alt.
1
: Feedrate controls bottleneck flow


Bottleneck: max. vapor


rate in column

FC


V
max


V

V
max
-
V
s
=Back
-
off


= Loss

V
s

Get “long loop”: Need back
-
off in V




76








MAX

Reactor
-
recycle process with max. feedrate:


Alt.
2

Optimal:
Set production rate at bottleneck (MAX)


Feedrate used for lost task (xb)

Get “long loop”: May need back
-
off in xB instead…

Bottleneck: max. vapor


rate in column




77







Reactor
-
recycle process with max. feedrate:


Alt.
3
:

Optimal:
Set production rate at bottleneck (MAX)


Reconfigure upstream loops

MAX

OK, but reconfiguration undesirable…




78







Reactor
-
recycle process:


Alt.
3
: reconfigure (permanently)

F
0
s



For cases with given feedrate: Get “long loop” but no associated loss




79







Conclusion production rate manipulator


Think carefully about where to place it!


Difficult to undo later


One approach: Put MPC top that
coordinates flows

through plant

by manipulating feed rate and other ”unused” degrees of freedom:



E.M.B. Aske, S. Strand and S. Skogestad,

``Coordinator MPC for maximizing plant throughput'',


Computers and Chemical Engineering
,
32
,
195
-
204
(
2008
).






80







Outline


Control structure design (plantwide control)


A procedure for control structure design


I

Top Down


Step
1
: Degrees of freedom


Step
2
: Operational objectives (optimal operation)


Step
3
: What to control ? (self
-
optimizing control)


Step
4
: Where set production rate?


II Bottom Up


Step
5
: Regulatory control: What more to control ?


Step
6
: Supervisory control


Step
7
: Real
-
time optimization


Case studies




81







Step
5
. Regulatory control layer


Purpose
: “Stabilize” the plant using a
simple control configuration (usually:
local SISO PID controllers + simple
cascades)


Enable manual operation (by operators)


Main structural issues:


What more should we control?

y
2
=?


(secondary cv’s, y
2
, use of extra
measurements)


Pairing with manipulated variables
(mv’s u
2
)




y
1

= c

y
2

= ?




82







Example: Distillation


Primary controlled variable: y
1

= c = x
D
, x
B

(compositions top, bottom)


BUT: Delay in measurement of x + unreliable


Regulatory control: For “stabilization” need control of (y
2
):


Liquid level condenser (M
D
)


Liquid level reboiler (M
B
)


Pressure (p)


Holdup of light component in column

(temperature profile)

Unstable (Integrating) + No steady
-
state effect

Variations in p disturb other loops

Almost unstable (integrating)

TC

T
s

T
-
loop in bottom




86







Objectives regulatory control layer

1.
Allow for manual operation

2.
Simple decentralized (local) PID controllers that can be tuned on
-
line

3.
Take care of “fast” control

4.
Track setpoint changes from the layer above

5.
Local disturbance rejection

6.
Stabilization

(mathematical sense)

7.
Avoid “drift” (due to disturbances) so system stays in “linear region”


“stabilization”
(practical sense)

8.
Allow for “slow” control in layer above (supervisory control)

9.
Make control problem easy as seen from layer above


Implications for selection of
y
2
:

1.
Control of
y
2

“stabilizes the plant”

2.
y
2

is easy to control (favorable dynamics)




88







2
. “
y
2

is easy to control” (controllability)

1.
Statics: Want large gain
(from u
2

to y
2
)

2.
Main rule:
y
2

is easy to measure and located
close to available manipulated variable u
2

(“pairing”)


3.
Dynamics: Want small
effective delay

(from u
2

to y
2
)


“effective delay” includes


inverse response (RHP
-
zeros)


+ high
-
order lags




89







3
. Rules for selecting
u
2

(to be paired with
y
2
)

1.
Avoid using variable u
2

that may saturate

(especially in loops at the
bottom of the control hieararchy)


Alternatively: Need to use “input resetting” in higher layer (“mid
-
ranging”)


Example: Stabilize reactor with bypass flow (e.g. if bypass may saturate, then
reset in higher layer using cooling flow)


2.
“Pair close”:

The controllability, for example in terms a small
effective delay from u
2

to y
2
, should be good.




94







Outline


Control structure design (plantwide control)


A procedure for control structure design


I

Top Down


Step
1
: Degrees of freedom


Step
2
: Operational objectives (optimal operation)


Step
3
: What to control ? (primary CV’s) (self
-
optimizing control)


Step
4
: Where set production rate?


II Bottom Up


Step
5
: Regulatory control: What more to control (secondary CV’s) ?


Step
6
: Supervisory control


Step
7
: Real
-
time optimization


Case studies




95







Step
6
. Supervisory control layer


Purpose
: Keep primary controlled outputs c=y
1

at optimal setpoints c
s


Degrees of freedom: Setpoints y
2
s

in reg.control layer


Main structural issue:

Decentralized or multivariable?





96







Decentralized control

(single
-
loop controllers)

Use for
: Noninteracting process and no change in active constraints

+

Tuning may be done on
-
line

+

No or minimal model requirements

+

Easy to fix and change

-

Need to determine pairing

-

Performance loss compared to multivariable control

-


Complicated logic required for reconfiguration when active constraints
move







97







Multivariable control

(with explicit constraint handling = MPC)

Use for
: Interacting process and changes in active constraints

+

Easy handling of feedforward control

+

Easy handling of changing constraints



no need for logic



smooth transition

-

Requires multivariable dynamic model

-

Tuning may be difficult

-

Less transparent

-

“Everything goes down at the same time”






98







Outline


Control structure design (plantwide control)


A procedure for control structure design


I

Top Down


Step
1
: Degrees of freedom


Step
2
: Operational objectives (optimal operation)


Step
3
: What to control ? (self
-
optimizing control)


Step
4
: Where set production rate?


II Bottom Up


Step
5
: Regulatory control: What more to control ?


Step
6
: Supervisory control


Step
7
: Real
-
time optimization


Case studies




99







Step
7
. Optimization layer (RTO)


Purpose:

Identify active constraints and compute optimal setpoints (to
be implemented by supervisory control layer)


Main structural issue:

Do we need RTO?

(or is process self
-
optimizing)



RTO not needed when


Can “easily” identify change in active constraints (operating region)


For each operating region there exists self
-
optimizing variables




10
0







Conclusion I: Focus on “what to control”


1
. Control for economics (Top
-
down steady
-
state
arguments)


Primary CVs, c = y
1

:


Control active constraints


For remaining unconstrained degrees of freedom: Look for
“self
-
optimizing” variables



2
. Control for stabilization (Bottom
-
up; regulatory PID
control)


Secondary CVs, y
2
:


Control “drifting” variables


Identify pairings with MVs (u


Pair close and avoid MVs that saturate



Both cases: Control “sensitive” variables (large gain)!



c
s

y
2
s

u

MV = manipulated variable (u)

CV = controlled variable (c)




10
1







Conclusion II.

S
ystematic procedure for plantwide control

1.
Start “top
-
down” with economics:


Step
1
: Identify degrees of freeedom


Step
2
:

Define operational objectives and optimize steady
-
state operation.


Step
3
A
: Identify active constraints = primary CVs
c
. Should controlled to
maximize profit)


Step
3
B
: For remaining unconstrained degrees of freedom: Select CVs
c

based
on self
-
optimizing control.



Step
4
: Where to set the throughput (usually: feed)


2.
Regulatory control I: Decide on how to move mass through the plant:


Step
5
A:

Propose “local
-
consistent” inventory control structure (
y
2
= levels,…
).

3.
Regulatory control II: “Bottom
-
up” stabilization of the plant


Step
5
B:

Control variables to stop “drift” (
y
2
=
sensitive temperatures, pressures, ....)


Pair variables to avoid interaction and saturation

4.
Finally: make link between “top
-
down” and “bottom up”.


Step
6
: “Advanced control” system (MPC):


CVs: Active constraints and self
-
optimizing economic variables +



look after variables in layer below (e.g., avoid saturation)


MVs: Setpoints to regulatory control layer.


Coordinates within units and possibly between units



c
s

y
2
s

u