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PLANTWIDE CONTROL
How to design the control system for acomplete plant in a systematic manner
Sigurd Skogestad
Department of Chemical Engineering
Norwegian University of Science and Tecnology (NTNU)
Trondheim, Norway
Petrobras, March 2010
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Summary.
Systematic procedure for plantwide control
1. Start top-down with economics: Optimize steady-state operation
Identify active constraints (should normally be tightly controlled tomaxize profit)
For remaining degrees of freedom: Select controlled variables cbased onself-optimizing control.
2. Regulatory control I: Decide on how to move mass through the plant:
Where to set the throughput (usually: feed) Propose local-consistent inventory (level) control structure.
3. Regulatory control II: Bottom-up stabilization of the plant Control variables to stop drift (sensitive temperatures, pressures, ....)
Pair variables to avoid interaction and saturation
4. Finally: make link between top-down and bottom up.
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
cs
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Summary and 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 thefollowing review paper:
T. Larsson and S. Skogestad, ``Plantwide control: A review and a new
design procedure''Modeling, Identification and Control, 21, 209-240
(2000).
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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 andChemical Eng
ineering, 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 EngineeringResearch 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-optimizingcontrol'', 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 exchangernetworks'',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. Askoe and S. Skogestad, Consistent inventory control, Submitted (2009)
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Plantwide control intro course: Contents
Overview of plantwide control
Selection of primary controlled variables based on economic : The linkbetween the optimization (RTO) and the control (MPC; PID) layers- Degrees of freedom- Optimization- Self-optimizing control
- Applications- Many examples
Where to set the production rate and bottleneck
Design of the regulatory control layer ("what more should wecontrol")
- stabilization- secondary controlled variables (measurements)- pairing with inputs- controllability analysis
- cascade control and time scale separation. Design of supervisory control layer
- Decentralized versus centralized (MPC)- Design of decentralized controllers: Sequential and independent design- Pairing and RGA-analysis
Summary and case studies
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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 CVs) (self-optimizing control)
Step 4: Where set the production rate? (Inventory control)
II Bottom Up
Step 5: Regulatory control: What more to control (secondary CVs) ?
Step 6: Supervisory control
Step 7: Real-time optimization
Case studies
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Main message
1. Control for economics (Top-down steady-state arguments)
Primary controlled variables c = y1: Control active constraints
For remaining unconstrained degrees of freedom: Look for self-optimizingvariables
2. Control for stabilization (Bottom-up; regulatory PID control)
Secondary controlled variables y2(inner cascade loops)
Control variables which otherwise may drift
Both cases: Control sensitive variables (with a large gain)!
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Idealized view of control
(Ph.D. control)
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Practice: Tennessee Eastman challenge
problem (Downs, 1991)
(PID control)
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How we design a control system for a
complete chemical plant?
Where do we start?
What should we control? and why?
etc.
etc.
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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.
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Control structure design
Notthe tuning and behavior of each control loop,
But rather the control philosophyof the overall plant with emphasis on
the structural decisions:
Selection of controlled variables (outputs) Selection of manipulated variables (inputs)
Selection of (extra) measurements
Selection of control configuration (structure of overall controller that
interconnects the controlled, manipulated and measured variables)
Selection of controller type(LQG, H-infinity, PID, decoupler, MPC etc.). That is:Control structure designincludes all the decisions we need
make to get from ``PID controlto Ph.Dcontrol
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Process control:
Plantwide control = Control structure
design for complete chemical plant Large systems
Each plant usually differentmodeling expensive
Slow processesno problem with computation time
Structural issuesimportant
What to control? Extra measurements, Pairing of loops
Previous work on plantwide control:Page Buckley (1964) - Chapter on Overall process control(still industrial practice)
Greg Shinskey (1967)process control systems
Alan Foss (1973) - control system structure
Bill Luyben et al. (1975- )case studies ; snowball effect
George Stephanopoulos and Manfred Morari (1980)synthesis of control structures for chemical processes
Ruel Shinnar (1981- ) - dominant variables
Jim Downs (1991) - Tennessee Eastman challenge problem
Larsson and Skogestad (2000): Review of plantwide control
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Control structure selection issues are identified as important also in
other industries.
Professor Gary Balas (Minnesota) at ECC03 about flight control at Boeing:
The most important control issue has always been to select the right
controlled variables --- no systematic tools used!
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Main objectives control system
1. Stabilization
2. Implementation of acceptable (near-optimal) operation
ARE THESE OBJECTIVES CONFLICTING?
Usually NOT
Different time scales
Stabilization fast time scale
Stabilization doesnt use up any degrees of freedom Reference value (setpoint) available for layer above
But it uses up part of the time window (frequency range)
Dealing with complexity
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cs = y1s
MPC
PID
y2s
RTO
u (valves)
Follow path (+ look after)
CV=y1 (+ u); MV=y2s
Stabilize + avoid drift
CV=y2; MV=u
Min J (economics);MV=y1s
OBJECTIVE
Dealing with complexity
Main simplification: Hierarchical decomposition
Process control The controlled variables (CVs
interconnect the layers
Hierarchical decomposition
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Example: Bicycle riding
Note: design starts from the bottom
Regulatory control:
First need to learn to stabilize the bicycle
CV = y2 = tilt of bike
MV = body position
Supervisory control:
Then need to follow the road.
CV = y1= distance from right hand side
MV=y2s
Usually a constant setpoint policy is OK, e.g. y1s=0.5 m
Optimization:
Which road should you follow?
Temporary (discrete) changes in y1s
Hierarchical decomposition
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Summary: The three layers
Optimization layer (RTO; steady-state nonlinear model): Identifies active constraints and computes optimal setpoints for primary controlled variables (y1).
Supervisory control (MPC; linear model with constraints): Follow setpoints for y1(usually constant) by adjusting setpoints for secondary variables (MV=y2s)
Look after other variables (e.g., avoid saturation for us used in regulatory layer)
Regulatory control (PID): Stabilizes the plant and avoids drift, in addition to following setpoints for y2. MV=valves (u).
Problem definition and overall control objectives (y1, y2) starts from the top.
Design starts from the bottom.
A good example is bicycle riding:
Regulatory control: First you need to learn how to stabilize the bicycle (y2)
Supervisory control: Then you need to follow the road. Usually a constant setpoint policy is OK, for example, stay
y1s=0.5 m from the right hand side of the road (in this case the "magic" self-optimizing variableself-optimizing variable is y1=distance to right hand side of road)
Optimization: Which road (route) should you follow?
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Stepwise procedure plantwide control
I. TOP-DOWNStep 1. DEGREES OF FREEDOM
Step 2. OPERATIONAL OBJECTIVES
Step 3. WHAT TO CONTROL? (primary CVsc=y1)
Step 4. PRODUCTION RATE
II. BOTTOM-UP (structure control system):Step 5. REGULATORY CONTROL LAYER (PID)
Stabilization
What more to control? (secondary CVs y2)
Step 6. SUPERVISORY CONTROL LAYER (MPC)Decentralization
Step 7. OPTIMIZATION LAYER (RTO)
Can we do without it?
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Control structure design procedure
I Top Down Step 1: Identify degrees of freedom (MVs)
Step 2: Define operational objectives (optimal operation)
Cost function J (to be minimized)
Operational constraints
Step 3: Select primary controlled variables c=y1
(CVs)
Step 4: Where set the production rate? (Inventory control)
II Bottom Up Step 5: Regulatory / stabilizing control (PID layer)
What more to control (y2; local CVs)?
Pairing of inputs and outputs
Step 6: Supervisory control (MPC layer) Step 7: Real-time optimization
Understanding and using this procedure is the most important part of this course!!!!
y1
y2
Process
MVs
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Steady-statedegrees of freedom (DOFs)
IMPORTANT! No. of steady-state CVs = No. of steady-state DOFs
Three methods to obtain no. of steady-state degrees of freedom (Nss):
1. Equation-counting
Nss= no. of variablesno. of equations/specifications
Very difficult in practice (not covered here)
2. Valve-counting (easier!)
Nss= NvalvesN0ssNspecs
N0ss= variables with no steady-state effect
3. Typical number for some units (useful for checking!)
CV = controlled variable (c)
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Steady-state degrees of freedom (Nss):
2. Valve-counting
Nvalves = no. of dynamic (control) DOFs (valves)
Nss= NvalvesN0ssNspecs : no. of steady-state DOFs N0ss= N0y+ N0,valves : no. of variables with no steady-state effect
N0,valves: no. purely dynamic control DOFs
N0y: no. controlled variables (liquid levels) with no steady-state effect
Nspecs: No of equality specifications (e.g., given pressure)
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Nvalves= 6 , N0y= 2 , Nspecs= 2, NSS= 6 -2 -2 = 2
Distillation column with given feed and pressure
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Heat-integrated distillation process
Nvalves = 11 w/feed , N0 = 4 levels , Nss= 114=
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Heat-integrated distillation process
Nvalves = 11 w/feed , N0 = 4 levels , Nss= 114= 7
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Heat exchanger with bypasses
CW
Nvalves = 3, N0valves = 2 (of 3), Nss= 32 = 1
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Heat exchanger with bypasses
CW
Nvalves = 3, N0valves = 2 (of 3), Nss= 32 = 1
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Steady-state degrees of freedom (Nss):
3. Typical number for some process units
each external feedstream: 1 (feedrate)
splitter: n-1 (split fractions) where n is the number of exit streams
mixer: 0
compressor, turbine, pump: 1 (work/speed) adiabatic flash tank: 0*
liquid phase reactor: 1 (holdup-volume reactant)
gas phase reactor: 0*
heat exchanger: 1 (duty or net area)
column (e.g. distillation) excluding heat exchangers: 0*
+ no. of sidestreams pressure*: add 1DOF at each extra place you set pressure (using an extra
valve, compressor or pump), e.g. in adiabatic flash tank, gas phase reactor or
column
*Pressure is normally assumed to be given by the surrounding process and is then not a degree of
freedom
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Heat exchanger with bypasses
CW
Typical number heat exchanger Nss= 1
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Typical number,
Nss= 0 (distillation) + 2*1 (heat exchangers) = 2
Distillation column with given feed and pressure
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Heat-integrated distillation process
Typical number, Nss= 1 (feed) + 2*0 (columns) + 2*1
(column pressures) + 1 (sidestream) + 3 (hex) = 7
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HDA process
Mixer FEHE Furnace PFRQuench
Separator
Compressor
Cooler
StabilizerBenzeneColumn
TolueneColumn
H2+ CH4
Toluene
Toluene Benzene CH4
Diphenyl
Purge (H2+ CH4)
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HDA process: steady-state degrees of freedom
1
2
3
8 7
4
6
5
9
10
11
12
13
14
Conclusion: 14
steady-stateDOFs
Assume given column pressures
feed:1.2
hex: 3, 4, 6
splitter 5, 7
compressor: 8
distillation: 2 eachcolumn
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Check that there are enough manipulated variables (DOFs) - both
dynamically and at steady-state (step 2)
Otherwise: Need to add equipment extra heat exchanger
bypass
surge tank
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Outline
Introduction
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? (inventory control)
II Bottom Up
Step 5: Regulatory control: What more to control ? Step 6: Supervisory control
Step 7: Real-time optimization
Case studies
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Step 2. Define optimal operation (economics)
What are we going to use our degrees of freedom for?
Define scalar cost function J(u0,x,d)
u0: degrees of freedom
d: disturbances
x: states (internal variables)
Typical cost function:
Optimal operation for given d:
minuss J(uss,x,d)subject to:
Model equations: f(uss,x,d) = 0
Operational constraints: g(uss,x,d) < 0
J = cost feed + cost energyvalue products
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Optimal operation distillation column
Distillation at steady state with given p and F: N=2 DOFs, e.g. L and V
Cost to be minimized (economics)
J = - P where P= pDD + pBBpFFpVV
ConstraintsPurity D: For example xD, impuritymax
Purity B: For example, xB, impuritymax
Flow constraints: minD, B, L etc. max
Column capacity (flooding): VVmax, etc.
Pressure: 1) p given, 2) p free: pminp pmax
Feed: 1) F given 2) F free: FFmax
Optimal operation: Minimize J with respect to steady-state DOFs
value products
cost energy (heating+ cooling)
cost feed
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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 energyvalue products
maximize efficiency (energy)
maximize production
Two main cases (modes) depending on marked conditions:
Control: Operate at bottleneck (obvious)
Control: Operate at optimaltrade-off (not obvious how to do
and what to control)
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Comments optimal operation
Do not forget to include feedrate as a degree of freedom!!
For LNG plant it may be optimal to have max. compressor power or max.
compressor speed, and adjust feedrate of LNG For paper machine it may be optimal to have max. drying and adjust the
feedrate of paper (speed of the paper machine) to meet spec!
Control at bottleneck
see later: Where to set the production rate
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QUIZ
1. Degrees of freedom (Dynamic, steady-state)?
2. Expected active constraints?
3. Proposed control structure?
Reaktor
A+B C
Kompressor
Purge (mest A, litt B)
Fde
ca 51%A, 49% B
Oppvarming Kjling
Separator
Produkt (C)
HeatingCooling
Feed
51%A, 49%B
Purge (mostly A, some B, trace C)
Liquid Product (C)
Flash
Gas phase process
(e.g. ammonia, methanol)
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Implementation of optimal operation
Optimal operation for given d*:
minu J(u,x,d)subject to:
Model equations: f(u,x,d) = 0
Operational constraints: g(u,x,d) < 0
uopt
(d*)
Problem:Usally cannot keep uoptconstant because disturbances d change
How should we adjust the degrees of freedom (u)?
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Solution I: Optimal feedforward
With availability of perfect model and
measurement of all disturbances d,
degrees of freedom ucan be continuously
updated using online optimizer
Problem: UNREALISTIC!
Feedforward problems:
1. Lack of measurements of d2. Sensitive to model error
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Solution III (Practical!): Hierarchical
decomposition with separate layers
When disturbance d:
Degrees of freedom (u)
are updated indirectly tokeep controlled variables
at setpoints
y
Controlled variables that
link the optimization andcontrol layers
S lf O ti i i C t l
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Self-Optimizing Control
= Solution III with constant setpoints
When constantsetpoints are OK
y
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Formal Definition
Self-optimizing control is said to occur when we can achieve an acceptable loss (in comparison withtruly optimal operation) with constant setpoint values for the controlled variables without the needto reoptimize when disturbances occur.
Reference: S. Skogestad, Plantwide control: The search for the self-optimizing control structure'',
Journal of Process Control, 10, 487-507 (2000).
Acceptable loss)self-optimizing controlController
Processd
u(d)
c = f(y)
cse
-
+
+n
cm
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How does self-optimizing control (solution
III) work?
When disturbances d occur, controlled variable c deviates from setpoint cs
Feedback controller changes degree of freedom u to uFB(d) to keep cat cs
Near-optimal operation / acceptable loss (self-optimizing control) is achieved if uFB(d) uopt(d)
or more generally,J(uFB(d)) J(uopt(d))
Of course, variation of uFB(d) is different for different CVs c.
We need to look for variables, for whichJ(uFB(d)) J(uopt(d)) or Loss =J(uFB(d)) -J(uopt(d)) is small
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Remarks
Self-optimizing control provides a trade-off between complexity of control systemand optimality.
Old idea (Morari et al., 1980):
We want to find a function c of the process variables which when held constant,
leads automatically to the optimal adjustments of the manipulated variables, andwith it, the optimal operating conditions.
The term self -optimizing control is similar to self-regulation, where acceptabledynamic behavior is attained by keeping manipulated variables constant.
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Relation with Similar Techniques
Broadly, self-optimizing control can be seen as a measurement-based (or feedback-based)
optimization technique.
Some related ideas are:
Control of necessary conditions of optimality (Profs. Dominique Bonvin, B. Srinivasan and co-
workers)
Extremum seeking control (Profs. Miroslav Krstic, Martin Guay and co-workers)
In these techniques, uis updated to drive the gradient of Lagrange function (obtained
analytically or estimated) to zero.
Gradient of Lagrange function is a possible self-optimizing variable!
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Step 3. What should we control (c)?
(primary controlled variables y1=c)
Introductory example: Marathon runner
What should we
control?
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Optimal operationRunner
Cost: J=T
One degree of freedom (u=power)
Optimal operation?
Optimal operation - Runner
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Solution 1: Optimizing control
Even getting a reasonable model
requires > 10 PhDs and
the model has to be fitted to each
individual.
Clearly impractical!
Optimal operation - Runner
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Solution 2Feedback
(Self-optimizing control)
What should we control?
Optimal operation - Runner
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Self-optimizing control: Sprinter (100m)
1. Optimal operation of Sprinter, J=T
Active constraint control:
Maximum speed (no thinking required)
Optimal operation - Runner
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Optimal operation of Marathon runner, J=T
Any self-optimizing variable c (to control at
constant setpoint)? c1 = distance to leader of race c2 = speed
c3 = heart rate
c4= level of lactate in muscles
Self-optimizing control: Marathon (40 km)
Optimal operation - Runner
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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)
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Example: Cake Baking
Objective: Nice tasting cake with good texture
u1 = Heat input
u2 = Final time
d1=
oven specifications
d2 =oven door opening
d3 =ambient temperature
d4
=
initial temperature
y1 =oven temperature
y2 =cake temperature
y3 =cake color
MeasurementsDisturbances
Degrees of Freedom
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Further examples self-optimizing control
Marathon runner
Central bank
Cake baking
Business systems (KPIs) Investment portifolio
Biology
Chemical process plants: Optimal blending of gasoline
Define optimal operation (J) and look for magic variable
(c) which when kept constant gives acceptable loss (self-
optimizing control)
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More on further examples
Central bank. J = welfare. u = interest rate. c=inflation rate (2.5%) Cake baking.J = nice taste, u = heat input. c = Temperature (200C)
Business,J = profit. c = Key performance indicator (KPI), e.g.
Response time to order
Energy consumption pr. kg or unit
Number of employees Research spending
Optimal values obtained by benchmarking
Investment(portofolio management). J = profit. c = Fraction ofinvestment in shares (50%)
Biological systems:
Self-optimizing controlled variables c have been found by naturalselection
Need to do reverse engineering :
Find the controlled variables used in nature
From this possibly identify what overall objective J the biological system hasbeen attempting to optimize
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Step 3. What should we control (c)?
(primary controlled variables y1=c)
Selection of controlled variables c
1. Control active constraints!
2. Unconstrained variables: Control magic self-
optimizing variables!
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1. If c= u= manipulated input (MV): Implementation trivial: Keep uat constraint (uminor umax)
2. If c=y= output variable (CV):
Use uto controlyat constraint (feedback)
BUT: Need to introduceback-off (safety margin)
c cconstraint
Jopt
c
J
copt
Optimal solution is usually at constraints, that is, most of the
degrees of freedom are used to satisfy active constraints,
g(u,d) = 0 -> c=cconstraint
1. CONTROL ACTIVE CONSTRAINTS!
B k ff f i i
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Back-off for active output constraints
a) If constraint can be violated dynamically (only average matters)
Required Back-off= bias (steady-state measurement error for c)
b) If constraint cannotbe violated dynamically (hard constraint)
Required Back-off= bias+ maximum dynamic control error
Back-off
Loss
c cconstraint
Jopt
c
J
copt
Example Optimal operation = max throughput
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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 csto reduce backoff
Hard Constraints: SQUEEZE AND SHIFT
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Hard Constraints: SQUEEZE AND SHIFT
0 50 100 150 200 250 300 350 400 4500
0.5
1
1.5
2
OFF
SPEC
QUALITY
N Histogram
Q1
Sigma 1
Q2
Sigma 2
DELTA COST (W2-W1)
LEVEL 0 / LEVEL 1
Sigma 1 -- Sigma 2
LEVEL 2
Q1 -- Q2
W1
W2
COST FUNCTION
Richalet SHIFT
SQUEEZE
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Cost to be minimized (economics)
J = - P where P= pDD + pBBpFFpVV
ConstraintsPurity D: For example xD, impuritymax
Purity B: For example, xB, impuritymax
Flow constraints: 0 D, B, L etc. max
Column capacity (flooding): V Vmax, etc.
value products
cost energy (heating+ cooling)
cost feed
Optimal operation distillation
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Expected active constraints distillation
Valueable product: Purity spec. always active
Reason: Amount of valuable product (D or B)
should always be maximized
Avoid product give-away
(Sell water as methanol)
Also saves energy
Control implications valueable product: Control
purity at spec.
valuable
product
methanol+ max. 0.5%
water
cheap product
(byproduct)
water+ max. 0.1%
methanol
methanol
+ water
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Summary: Optimal operation distillation
Cost to be minimized
J = - P where P= pDD + pBBpFFpVV
N=2 steady-state degrees of freedom
Active constraints distillation:
Purity spec. valuable product is always active (avoid give-away of valuable product).
Purity spec. cheap product may not be active (may want to
overpurify to avoid loss of valuable productbut costs energy)
Three cases:
1. Nactive=2: Two active constraints (for example, xD, impurity= max. xB,
impurity= max, TWO-POINT COMPOSITION CONTROL)
2. Nactive=1: One constraint active (1 unconstrained DOF)
3. Nactive=0: No constraints active (2 unconstrained DOFs)
Can happen if no purity specifications
(e.g. byproducts or recycle)
WHAT SHOULD WE
CONTROL (TO SATISFY
UNCONSTRAINED DOFs)?
Solution:
Often compositions
but not always!
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QUIZ (again)
1. Degrees of freedom (Dynamic, steady-state)?
2. Expected active constraints? (1. Feed given; 2. Feed free)
3. Proposed control structure?
Reaktor
A+B C
Kompressor
Purge (mest A, litt B)
Fde
ca 51%A, 49% B
Oppvarming Kjling
Separator
Produkt (C)
Heating Cooling
Feed
51%A, 49%B
Purge (mostly A, some B, trace C)
Liquid Product (C)
Flash
Gas phase process
(e.g. ammonia, methanol)
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2. UNCONSTRAINED VARIABLES:
WHAT MORE SHOULD WE CONTROL?
Intuition:Dominant variables (Shinnar)
Is there any systematic procedure?
A. Senstive variables: Max. gain rule (Gain= Minimum singular value)
B. Brute force loss evaluation
C. Optimal linear combination of measurements, c = Hy