plantwide_control.ppt

8/10/2019 plantwide_control.ppt

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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).
http://www.nt.ntnu.no/users/skoge/publications/2004/control_structure_design_ccehttp://www.nt.ntnu.no/users/skoge/publications/2000/plantwide_review3/http://www.nt.ntnu.no/users/skoge/publications/2000/plantwide_review3/http://www.nt.ntnu.no/users/skoge/publications/2000/plantwide_review3/http://www.nt.ntnu.no/users/skoge/publications/2000/plantwide_review3/http://www.nt.ntnu.no/users/skoge/publications/2004/control_structure_design_cce


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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, `Èvaluation 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, `Òptimal 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, `Àpplication 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, `Àpplication 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, `Òptimal 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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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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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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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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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!



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Solution 2Feedback

(Self-optimizing control)

What should we control?



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Self-optimizing control: Sprinter (100m)

1. Optimal operation of Sprinter, J=T

Active constraint control:

Maximum speed (no thinking required)



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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)



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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)


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


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

plantwide_control.ppt

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