1 control structure design: what should we measure, control and manipulate? sigurd skogestad...

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Control structure design: What should we measure, control and manipulate?

Sigurd Skogestad

Department of Chemical Engineering

NTNU, Trondheim

First African Control Conference, Cape Town, 04 December 2003

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Outline

• About myself

• Control structure design

• A procedure for control structure design

• Selection of primary controlled variables

• Example stabilizing control: Anti slug control

• Conclusion

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Sigurd Skogestad

• Born in 1955• 1956-1961: Lived in South Africa (Durban & Johannesburg)• 1978: Siv.ing. Degree (MS) in Chemical Engineering from NTNU (NTH)• 1980-83: Process modeling group at the Norsk Hydro Research Center in

Porsgrunn• 1983-87: Ph.D. student in Chemical Engineering at Caltech, Pasadena, USA.

Thesis on “Robust distillation control”. Supervisor: Manfred Morari• 1987 - : Professor in Chemical Engineering at NTNU• Since 1994: Head of process systems engineering center in Trondheim

(PROST)• Since 1999: Head of Department of Chemical Engineering• 1996: Book “Multivariable feedback control” (Wiley)• 2000,2003: Book “Prosessteknikk” (Tapir)• Group of about 10 Ph.D. students in the process control area

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Research: Develop simple yet rigorous methods to solve problems of

engineering significance.

• Use of feedback as a tool to1. reduce uncertainty (including robust control),

2. change the system dynamics (including stabilization; anti-slug control),

3. generally make the system more well-behaved (including self-optimizing control).

• limitations on performance in linear systems (“controllability”),

• control structure design and plantwide control,

• interactions between process design and control,

• distillation column design, control and dynamics.

• Natural gas processes

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Outline

• About myself

• Control structure design

• A procedure for control structure design

• Selection of primary controlled variables

• Example stabilizing control: Anti slug control

• Conclusion

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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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Control structure design

• Not the tuning and behavior of each control loop,

• But rather the control philosophy of 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 design includes all the decisions we need make to get from ``PID control’’ to “Ph.D” control

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Process control:Control structure design = plantwide control

• Large systems

• Each plant usually different – modeling expensive

• Slow processes – no problem with computation time

• Structural issues important– What to control?

– Extra measurements

– Pairing of loops

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• Control structure selection issues are identified as important also in other industries.

Professor Gary Balas at ECC’03 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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Process operation: Hierarchical structure

Need to define objectives and identify main issues for each

layer

PID

RTO

MPC

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Regulatory control (seconds)

• Purpose: “Stabilize” the plant by controlling selected ‘’secondary’’ variables (y2) such that the plant does not drift too far away from its desired operation

• Use simple single-loop PI(D) controllers

• Status: Many loops poorly tuned– Most common setting: Kc=1, I=1 min (default)

– Even wrong sign of gain Kc ….

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Regulatory control……...

• Trend: Can do better! Carefully go through plant and retune important loops using standardized tuning procedure

• Exists many tuning rules, including Skogestad (SIMC) rules: – Kc = 0.5/k (1/) I = min (1, 8)

– “Probably the best simple PID tuning rules in the world”

• Outstanding structural issue: What loops to close, that is, which variables (y2) to control?

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Supervisory control (minutes)

• Purpose: Keep primary controlled variables (y1) at desired values, using as degrees of freedom the setpoints y2s for the regulatory layer.

• Status: Many different “advanced” controllers, including feedforward, decouplers, overrides, cascades, selectors, Smith Predictors, etc.

• Issues: – Which variables to control may change due to change of “active

constraints”

– Interactions and “pairing”

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Supervisory control…...

• Trend: Model predictive control (MPC) used as unifying tool.

– Linear multivariable models with input constraints

– Tuning (modelling) is time-consuming and expensive

• Issue: When use MPC and when use simpler single-loop decentralized controllers ?– MPC is preferred if active constraints (“bottleneck”) change.

– Avoids logic for reconfiguration of loops

• Outstanding structural issue:– What primary variables y1 to control?

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Local optimization (hour)

• Purpose: Identify active constraints and possibly recompute optimal setpoints y1s for controlled variables

• Status: Done manually by clever operators and engineers

• Trend: Real-time optimization (RTO) based on detailed nonlinear steady-state model

• Issues: – Optimization not reliable.

– Modelling is time-consuming and expensive

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Outline

• About myself

• Control structure design

• A procedure for control structure design

• Selection of primary controlled variables

• Example stabilizing control: Anti slug control

• Conclusion

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Stepwise procedure plantwide control

I. TOP-DOWN

Step 1. DEFN. OF OPERATIONAL OBJECTIVES

Step 2. MANIPULATED VARIABLES and DEGREE OF FREEDOM ANALYSIS

Step 3. WHAT TO CONTROL? (primary outputs, c= y1)

Step 4. PRODUCTION RATE

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II. BOTTOM-UP (structure control system):

Step 5. REGULATORY CONTROL LAYER

Stabilization and Local disturbance rejection What more to control? (secondary outputs y2)

Step 6. SUPERVISORY CONTROL LAYER

Decentralized control or MPC?

Step 7. OPTIMIZATION LAYER (RTO)

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Outline

• About myself

• Control structure design

• A procedure for control structure design

• Selection of primary controlled variables

• Example stabilizing control: Anti slug control

• Conclusion

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What should we control?

y1 = c ? (economics)

y2 = ? (“stabilization”)

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Optimal operation (economics)

• Define scalar cost function J(u0,d)

– u0: degrees of freedom

– d: disturbances

• Optimal operation for given d:

minu0 J(u0,d)subject to:

f(u0,d) = 0

g(u0,d) < 0

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Active constraints

• Optimal solution is usually at constraints, that is, most of the degrees of freedom are used to satisfy “active constraints”, g(u0,d) = 0

• Implementation of active constraints is usually simple.

• We here concentrate on the remaining unconstrained degrees of freedom u.

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Optimal operation

Cost J

Independent variable u(remaining unconstrained)

uuoptopt

JJoptopt

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Implementation: How do we deal with uncertainty?

• 1. Disturbances d

• 2. Implementation error n

us = uopt(d*) – nominal optimization

nu = us + n

d

Cost J Jopt(d)

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Problem no. 1: Disturbance d

Cost J

Independent variable uuuoptopt(d(d00))

JJoptopt

d*d*

dd

Loss with constant value for u

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Problem no. 2: Implementation error n

Cost J

Independent variable u

uuss=u=uoptopt(d(d00))

JJoptopt

dd00 Loss due to implementation error for u

u = us + n

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Probem: Too complicated

”Obvious” solution: Optimizing control

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Alternative: Look for another variable c to control

Cost J

Controlled variable cccoptopt

JJoptopt

and keep at constant setpoint cs = copt(d*)

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Self-optimizing Control

• Self-optimizing Control– Self-optimizing control is when acceptable

loss can be achieved using constant set points (c

s)

for the controlled variables c (without re-

optimizing when disturbances occur).

• Define loss:

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Controlled variable: Feedback implementation

Issue:What should we control?

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Constant setpoint policy:Effect of disturbances (“problem 1”)

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Effect of implementation error (“problem 2”)

BADGoodGood

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Self-optimizing Control – Illustrating Example

• Optimal operation of Marathon runner, J=T– Any self-optimizing variable c (to control at constant

setpoint)?

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Self-optimizing Control – Illustrating Example

• 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

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Further examples

• Central bank. J = welfare. c=inflation rate

• Cake baking. J = nice taste, c = Temperature

• Biology. J = ?, c = regulatory mechanism

• Business, J = profit. c = KPI = response time to order

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Good controlled Variables c: Guidelines

• Requirements for good candidate controlled variables (Skogestad & Postlethwaite, 1996):– Its optimal value copt(d) is insensitive to disturbances d (to

avoid problem 1)– It should be easy to measure and control accurately (n small

to avoid problem 1)– The variables c should be sensitive to change in inputs (to

avoid problem 2)– The selected variables c should be independent (to avoid

problem 2)

• Rule: Maximize minimum singular value of scaled G • c = G u

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Candidate controlled variables

• Selected among available measurements y,

• More generally: Find the optimal linear combination (matrix H):

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Candidate Controlled Variables: Guidelines

• Recall first requirement:

Its optimal value copt(d) is insensitive to disturbances (to avoid problem 1)

• Can we always find a variable combination c = H y

which satisfies

• YES!! Provided

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Derivation of optimal combination (Alstad)

• Starting point: Find optimal operation as a function of d:– uopt(d), yopt(d)

• Linearize this relationship: yopt = F d

• Look for a linear combination c = Hy which satisfies: copt = 0

• To achieve

• Always possible if

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Applications of self-optimizing control

• Distillation

• Tennessee Eastman Challenge problem

• Power plant

• +++

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Outline

• About myself

• Control structure design

• A procedure for control structure design

• Selection of primary controlled variables

• Example stabilizing control: Anti-slug control

• Conclusion

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Application: Anti-slug control

Slug (liquid) buildup

Two-phase pipe flow(liquid and vapor)

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Slug cycle (stable limit cycle) Experiments performed by the Multiphase Laboratory, NTNU

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Experimental mini-loop

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p1

p2

z

Experimental mini-loopValve opening (z) = 100%

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p1

p2

z

Experimental mini-loopValve opening (z) = 25%

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p1

p2

z

Experimental mini-loopValve opening (z) = 15%

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p1

p2

z

Experimental mini-loop:Bifurcation diagram

Valve opening z %

No slug

Slugging

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p1

p2

z

Avoid slugging:1. Close valve (but increases pressure)

Valve opening z %

No slugging when valve is closed

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Avoid slugging:2. Build large slug-catcher

• Most common strategy in practice

p1

p2

z

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Avoid slugging:3. Other design changes to avoid slugging

p1

p2

z

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Avoid slugging: 4. Control?

Valve opening z %

Predicted smooth flow: Desirable but open-loop unstable

Comparison with simple 3-state model:

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Avoid slugging:4. ”Active” feedback control

PT

PCref

Simple PI-controller

p1

z

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Anti slug control: Mini-loop experiments

Controller ON Controller OFF

p1 [bar]

z [%]

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Anti slug control: Full-scale offshore experiments at Hod-Vallhall field (Havre,1999)

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Poles and zeros

y

zP1 [Bar] DP[Bar] ρT [kg/m3] FQ [m3/s] FW [kg/s]

0.175-0.0034 3.2473

0.0142

-0.0004

0.0048

-4.5722

-0.0032

-0.0004

-7.6315

-0.0004

0

0.25-0.0034 3.4828

0.0131

-0.0004

0.0048

-4.6276

-0.0032

-0.0004

-7.7528

-0.0004

0

Operation points:

Zeros:

zP1 DP Poles

0.175 70.05 1.94-6.11

0.0008±0.0067i

0.25 69 0.96-6.21

0.0027±0.0092i

P1

ρT

DP

FTTopside

Topside measurements: Ooops.... RHP-zeros or zeros close to origin

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Stabilization with topside measurements:Avoid “RHP-zeros by using 2 measurements

• Model based control (LQG) with 2 top measurements: DP and density ρT

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Summary anti slug control

• Stabilization of smooth flow regime = $$$$! (or Rand!)

• Stabilization using downhole pressure simple

• Stabilization using topside measurements possible

• Control can make a difference!

Thanks to: Espen Storkaas + Heidi Sivertsen and Ingvald Bårdsen

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Conclusion

What would I do if I was manager in a large chemical company?

• Define objective of control: Better operation (objective is not just to collect data)

• Define control as a function in my organization

• Define operational objectives for each plant ($ + other..)

• Unified approach (”company policy”):– Stabilizing control. PID rules

– MPC

– Avoid rule-based systems / Artificial intelligens /operator support systems - people are better at this

• Set high standards for acceptable control

My view

More information: Home page of Sigurd Skogestad - http://www.nt.ntnu.no/users/skoge/