Feedback Applications to self-optimizing control and stabilization of new operating regimes

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FeedbackApplications to self-optimizing control
and stabilization of new operating regimes

• Sigurd Skogestad
• Department of Chemical Engineering
• Norwegian University of Science and Technlogy
  (NTNU)
• Trondheim

South China University of Technology, Guangzhou,
05 January 2004
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Outline

• About myself
• Example 1 Why feedback (and not feedforward) ?
• What should we control? Secondary variables
  (Example 2)
• What should we control? Primary controlled
  variables
• A procedure for control structure design
  (plantwide control)
• Example stabilizing control Anti-slug control
• Conclusion

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Sigurd Skogestad

• Born in 1955
• 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 (Norwegian)
• Group of about 10 Ph.D. students in the process
  control area

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Arctic circle
North Sea
Trondheim!!
SWEDEN
NORWAY
Oslo
DENMARK
GERMANY
UK
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NTNU, Trondheim - view from south-west
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NTNU, Trondheim - view from south-east
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Chemical Engineering Dept. Building
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Research Develop simple yet rigorous methods to
solve problems of engineering significance.

• Use of feedback as a tool to
• reduce uncertainty (including robust control),
• change the system dynamics (including
  stabilization anti-slug control),
• 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
• Example 1 Why feedback (and not feedforward) ?
• What should we control? Secondary variables
  (Example 2)
• What should we control? Primary controlled
  variables
• A procedure for control structure design
  (plantwide control)
• Example stabilizing control Anti-slug control
• Conclusion

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Example 1
1
d
Gd
G
u
y
Plant (uncontrolled system)
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Model-based control Feedforward (FF) control
d
Gd
G
u
y
Perfect feedforward control u - G-1 Gd d Our
case GGd ? Use u -d
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d
Gd
G
u
y
FF control Nominal case (perfect model)
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d
Gd
G
u
y
FF control change in gain in G
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d
Gd
G
u
y
FF control change in time constant
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d
Gd
G
u
y
FF control change in delay (in G or Gd)
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Measurement-based correction Feedback (FB)
control
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Output y
Input u
Feedback generates inverse!
Resulting output
Feedback PI-control Nominal case
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d
Gd
ys
e
C
G
u
y
Feedback PI control change in gain in G
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FB control change in time constant in G
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FB control change in time delay in G
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FB control all cases
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d
Gd
G
u
y
FF control all cases
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Comment

• Time delay error in disturbance model (Gd) No
  effect (!) with feedback (except time shift)
• Feedforward Similar effect as time delay error
  in G

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Why feedback?(and not feedforward control)

• Counteract unmeasured disturbances
• Reduce effect of changes / uncertainty
  (robustness)
• Change system dynamics (including stabilization)
• No explicit model required
• MAIN PROBLEM
• Potential instability (may occur suddenly)

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Outline

• About myself
• Example 1 Why feedback (and not feedforward) ?
• What should we control? Secondary variables
  (Example 2)
• What should we control? Primary controlled
  variables
• A procedure for control structure design
  (plantwide control)
• Example stabilizing control Anti-slug control
• Conclusion

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Example 2 Plant with delay
PI-control
ys1
d6
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Fundamental limitation feedback Delay ?

• Effective delay PI-control original delay
  inverse response half of second time
  constant all smaller time constants

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Improve control?

• Feedback Some improvement possible with more
  complex controller
• For example, add derivative action
  (PID-controller)
• May reduce ?eff from 5 s to 2 s
• Problem Sensitive to measurement noise
• Does not remove the fundamental limitation
• Feedforward Good for time delay systems, but
  need model measurement of disturbance.
  Sensitive to uncertainty.
• Feedback cascade Add extra measurement and
  introduce local control
• May remove the fundamental limitation from
  high-order dynamics

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Cascade control w/ extra secondary measurement (2
PIs)
d
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Cascade control

• Inner fast (secondary) loop that control
  secondary variable
• P or PI-control
• Local disturbance rejection
• Much smaller effective delay (0.2 s)
• Outer slower primary loop
• Reduced effective delay (2 s)
• No loss in degrees of freedom
• Setpoint in inner loop new degree of freedom
• Time scale separation
• Inner loop can be modelled as gain1 effective
  delay
• Very effective for control of large-scale systems

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Outline

• About myself
• Example 1 Why feedback (and not feedforward) ?
• What should we control? Secondary variables
  (Example 2)
• What should we control? Primary controlled
  variables
• A procedure for control structure design
  (plantwide control)
• Example stabilizing control Anti-slug control
• Conclusion

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Process operation Hierarchical structure
RTO
MPC
Includes stabilizing control. As just shown Can
itself be hiearchical (cascaded)
PID
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Engineering systems

• Most (all?) large-scale engineering systems are
  controlled using hierarchies of quite simple
  single-loop controllers
• Commercial aircraft
• Large-scale chemical plant (refinery)
• 1000s of loops
• Simple components
• on-off P-control PI-control nonlinear
  fixes some feedforward

Same in biological systems
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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?
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What should we control?
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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) lt 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
• CONTROL ACTIVE CONSTRAINTS!
• Implementation of active constraints is usually
  simple.
• WHAT MORE SHOULD WE CONTROL?
• We here concentrate on the remaining
  unconstrained degrees of freedom u.

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Optimal operation
Cost J
Jopt
uopt
Independent variable u (remaining unconstrained)
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Implementation How do we deal with uncertainty?

• 1. Disturbances d
• 2. Implementation error n

us uopt(d0) nominal optimization
n
u us n
d
Cost J ? Jopt(d)
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Problem no. 1 Disturbance d
d ? d0
Cost J
d0
Jopt
Loss with constant value for u
uopt(d0)
Independent variable u
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Problem no. 2 Implementation error n
Cost J
d0
Loss due to implementation error for u
Jopt
usuopt(d0)
u us n
Independent variable u
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Obvious solution Optimizing control
Probem Too complicated
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Alternative Feedback implementation
Issue What should we control?
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Self-optimizing Control

• Define loss

• Self-optimizing Control
• Self-optimizing control is when acceptable loss
  can be achieved using constant set points (cs)
  for the controlled variables c (without
  re-optimizing when disturbances occur).

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Constant setpoint policy Effect of disturbances
(problem 1)
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Effect of implementation error (problem 2)
Good
BAD
Good
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Self-optimizing Control Marathon

• Optimal operation of Marathon runner, JT
• Any self-optimizing variable c (to control at
  constant setpoint)?

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Self-optimizing Control Marathon

• Optimal operation of Marathon runner, JT
• 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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Self-optimizing control Recycle processJ V
(minimize energy)
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4
1
Given feedrate F0 and column pressure
2
3
Nm 5 3 economic (steady-state) DOFs
Constraints Mr lt Mrmax, xB gt xBmin 0.98
DOF degree of freedom
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Recycle process Control active constraints
Active constraint Mr Mrmax
Remaining DOFL
Active constraint xB xBmin
One unconstrained DOF left for optimization
What more should we control?
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Recycle process Loss with constant setpoint, cs
Large loss with c F (Luyben rule)
Negligible loss with c L/F or c temperature
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Recycle process Proposed control structurefor
case with J V (minimize energy)
Active constraint Mr Mrmax
Active constraint xB xBmin
Self-optimizing loop Adjust L such that L/F is
constant
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Further examples

• Central bank. J welfare. cinflation rate (3)
• Cake baking. J nice taste, c Temperature
  (200C)
• Business, J profit. c Key performance
  indicator (KPI) (e.g. response time to order)
• Investment (portofolio management). J profit. c
  Fraction of investment in shares (50)
• Biological systems
• Self-optimizing controlled variables c have
  been found by natural selection
• Need to do reverse engineering
• Find the controlled variables used in nature
• From this identify what overall objective J the
  biological system has been attempting to optimize

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Looking for magic variables to keep at constant
setpoints.How can we find them?

• Consider available measurements y, and evaluate
  loss when they are kept constant (brute force)

• More general Find optimal linear combination
  (matrix H)

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Good candidate controlled variables c (for
self-optimizing control)

• Requirements
• The optimal value of c should be insensitive to
  disturbances (avoid problem 1)
• c should be easy to measure and control (rest
  avoid problem 2)
• The value of c should be sensitive to changes in
  the degrees of freedom
• (Equivalently, J as a function of c should be
  flat)
• For cases with more than one unconstrained
  degrees of freedom, the selected controlled
  variables should be independent.

Singular value rule (Skogestad and Postlethwaite,
1996) Look for variables that maximize the
minimum singular value of the appropriately
scaled steady-state gain matrix G from u to c
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Optimal measurement combination

• 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
• F sensitivity matrix
• Look for a linear combination c Hy which
  satisfies ?copt 0
• To achieve
• Always possible if
• Application See Adchem-paper by Alstad and
  Skogestad (Hong Kong, Jan. 2004)

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Conclusion so far

• Negative Feedback is an extremely powerful tool
• Complex systems can be controlled by hierarchies
  (cascades) of single-input-single-output (SISO)
  control loops
• Control extra local variables (secondary outputs)
  to avoid fundamental feedback control limitations
• Control the right variables (primary outputs) to
  achieve self-optimizing control
• Optimal linear combination

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Outline

• About myself
• Example 1 Why feedback (and not feedforward) ?
• What should we control? Secondary variables
  (Example 2)
• What should we control? Primary controlled
  variables
• Example stabilizing control Anti-slug control
• A procedure for control structure design
  (plantwide control)
• Conclusion

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Hierarchical structure
RTO
MPC
Includes stabilizing control.
PID
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Application stabilizing feedback control
Anti-slug control
Two-phase pipe flow (liquid and vapor)
Slug (liquid) buildup
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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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Experimental mini-loopValve opening (z) 100
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Experimental mini-loopValve opening (z) 25
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Experimental mini-loopValve opening (z) 15
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Experimental mini-loopBifurcation diagram
No slug
Valve opening z
Slugging
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Avoid slugging1. Close valve (but increases
pressure)
No slugging when valve is closed
Valve opening z
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Avoid slugging2. Build large slug-catcher

• Most common strategy in practice

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Avoid slugging3. Other design changes to avoid
slugging
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Avoid slugging 4. Control?
Comparison with simple 3-state model
Valve opening z
Predicted smooth flow Desirable but open-loop
unstable
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Avoid slugging4. Active feedback control
z
p1
Simple PI-controller
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Anti slug control Mini-loop experiments
p1 bar
z
Controller ON
Controller OFF
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Anti slug control Full-scale offshore
experiments at Hod-Vallhall field (Havre,1999)
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Analysis Poles and zeros
Topside
Operation points
Zeros
Topside measurements Ooops.... RHP-zeros or
zeros close to origin
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Stabilization with topside measurementsAvoid
RHP-zeros by using 2 measurements

• Model based control (LQG) with 2 top
  measurements DP and density ?T

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Summary anti slug control

• Stabilization of smooth flow regime !
• 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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Outline

• About myself
• Example 1 Why feedback (and not feedforward) ?
• What should we control? Secondary variables
  (Example 2)
• What should we control? Primary controlled
  variables
• Example stabilizing control Anti-slug control
• A procedure for control structure design
  (plantwide control)
• Conclusion

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Stepwise procedure for design of control system
in chemical plant
Stepwise procedure chemical plant

• I. TOP-DOWN
• Step 1. DEFINE OVERALL CONTROL OBJECTIVE
• Step 2. DEGREE OF FREEDOM ANALYSIS
• Step 3. WHAT TO CONTROL? (primary outputs)
• control active constraints
• unconstrained self-optimizing variables
• Mainly economic considerations
• Little control knowledge required!

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Stepwise procedure chemical plant
II. BOTTOM-UP (structure control system) Step
4. REGULATORY CONTROL LAYER
5.1 Stabilization 5.2 Local disturbance
rejection (inner cascades) ISSUE What more
to control? (secondary variables) Step 5.
SUPERVISORY CONTROL LAYER
Decentralized or multivariable control
(MPC)? Pairing? Step 6. OPTIMIZATION LAYER
(RTO)
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Summary
Stepwise procedure chemical plant

• Procedure plantwide control
• I. Top-down analysis to identify degrees of
  freedom and primary controlled variables (look
  for self-optimizing variables)
• II. Bottom-up analysis to determine secondary
  controlled variables and structure of control
  system (pairing).

• Skogestad, S. (2000), Plantwide control -towards
  a systematic procedure, Proc. ESCAPE12
  Symposium, Haag, Netherlands, May 2002.
• S. Skogestad, Control structure design for
  complete chemical plants'', Computers and
  Chemical Engineering, 28 (1-2), 219-234 (2004).
• Larsson, T. and S. Skogestad, 2000, Plantwide
  control A review and a new design procedure,
  Modeling, Identification and Control, 21,
  209-240.
• Skogestad, S. (2000). Plantwide control The
  search for the self-optimizing control
  structure. J. Proc. Control 10, 487-507.

See also the home page of Sigurd
Skogestad http//www.chembio.ntnu.no/users/skoge/
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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
  intelligense - people are better at this
• Set high standards for acceptable control
• Do not forget the simple and effective idea of
  feedback

More information Home page of Sigurd Skogestad
- http//www.nt.ntnu.no/users/skoge/ Or even
simpler Search for Skogestad on google
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