PLANTWIDE CONTROL

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PLANTWIDE CONTROL

• Sigurd Skogestad
• Department of Chemical Engineering
• Norwegian University of Science and Tecnology
  (NTNU)
• Trondheim, Norway
• August/September/December 2006

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Summary and references

• We have developed a systematic procedure for
  plantwide control. An important part is the
  selection of controlled variables based on
  self-optimizing control. These are the controlled
  variables for the "supervisory" control layer. In
  addition, we need a regulatory control system to
  stabilize the plant and avoid drift.
• The following paper summarizes the procedure
• S. Skogestad, Control structure design for
  complete chemical plants'', Computers and
  Chemical Engineering, 28 (1-2), 219-234 (2004).
• There are many approaches to plantwide control as
  discussed in the following review paper
• T. Larsson and S. Skogestad, Plantwide control
  A review and a new design procedure'' Modeling,
  Identification and Control, 21, 209-240 (2000).

3
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 production rate?
• 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-optimizing variables
• 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 variables with a large gain!

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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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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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Main simplification Hierarchical structure
RTO
Need to define objectives and identify main
issues for each layer
MPC
PID
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Objectives of layers MVs and CVs
RTO
Min J (economics) MVy1s
cs y1s
CVy1 MVy2s
MPC
y2s
PID
CVy2 MVu
u (valves)
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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
  (MVy2s)
• Regulatory control (PID)
• Stabilizes the plant and avoids drift, in
  addition to following setpoints for y2. MVvalves
  (u).
• Design starts from the bottom. A good example is
  bicycle riding
• Regulatory control
• First you need to learn how to stabilize the
  bicycle
• Supervisory control
• Then you need to follow the road. Usually a
  constant setpoint policy is OK, for example, stay
  y1s0.5 m from the right hand side of the road
  (in this case the "magic" self-optimizing
  variable self-optimizing variable is y1distance
  to right hand side of road)
• Optimization
• Which road (route) should you follow?

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Stepwise procedure plantwide control
I. TOP-DOWN Step 1. DEGREES OF FREEDOM Step 2.
OPERATIONAL OBJECTIVES Step 3. WHAT TO CONTROL?
(primary CVs cy1) 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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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) lt 0

J cost feed cost energy value products
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Optimal operation distillation column

• Distillation at steady state with given p and F
  N2 DOFs, e.g. L and V
• Cost to be minimized (economics)
• J - P where P pD D pB B pF F pV V
• Constraints
• Purity D For example xD, impurity max
• Purity B For example, xB, impurity max
• Flow constraints min D, B, L etc. max
• Column capacity (flooding) V Vmax, etc.
• Pressure 1) p given, 2) p free pmin p
  pmax
• Feed 1) F given 2) F free F Fmax
• Optimal operation Minimize J with respect to
  steady-state DOFs

cost energy (heating cooling)
value products
cost feed
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Optimal operation
minimize J cost feed cost energy value
products
Two main cases (modes) depending on marked
conditions

• Given feed
• Amount of products is then usually indirectly
  given and J cost energy. Optimal operation is
  then usually unconstrained
• Feed free
• Products usually much more valuable than feed
  energy costs small.
• Optimal operation is then usually constrained

maximize efficiency (energy)
Control Operate at optimal trade-off (not
obvious how to do and what to control)
maximize production
Control Operate at bottleneck (obvious)
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Step 3 What cs should we control?

• Optimal solution is usually at constraints, that
  is, most of the degrees of freedom are used to
  satisfy active constraints, g(u,d) 0
• CONTROL ACTIVE CONSTRAINTS!
• cs value of active constraint
• Implementation of active constraints is usually
  simple.
• WHAT MORE SHOULD WE CONTROL?
• Find self-optimizing variables c for remaining
• unconstrained degrees of freedom u.

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What should we control? Sprinter

• Optimal operation of Sprinter (100 m), JT
• One input power/speed
• Active constraint control
• Maximum speed (no thinking required)

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What should we control? Marathon

• Optimal operation of Marathon runner, JT
• No active constraints
• 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

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

ccs
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Step 4. Where set production rate?

• Very important!
• Determines structure of remaining inventory
  (level) control system
• Set production rate at (dynamic) bottleneck
• Link between Top-down and Bottom-up parts

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Production rate set at inlet Inventory control
in direction of flow
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Production rate set at outletInventory control
opposite flow
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Production rate set inside process
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Where set the production rate?

• Very important decision that determines the
  structure of the rest of the control system!
• May also have important economic implications

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Often optimal Set production rate at bottleneck!

• A unit is a bottleneck if maximum throughput is
  obtained by operating this unit at maximum flow
• If feed is cheap and available Optimal with
  maximum throughput
• If the flow for some time is not at its maximum
  through the bottleneck, then this loss can never
  be recovered.
• To reduce back-off Optimal to set throughput
  (production rate) at bottleneck
• Throughput manipulator Bottleneck flow

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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 ? (self-optimizing
  control)
• Step 4 Where set production rate?
• II Bottom Up
• Step 5 Regulatory control What more to control
  ?
• Step 6 Supervisory control
• Step 7 Real-time optimization
• Case studies

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Step 5. Regulatory control layer

• Purpose Stabilize the plant using local SISO
  PID controllers
• Enable manual operation (by operators)
• Main structural issues
• What more should we control? (secondary cvs, y2)
• Pairing with manipulated variables (mvs u2)

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Objectives regulatory control layer

• Allow for manual operation
• Simple decentralized (local) PID controllers that
  can be tuned on-line
• Take care of fast control
• Track setpoint changes from the layer above
• Local disturbance rejection
• Stabilization (mathematical sense)
• Avoid drift (due to disturbances) so system
  stays in linear region
• stabilization (practical sense)
• Allow for slow control in layer above
  (supervisory control)
• Make control problem easy as seen from layer
  above

• Implications for selection of y2
• Control of y2 stabilizes the plant
• y2 is easy to control (favorable dynamics)

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Cascade control distillation
ys
y
With flow loop T-loop in top
XC
Ts
T
TC
Ls
L
FC
z
XC
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Step 6. Supervisory control layer

• Purpose Keep primary controlled outputs cy1 at
  optimal setpoints cs
• Degrees of freedom Setpoints y2s in reg.control
  layer
• Main structural issue Decentralized or
  multivariable?

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Step 7. Optimization layer (RTO)

• Purpose Identify active constraints and compute
  optimal setpoints (to be implemented by
  supervisory control layer)
• Main structural issue Do we need RTO? (or is
  process self-optimizing)
• RTO not needed when
• Can easily identify change in active
  constraints (operating region)
• For each operating region there exists
  self-optimizing var

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Summary Main steps

• What should we control (y1cz)?
• Must define optimal operation!
• Where should we set the production rate?
• At bottleneck
• What more should we control (y2)?
• Variables that stabilize the plant
• Control of primary variables
• Decentralized?
• Multivariable (MPC)?

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References

• Halvorsen, I.J, Skogestad, S., Morud, J.C.,
  Alstad, V. (2003), Optimal selection of
  controlled variables, Ind.Eng.Chem.Res., 42,
  3273-3284.
• Larsson, T. and S. Skogestad (2000), Plantwide
  control A review and a new design procedure,
  Modeling, Identification and Control, 21,
  209-240.
• Larsson, T., K. Hestetun, E. Hovland and S.
  Skogestad (2001), Self-optimizing control of a
  large-scale plant The Tennessee Eastman
  process, Ind.Eng.Chem.Res., 40, 4889-4901.
• Larsson, T., M.S. Govatsmark, S. Skogestad and
  C.C. Yu (2003), Control of reactor, separator
  and recycle process, Ind.Eng.Chem.Res., 42,
  1225-1234
• Skogestad, S. and Postlethwaite, I. (1996, 2005),
  Multivariable feedback control, Wiley
• Skogestad, S. (2000). Plantwide control The
  search for the self-optimizing control
  structure. J. Proc. Control 10, 487-507.
• Skogestad, S. (2003), Simple analytic rules for
  model reduction and PID controller tuning, J.
  Proc. Control, 13, 291-309.
• Skogestad, S. (2004), Control structure design
  for complete chemical plants, Computers and
  Chemical Engineering, 28, 219-234. (Special issue
  from ESCAPE12 Symposium, Haag, May 2002).
• more..

See home page of S. Skogestad http//www.nt.ntnu.
no/users/skoge/