Outline

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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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II. Bottom-up

• Determine secondary controlled variables and
  structure (configuration) of control system
  (pairing)
• A good control configuration is insensitive to
  parameter changes

Step 5. REGULATORY CONTROL LAYER
5.1 Stabilization (including level control)
5.2 Local disturbance rejection (inner
cascades) What more to control? (secondary
variables) Step 6. SUPERVISORY CONTROL
LAYER Decentralized or multivariable control
(MPC)? Pairing? Step 7. OPTIMIZATION LAYER
(RTO)
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Step 5. Regulatory control layer

• Purpose Stabilize the plant using a simple
  control configuration (usually local SISO PID
  controllers simple cascades)
• Enable manual operation (by operators)
• Main structural issues
• What more should we control? (secondary cvs, y2,
  use of extra measurements)
• 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

• The key decisions here (to be made by the control
  engineer) are
• Which extra secondary (dynamic) variables y2
  should we control?
• Propose a (simple) control configuration

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Control configuration elements

• Control configuration. The restrictions imposed
  on the overall controller by decomposing it into
  a set of local controllers (subcontrollers,
  units, elements, blocks) with predetermined links
  and with a possibly predetermined design sequence
  where subcontrollers are designed locally.
• Some control configuration elements
• Cascade controllers
• Decentralized controllers
• Feedforward elements
• Decoupling elements
• Selectors
• Split-range control

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• Cascade control arises when the output from one
  controller is the input to another. This is
  broader than the conventional definition of
  cascade control which is that the output from one
  controller is the reference command (setpoint) to
  another. In addition, in cascade control, it is
  usually assumed that the inner loop K2 is much
  faster than the outer loop K1.
• Feedforward elements link measured disturbances
  to manipulated inputs.
• Decoupling elements link one set of manipulated
  inputs (measurements) with another set of
  manipulated inputs. They are used to improve the
  performance of decentralized control systems, and
  are often viewed as feedforward elements
  (although this is not correct when we view the
  control system as a whole) where the measured
  disturbance is the manipulated input computed by
  another decentralized controller.

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Why simplified configurations?

• Fundamental Save on modelling effort
• Other
• easy to understand
• easy to tune and retune
• insensitive to model uncertainty
• possible to design for failure tolerance
• fewer links
• reduced computation load

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Use of (extra) measurements (y2) as (extra)
CVsCascade control
Primary CV
y1
G
K
y2s
u2
y2
Secondary CV (control for dynamic reasons)
Key decision Choice of y2 (controlled
variable) Also important (since we almost always
use single loops in the regulatory control
layer) Choice of u2 (pairing)
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Degrees of freedom unchanged

• No degrees of freedom lost by control of
  secondary (local) variables as setpoints become
  y2s replace inputs u2 as new degrees of freedom

Cascade control
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Example Distillation

• Primary controlled variable y1 c xD, xB
  (compositions top, bottom)
• BUT Delay in measurement of x unreliable
• Regulatory control For stabilization need
  control of (y2)
• Liquid level condenser (MD)
• Liquid level reboiler (MB)
• Pressure (p)
• Holdup of light component in column
• (temperature profile)

Unstable (Integrating) No steady-state effect
Variations in p disturb other loops
Almost unstable (integrating)
Ts
TC
T-loop in bottom
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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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Hierarchical control Time scale separation

• With a reasonable time scale separation between
  the layers
• (typically by a factor 5 or more in terms of
  closed-loop response time)
• we have the following advantages
• The stability and performance of the lower
  (faster) layer (involving y2) is not much
  influenced by the presence of the upper (slow)
  layers (involving y1)
• Reason The frequency of the disturbance from
  the upper layer is well inside the bandwidth of
  the lower layers
• With the lower (faster) layer in place, the
  stability and performance of the upper (slower)
  layers do not depend much on the specific
  controller settings used in the lower layers
• Reason The lower layers only effect frequencies
  outside the bandwidth of the upper layers

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QUIZ What are the benefits of adding a flow
controller (inner cascade)?
qs
Extra measurement y2 q
q
z

• Counteracts nonlinearity in valve, f(z)
• With fast flow control we can assume q qs
• Eliminates effect of disturbances in p1 and p2

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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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1. Control of y2 stabilizes the plant

• A. Mathematical stabilization (e.g. reactor)
• Unstable mode is quickly detected (state
  observability) in the measurement (y2) and is
  easily affected (state controllability) by the
  input (u2).
• Tool for selecting input/output Pole vectors
• y2 Want large element in output pole vector
  Instability easily detected relative to noise
• u2 Want large element in input pole vector
  Small input usage required for stabilization
• B. Practical extended stabilization (avoid
  drift due to disturbance sensitivity)
• Intuitive y2 located close to important
  disturbance
• Maximum gain rule Controllable range for y2 is
  large compared to sum of optimal variation and
  control error
• More exact tool Partial control analysis

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Recall maximum gain rule for selecting primary
controlled variables c
Controlled variables c for which their
controllable range is large compared to their sum
of optimal variation and control error
Restated for secondary controlled variables y2
Control variables y2 for which their controllable
range is large compared to their sum of optimal
variation and control error
controllable range range y2 may reach by
varying the inputs optimal variation due to
disturbances control error implementation error
n
Want large
Want small
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What should we control (y2)?Rule Maximize the
scaled gain

• General case Maximize minimum singular value of
  scaled G
• Scalar case Gs G / span
• G gain from independent variable (u2) to
  candidate controlled variable (y2)
• IMPORTANT The gain G should be evaluated at
  the (bandwidth) frequency of the layer above in
  the control hierarchy!
• If the layer above is slow OK with steady-state
  gain as used for selecting primary controlled
  variables (y1c)
• BUT In general, gain can be very different
• span (of y2) optimal variation in y2 control
  error for y2
• Note optimal variation This is often the same as
  the optimal variation used for selecting primary
  controlled variables (c).
• Exception If we at the fast regulatory time
  scale have some yet unused slower inputs (u1)
  which are constant then we may want find a more
  suitable optimal variation for the fast time
  scale.

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Minimize state drift by controlling y2

• Problem in some cases optimal variation for y2
  depends on overall control objectives which may
  change
• Therefore May want to decouple tasks of
  stabilization (y2) and optimal operation (y1)
• One way of achieving this Choose y2 such that
  state drift dw/dd is minimized
• w Wx weighted average of all states
• d disturbances
• Some tools developed
• Optimal measurement combination y2Hy that
  minimizes state drift (Hori) see Skogestad and
  Postlethwaite (Wiley, 2005) p. 418
• Distillation column application Control average
  temperature column

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2. y2 is easy to control (controllability)

• Statics Want large gain (from u2 to y2)
• Main rule y2 is easy to measure and located
  close to available manipulated variable u2
  (pairing)
• Dynamics Want small effective delay (from u2 to
  y2)
• effective delay includes
• inverse response (RHP-zeros)
• high-order lags

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Rules for selecting u2 (to be paired with y2)

• Avoid using variable u2 that may saturate
  (especially in loops at the bottom of the control
  hieararchy)
• Alternatively Need to use input resetting in
  higher layer (mid-ranging)
• Example Stabilize reactor with bypass flow (e.g.
  if bypass may saturate, then reset in higher
  layer using cooling flow)
• Pair close The controllability, for example in
  terms a small effective delay from u2 to y2,
  should be good.

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Effective delay and tunings
LATER !!

• ? effective delay
• PI-tunings from SIMC rule
• Use half rule to obtain first-order model
• Effective delay ? True delay inverse
  response time constant half of second time
  constant all smaller time constants
• Time constant t1 original time constant half
  of second time constant
• NOTE The first (largest) time constant is NOT
  important for controllability!

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Summary Rules for selecting y2 (and u2)

• Selection of y2
• Control of y2 stabilizes the plant
• The (scaled) gain for y2 should be large
• Measurement of y2 should be simple and reliable
• For example, temperature or pressure
• y2 should have good controllability
• small effective delay
• favorable dynamics for control
• y2 should be located close to a manipulated
  input (u2)
• Selection of u2 (to be paired with y2)
• Avoid using inputs u2 that may saturate
• Should generally avoid failures, including
  saturation, in lower layers
• Pair close!
• The effective delay from u2 to y2 should be small

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Use of extra inputs

• Two different cases
• Have extra dynamic inputs (degrees of freedom)
• Cascade implementation Input resetting to ideal
  resting value
• Example Heat exchanger with extra bypass
• Need several inputs to cover whole range (because
  primary input may saturate) (steady-state)
• Split-range control
• Example 1 Control of room temperature using AC
  (summer), heater (winter), fireplace (winter
  cold)
• Example 2 Pressure control using purge and inert
  feed (distillation)

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QUIZ Heat exchanger with bypass
closed
qB
Thot

• Want tight control of Thot
• Primary input CW
• Secondary input qB
• Proposed control structure?

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Alternative 1
closed
TC
Use primary input CW TOO SLOW
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Alternative 2
closed
TC
Use dynamic input qB Advantage Very fast
response (no delay) Problem qB is too small to
cover whole range has
small steady-state effect
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Alternative 3 Use both inputs (with input
resetting of dynamic input)
closed
qBs
FC
TC
TC Gives fast control of Thot using the
dynamic input qB FC Resets qB to its setpoint
(IRV) (e.g. 5) using the primary input CW
IRV ideal resting value
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Extra inputs

• Exercise Explain how valve position control
  fits into this framework. As en example consider
  a heat exchanger with bypass

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Exercise

• Exercise
• In what order would you tune the controllers?
• Give a practical example of a process that fits
  into this block diagram

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Too few inputs

• Must decide which output (CV) has the highest
  priority
• Selectors

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Cascade control(conventional with extra
measurement)
The reference r2 ( setpoint ys2) is an output
from another controller
General case (parallel cascade)
Special common case (series cascade)
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Series cascade

• Disturbances arising within the secondary loop
  (before y2) are corrected by the secondary
  controller before they can influence the primary
  variable y1
• Phase lag existing in the secondary part of the
  process (G2) is reduced by the secondary loop.
  This improves the speed of response of the
  primary loop.
• Gain variations in G2 are overcome within its own
  loop.
• Thus, use cascade control (with an extra
  secondary measurement y2) when
• The disturbance d2 is significant and G1 has an
  effective delay
• The plant G2 is uncertain (varies) or nonlinear
• Design / tuning (see also later in tuning-part)
• First design K2 (fast loop) to deal with d2
• Then design K1 to deal with d1

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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 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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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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Decentralized control(single-loop controllers)

• Use for Noninteracting process and no change in
  active constraints
• Tuning may be done on-line
• No or minimal model requirements
• Easy to fix and change
• - Need to determine pairing
• - Performance loss compared to multivariable
  control
• - Complicated logic required for reconfiguration
  when active constraints move

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Multivariable control(with explicit constraint
handling MPC)

• Use for Interacting process and changes in
  active constraints
• Easy handling of feedforward control
• Easy handling of changing constraints
• no need for logic
• smooth transition
• - Requires multivariable dynamic model
• - Tuning may be difficult
• - Less transparent
• - Everything goes down at the same time

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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 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 variables

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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
• Conclusion / References

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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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Conclusion

• 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).

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More examples and case studies

• HDA process
• Cooling cycle
• Distillation (C3-splitter)
• Blending

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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/
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Extra

• For students that take PhD course!

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Partial control

• Cascade control y2 not important in itself, and
  setpoint (r2) is available for control of y1
• Decentralized control (using sequential design)
  y2 important in itself

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Partial control analysis
Assumption Perfect control (K2 -gt infinity) in
inner loop
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Partial control Distillation
u1 V
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Limitations of partial control?

• Cascade control Closing of secondary loops does
  not by itself impose new problems
• Theorem 10.2 (SP, 2005). The partially controlled
  system P1 Pr1
• from u1 r2 to y1
• has no new RHP-zeros that are not present in the
  open-loop system G11 G12
• from u1 u2 to y1
• provided
• r2 is available for control of y1
• K2 has no RHP-zeros
• Decentralized control (sequential design) Can
  introduce limitations.
• Avoid pairing on negative RGA for u2/y2
  otherwise Pu likely has a RHP-zero

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Selecting measurements and inputs for
stabilization Pole vectors

• Maximum gain rule is good for integrating
  (drifting) modes
• For fast unstable modes (e.g. reactor) Pole
  vectors useful for determining which input
  (valve) and output (measurement) to use for
  stabilizing unstable modes
• Assumes input usage (avoiding saturation) may be
  a problem
• Compute pole vectors from eigenvectors of
  A-matrix

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Example Tennessee Eastman challenge problem
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