ECONOMIC PLANTWIDE CONTROL: Control structure design for complete processing plants

1
ECONOMICPLANTWIDE CONTROL Control structure
design for complete processing plants

• Sigurd Skogestad
• Department of Chemical Engineering
• Norwegian University of Science and Tecnology
  (NTNU)
• Trondheim, Norway
• ICCAS 2011, Korea

2
Abstract and bio

• ECONOMIC PLANTWIDE CONTROL Control structure
  design for complete processing plants.
• Sigurd Skogestad , Department of Chemical
  Engineering, Norwegian University of Science and
  Technology (NTNU), Trondheim, Norway
• Abstract A chemical plant may have thousands of
  measurements and control loops. By the term
  plantwide control it is not meant the tuning and
  behavior of each of these loops, but rather the
  control philosophy of the overall plant with
  emphasis on the structural decisions. In
  practice, the control system is usually divided
  into several layers, separated by time scale
  scheduling (weeks) , site-wide optimization
  (day), local optimization (hour), supervisory
  (predictive, advanced) control (minutes) and
  regulatory control (seconds). Such a hiearchical
  (cascade) decomposition with layers operating on
  different time scale is used in the control of
  all real (complex) systems including biological
  systems and airplanes, so the issues in this
  section are not limited to process control. In
  the talk the most important issues are discussed,
  especially related to the choice of variables
  that provide the link the control layers.
• Bio Sigurd Skogestad received his Ph.D. degree
  from the California Institute of Technology,
  Pasadena, USA in 1987. He has been a full
  professor at Norwegian University of Science and
  Technology (NTNU), Trondheim, Norway since 1987
  and he was Head of the Department of Chemical
  Engineering from 1999 to 2009. He is the
  principal author, together with Prof. Ian
  Postlethwaite, of the book "Multivariable
  feedback control" published by Wiley in 1996
  (first edition) and 2005 (second edition). He
  received the Ted Peterson Award from AIChE in
  1989, the George S. Axelby Outstanding Paper
  Award from IEEE in 1990, the O. Hugo Schuck Best
  Paper Award from the American Automatic Control
  Council in 1992, and the Best Paper Award 2004
  from Computers and Chemical Engineering. He was
  an Editor of Automatica during the period
  1996-2002. His research interests include the use
  of feedback as a tool to make the system
  well-behaved (including self-optimizing control),
  limitations on performance in linear systems,
  control structure design and plantwide control,
  interactions between process design and control,
  and distillation column design, control and
  dynamics.

3
Arctic circle
North Sea
Trondheim
SWEDEN
NORWAY
Oslo
DENMARK
GERMANY
UK
4
NTNU, Trondheim
5
How we design a control system for a complete
chemical plant?

• Where do we start?
• What should we control? and why?
• etc.
• etc.

6

• 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.

• 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

7
Dealing with complexity
Plantwide control
The controlled variables (CVs) interconnect the
layers
OBJECTIVE
Min J (economics)
RTO
cs y1s
Follow path ( look after other variables)
MPC
y2s
Stabilize avoid drift
PID
u (valves)


8
Control structure design procedure

• I Top Down
• Step 1 Define operational objectives (optimal
  operation)
• Cost function J (to be minimized)
• Operational constraints
• Step 2 Identify degrees of freedom (MVs) and
  optimize for
• expected disturbances
• Step 3 Select primary controlled variables cy1
  (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 (Do we need it?)

y1
y2
MVs
Process
9
Step 1. Define optimal operation (economics)

• What are we going to use our degrees of freedom u
  (MVs) for?
• Define scalar cost function J(u,x,d)
• u degrees of freedom (usually steady-state)
• d disturbances
• x states (internal variables)
• Typical cost function
• Optimize operation with respect to u for given d
  (usually steady-state)
• minu J(u,x,d)
• subject to
• Model equations f(u,x,d) 0
• Operational constraints g(u,x,d) lt 0

J cost feed cost energy value products
10
Step 2 Identify degrees of freedom and optimize
for expected disturbances

• Optimization Identify regions of active
  constraints
• Time consuming!

31
Control 2 active constraints (xA, xB) 2
selfoptimizing
Example (Magnus G. Jacobsen) Two distillation
columns in series. 4 degrees of freedom
5
31
40
13
11
Step 3 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) lt 0

? uopt(d)
Problem Usally cannot keep uopt constant because
disturbances d change
How should we adjust the degrees of freedom (u)?
12
Implementation (in practice) Local feedback
control!
y
Self-optimizing control Constant setpoints for
c gives acceptable loss
d
Feedforward
Optimizing control
Local feedback Control c (CV)
13
Question What should we control (c)? (primary
controlled variables y1c)

• Introductory example Runner

14
Optimal operation of runner
Optimal operation - Runner

• Cost to be minimized, JT
• One degree of freedom (upower)
• What should we control?

15
Sprinter (100m)
Optimal operation - Runner

• 1. Optimal operation of Sprinter, JT
• Active constraint control
• Maximum speed (no thinking required)

16
Marathon (40 km)
Optimal operation - Runner

• 2. Optimal operation of Marathon runner, JT
• Unconstrained optimum!
• 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

17
Conclusion Marathon runner
Optimal operation - Runner
select one measurement
c heart rate

• Simple and robust implementation
• Disturbances are indirectly handled by keeping a
  constant heart rate
• May have infrequent adjustment of setpoint
  (heart rate)

18
Step 3. What should we control (c)? (primary
controlled variables y1c)

• Selection of controlled variables c
• Control active constraints!
• Unconstrained variables Control self-optimizing
  variables!

19
Example active constraint Optimal operation
max. throughput (active constraint)
Want tight bottleneck control to reduce backoff!
Rule for control of hard output constraints
Squeeze and shift! Reduce variance
(Squeeze) and shift setpoint cs to reduce
backoff
20
Control self-optimizing variables
Unconstrained degrees of freedom

• 1. 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, and with it, the optimal
  operating conditions.
• 2. The ideal self-optimizing variable c is the
  gradient (c ? J/? u Ju)
• Keep gradient at zero for all disturbances (c
  Ju0)
• Problem no measurement of gradient

Ju
Ju0
21
H
Ideal c Ju In practise c H y
22
Optimal operation
Unconstrained optimum
Cost J
Jopt
copt
Controlled variable c
23
Optimal operation
Unconstrained optimum
Cost J
d
Jopt
n
copt
Controlled variable c

• Two problems
• 1. Optimum moves because of disturbances d
  copt(d)
• 2. Implementation error, c copt n

24
H
25
Guidelines for selecting measurements as CVs

• Rule 1 Optimal value for CV (cHy) is
  insensitive to disturbances d (minimizes effect
  of moving optimum)
• dcopt/dd is small
• Rule 2 c should be easy to measure and control
  (small implementation error n)
• Rule 3 Maximum gain rule c should be
  sensitive to input changes (large gain G from u
  to c) or equivalently the optimum Jopt should be
  flat with respect to c (minimizes effect of
  implementation error n)
• G dc/du is large

Reference S. Skogestad, Plantwide control The
search for the self-optimizing control
structure, Journal of Process Control, 10,
487-507 (2000).
26
Optimal measurement combination

• Candidate measurements (y) Include also inputs u

H
27
Nullspace method
No measurement noise
28
With measurement noise
Optimal measurement combination, c Hy
0 in nullspace method (no noise)
Minimize in Maximum gain rule ( maximize S1 G
Juu-1/2 , GHGy )
Scaling S1
29
Example CO2 refrigeration cycle
pH
J Ws (work supplied) DOF u (valve opening,
z) Main disturbances d1 TH d2 TCs
(setpoint) d3 UAloss What should we
control?
30
CO2 refrigeration cycle

• Step 1. One (remaining) degree of freedom (uz)
• Step 2. Objective function. J Ws (compressor
  work)
• Step 3. Optimize operation for disturbances
  (d1TC, d2TH, d3UA)
• Optimum always unconstrained
• Step 4. Implementation of optimal operation
• No good single measurements (all give large
  losses)
• ph, Th, z,
• Nullspace method Need to combine nund134
  measurements to have zero disturbance loss
• Simpler Try combining two measurements. Exact
  local method
• c h1 ph h2 Th ph k Th k -8.53 bar/K
• Nonlinear evaluation of loss OK!

31
CO2 cycle Maximum gain rule
32
Refrigeration cycle Proposed control structure
Control c temperature-corrected high pressure
33
Step 4. Where set production rate?

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

34
Production rate set at inlet Inventory control
in direction of flow
TPM
Required to get local-consistent inventory
control
35
Production rate set at outletInventory control
opposite flow
TPM
36
Production rate set inside process
TPM
37
LOCATE TPM?

• Default choice place the TPM at the feed
• Consider moving if there is an important active
  constraint that could otherwise not be well
  controlled.

38
Degrees of freedom for optimization (usually
steady-state DOFs), MVopt CV1s Degrees of
freedom for supervisory control, MV1CV2s
unused valves Physical degrees of freedom for
stabilizing control, MV2 valves (dynamic
process inputs)
39
Step 5 Regulatory control layer

• Step 5. Choose structure of regulatory
  (stabilizing) layer
• (a) Identify stabilizing CV2s (levels,
  pressures, reactor temperature,one temperature in
  each column, etc.).
• In addition, active constraints (CV1) that
  require tight control (small backoff) may be
  assigned to the regulatory layer.
• (Comment usually not necessary with tight
  control of unconstrained CVs because optimum is
  usually relatively flat)
• (b) Identify pairings (MVs to be used to control
  CV2), taking into account
• Want local consistency for the inventory
  control
• Want tight control of important active
  constraints
• Avoid MVs that may saturate in the regulatory
  layer, because this would require either
• reassigning the regulatory loop (complication
  penalty), or
• requiring back-off for the MV variable (economic
  penalty)
• Preferably, the same regulatory layer should be
  used for all operating regions without the need
  for reassigning inputs or outputs.

40
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
41
Why simplified configurations?Why control
layers?Why not one big multivariable
controller?

• 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

42
Advanced control STEP 6. SUPERVISORY LAYER

• Objectives of supervisory layer
• 1. Switch control structures (CV1) depending on
  operating region
• Active constraints
• self-optimizing variables
• 2. Perform advanced economic/coordination
  control tasks.
• Control primary variables CV1 at setpoint using
  as degrees of freedom (MV)
• Setpoints to the regulatory layer (CV2s)
• unused degrees of freedom (valves)
• Keep an eye on stabilizing layer
• Avoid saturation in stabilizing layer
• Feedforward from disturbances
• If helpful
• Make use of extra inputs
• Make use of extra measurements
• Implementation
• Alternative 1 Advanced control based on simple
  elements
• Alternative 2 MPC

43
Summary. Systematic procedure for plantwide
control

• Start top-down with economics
• Step 1 Define operational objectives and
  identify degrees of freeedom
• Step 2 Optimize steady-state operation.
• Step 3A Identify active constraints primary
  CVs c. Should controlled to maximize profit)
• Step 3B For remaining unconstrained degrees of
  freedom Select CVs c based on self-optimizing
  control.
• Step 4 Where to set the throughput (usually
  feed)
• Regulatory control I Decide on how to move mass
  through the plant
• Step 5A Propose local-consistent inventory
  (level) control structure.
• Regulatory control II Bottom-up stabilization
  of the plant
• Step 5B Control variables to stop drift
  (sensitive temperatures, pressures, ....)
• Pair variables to avoid interaction and
  saturation
• Finally make link between top-down and bottom
  up.
• Step 6 Advanced/supervisory 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
http//www.nt.ntnu.no/users/skoge/plantwide
44
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 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).
• The following paper updates the procedure
• S. Skogestad, Economic plantwide control,
  Book chapter in V. Kariwala and V.P. Rangaiah
  (Eds), Plant-Wide Control Recent Developments
  and Applications, Wiley (late 2011).
• More information

http//www.nt.ntnu.no/users/skoge/plantwide
45

• 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,
  Evaluation 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, Optimal 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 and Chemical Engineering, 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
  Engineering Research and Design (Trans IChemE,
  Part A), 85 (A3), 293-306 (2007).
• A.C.B. Araujo, M. Govatsmark and S. Skogestad,
  Application of plantwide control to the HDA
  process. I Steady-state and self-optimizing
  control'', Control Engineering Practice, 15,
  1222-1237 (2007).
• A.C.B. Araujo, E.S. Hori and S. Skogestad,
  Application 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 exchanger networks'',
  AIChE J., 54 (1), 150-162 (2008). DOI
  10.1002/aic.11366