Control structure design for
complete chemical plants
(a systematic procedure to plantwide control)
Sigurd Skogestad
Department of Chemical Engineering
Norwegian University of Science and Tecnology (NTNU)
Trondheim, Norway
Based on: Plenary presentation at ESCAPE’12, May 2002
Updated/expanded April 2004 for 2.5 h tutorial in Vancouver, Canada
Further updated: August 2004
1
Outline
• About Trondheim and myself
• 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-optimzing 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
2
Idealized view of control
(“Ph.D. control”)
3
Practice: Tennessee Eastman challenge
problem (Downs, 1991)
(“PID control”)
4
Idealized view II: Optimizing control
5
Practice II: Hierarchical
decomposition with separate layers
What should we control?
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.
• Carl Nett (1989):
Minimize control system complexity subject to the achievement of accuracy
specifications in the face of uncertainty.
7
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
8
Process control:
“Plantwide control” = “Control structure
design for complete chemical plant”
•
•
•
•
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
9
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
10
• Control structure selection issues are identified as important also in
other industries.
Professor Gary Balas (Minnesota) 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!
11
Main simplification: Hierarchical structure
RTO
MPC
PID
12
Need to define
objectives and identify
main issues for each
layer
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 ….
13
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 = (1/k) (1/ [c +]) I = min (1, 4[c + ]), Typical: c=
– “Probably the best simple PID tuning rules in the world” © Carlsberg
• Outstanding structural issue: What loops to close, that is, which
variables (y2) to control?
14
Supervisory control (minutes)
• Purpose: Keep primary controlled variables (c=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”
15
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 c=y1 to control?
16
Local optimization (hour)
•
Purpose: Minimize cost function J and:
– Identify active constraints
– Recompute optimal setpoints y1s for the 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.
– Need nonlinear steady-state model
– Modelling is time-consuming and expensive
17
Objectives of layers: MV’s and CV’s
RTO
Min J; MV=y1s
cs = y1s
CV=y1; MV=y2s
MPC
y2s
PID
18
CV=y2; MV=u
u (valves)
Outline
• About Trondheim and myself
• 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
19
Stepwise procedure plantwide control
I. TOP-DOWN
Step 1. DEGREES OF FREEDOM
Step 2. OPERATIONAL OBJECTIVES
Step 3. WHAT TO CONTROL? (primary CV’s c=y1)
Step 4. PRODUCTION RATE
II. BOTTOM-UP (structure control system):
Step 5. REGULATORY CONTROL LAYER (PID)
“Stabilization”
What more to control? (secondary CV’s y2)
Step 6. SUPERVISORY CONTROL LAYER (MPC)
Decentralization
Step 7. OPTIMIZATION LAYER (RTO)
Can we do without it?
20
Outline
• About Trondheim and myself
• 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-optimzing 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
21
Step 1. Degrees of freedom (DOFs)
• m – dynamic (control) degrees of freedom = valves
• u0 – steady-state degrees of freedom
• Nm : no. of dynamic (control) DOFs (valves)
• Nu0 = Nm- N0 : no. of steady-state DOFs
– N0 = N0y + N0m : no. of variables with no steady-state effect
• N0m : no. purely dynamic control DOFs
• N0y : no. controlled variables (liquid levels) with no steady-state effect
• Cost J depends normally only on steady-state DOFs
22
Distillation column with given feed
Nm = 5, N0y = 2, Nu0 = 5 - 2 = 3 (2 with given pressure)
23
Heat-integrated distillation process
Nm = 11 (w/feed), N0y = 4 (levels), Nu0 = 11 – 4 = 7
24
Heat exchanger with bypasses
CW
Nm = 3, N0m = 2 (of 3), N0y = 3 – 2 = 1
25
Typical number of steady-state degrees of
freedom (u0) for some process units
•
•
•
•
•
•
•
•
•
26
each external feedstream: 1 (feedrate)
splitter: n-1 (split fractions) where n is the number of exit streams
mixer: 0
compressor, turbine, pump: 1 (work)
adiabatic flash tank: 1 (0 with fixed pressure)
liquid phase reactor: 1 (volume)
gas phase reactor: 1 (0 with fixed pressure)
heat exchanger: 1 (duty or net area)
distillation column excluding heat exchangers: 1 (0 with fixed
pressure) + number of sidestreams
• Check that there are enough manipulated variables (DOFs) - both
dynamically and at steady-state (step 2)
• Otherwise: Need to add equipment
– extra heat exchanger
– bypass
– surge tank
27
Outline
• About Trondheim and myself
• 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-optimzing 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
28
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:
J = cost feed + cost energy – value products
•
Optimal operation for given d:
minu0 J(u0,x,d)
subject to:
Model equations:
Operational constraints:
29
f(u0,x,d) = 0
g(u0,x,d) < 0
Outline
• About Trondheim and myself
• 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-optimzing 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
30
Step 3. What should we control (c)?
Outline
• Implementation of optimal operation
• Self-optimizing control
• Uncertainty (d and n)
• Example: Marathon runner
• Methods for finding the “magic” self-optimizing variables:
A. Large gain: Minimum singular value rule
B. “Brute force” loss evaluation
C. Optimal combination of measurements
• Example: Recycle process
• Summary
31
Implementation of optimal operation
• Optimal operation for given d*:
minu0 J(u0,x,d)
subject to:
Model equations:
Operational constraints:
→ u0opt(d*)
f(u0,x,d) = 0
g(u0,x,d) < 0
Problem: Cannot keep u0opt constant because disturbances d change
32
Implementation of optimal operation (Cannot keep u0opt constant)
”Obvious” solution:
Optimizing control
Estimate d from measurements
and recompute u0opt(d)
Problem: Too complicated
(requires detailed model and
description of uncertainty)
33
Implementation of optimal operation (Cannot keep u0opt constant)
Simpler solution: Look for another variable c
which is better to keep constant
Note: u0 will indirectly
change when d changes
and control c at constant setpoint cs = copt(d*)
34
What c’s should we control?
• 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!
– cs = value of active constraint
– Implementation of active constraints is usually simple.
• WHAT MORE SHOULD WE CONTROL?
– Find variables c for remaining
unconstrained degrees of freedom u.
35
What should we control?
(primary controlled variables y1=c)
•
Intuition: “Dominant variables” (Shinnar)
•
Systematic: Minimize cost J(u0,d*) w.r.t.
DOFs u0.
1. Control active constraints (constant setpoint
is optimal)
2. Remaining unconstrained DOFs: Control
“self-optimizing” variables c for which
constant setpoints cs = copt(d*) give small
(economic) loss
Loss = J - Jopt(d)
when disturbances d ≠ d* occur
36
c = ? (economics)
y2 = ? (stabilization)
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).
c=cs
37
The difficult unconstrained variables
Cost J
Jopt
c
copt
38
Selected controlled variable
(remaining unconstrained)
Implementation of unconstrained variables is not trivial:
How do we deal with uncertainty?
• 1. Disturbances d (copt(d) changes)
• 2. Implementation error n (actual c ≠ copt)
cs = copt(d*) – nominal optimization
n
c = cs + n
d
Cost J  Jopt(d)
39
Problem no. 1: Disturbance d
d ≠ d*
Cost J
d*
Jopt
Loss with constant value for c
copt(d*)
40
) Want copt independent of d
Controlled variable
Example: Tennessee Eastman plant
J
Oopss..
bends backwards
c = Purge rate
Nominal optimum setpoint is infeasible with disturbance 2
Conclusion: Do not use purge rate as controlled variable
41
Problem no. 2: Implementation error n
Cost J
d*
Loss due to implementation error for c
Jopt
cs=copt(d*)
42
c = cs + n
) Want n small and ”flat” optimum
Effect of implementation error on cost (“problem 2”)
Good
43
Good
BAD
Example sharp optimum. High-purity distillation :
c = Temperature top of column
Ttop
Water (L) - acetic acid (H)
Max 100 ppm acetic acid
100 C: 100% water
100.01C: 100 ppm
99.99 C: Infeasible
Temperature
44
Summary unconstrained variables:
Which variable c to control?
• Self-optimizing control:
Constant setpoints cs give
”near-optimal operation”
(= acceptable loss L for expected
disturbances d and
implementation errors n)
45
Acceptable loss )
self-optimizing control
Examples self-optimizing control
•
•
•
•
•
•
•
Marathon runner
Central bank
Cake baking
Business systems (KPIs)
Investment portifolio
Biology
Chemical process plants: Optimal blending of gasoline
Define optimal operation (J) and look for ”magic” variable
(c) which when kept constant gives acceptable loss (selfoptimizing control)
46
Self-optimizing Control – Marathon
• Optimal operation of Marathon runner, J=T
– Any self-optimizing variable c (to control at constant
setpoint)?
47
Self-optimizing Control – Marathon
• Optimal operation of Marathon runner, J=T
– Any self-optimizing variable c (to control at constant
setpoint)?
•
•
•
•
48
c1 = distance to leader of race
c2 = speed
c3 = heart rate
c4 = level of lactate in muscles
Self-optimizing Control – Marathon
• Optimal operation of Marathon runner, J=T
– Any self-optimizing variable c (to control at constant
setpoint)?
•
•
•
•
49
c1 = distance to leader of race (Problem: Feasibility for d)
c2 = speed (Problem: Feasibility for d)
c3 = heart rate (Problem: Impl. Error n)
c4 = level of lactate in muscles (Problem: Large impl.error
n)
Self-optimizing Control – Sprinter
• Optimal operation of Sprinter (100 m), J=T
– Active constraint control:
• Maximum speed (”no thinking required”)
50
Further examples
•
•
•
Central bank. J = welfare. u = interest rate. c=inflation rate (2.5%)
Cake baking. J = nice taste, u = heat input. c = Temperature (200C)
Business, J = profit. c = ”Key performance indicator (KPI), e.g.
– Response time to order
– Energy consumption pr. kg or unit
– Number of employees
– Research spending
Optimal values obtained by ”benchmarking”
•
•
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” :
•
•
51
Find the controlled variables used in nature
From this possibly identify what overall objective J the biological system has
been attempting to optimize
Unconstrained degrees of freedom:
Looking for “magic” variables to keep at constant setpoints.
What properties do they have?
Shinnar (1981): Control “Dominant variables” (undefined..)
52
Skogestad and Postlethwaite (1996):
• The optimal value of c should be insensitive to
disturbances
• c should be easy to measure and control accurately
• The value of c should be sensitive to changes in the
steady-state 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.
• Summarized by minimum singular value rule
Avoid problem 1 (d)
Avoid problem 2 (n)
Unconstrained degrees of freedom:
Looking for “magic” variables to keep at constant setpoints.
How can we find them systematically?
A. Minimum singular value rule:
B. “Brute force”: Consider available measurements y, and evaluate
loss when they are kept constant:
C. More general: Find optimal linear combination (matrix H):
53
Unconstrained degrees of freedom:
A. Minimum singular value rule
J
Optimizer
c
cs
Controller that
adjusts u to keep
cm = cs
cm=c+n
n
n
cs=copt
u
d
c
Plant
uopt
Want the slope (= gain G from u to y)
as large as possible
54
u
Unconstrained degrees of freedom:
A. Minimum singular value rule
Minimum singular value rule (Skogestad and Postlethwaite, 1996):
Look for variables c that maximize the minimum singular value
(G) of the appropriately scaled steady-state gain matrix G from u to c
• u: unconstrained degrees of freedom
• Loss
• Scaling is important:
– Scale c such that their expected variation is similar (divide by optimal
variation + noise)
– Scale inputs u such that they have similar effect on cost J (Juu unitary)
•
•
55
(G) is called the Morari Resiliency index (MRI) by Luyben
Detailed proof: 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).
Minimum singular value rule in words
Select controlled variables c for which
their controllable range is large compared to
their sum of optimal variation and control error
controllable range = range c may reach by varying the inputs
optimal variation: due to disturbance
control error = implementation error n
56
B. “Brute-force” procedure for selecting
(primary) controlled variables (Skogestad, 2000)
•
•
•
•
•
•
•
Step 3.1 Determine DOFs for optimization
Step 3.2 Definition of optimal operation J (cost and constraints)
Step 3.3 Identification of important disturbances
Step 3.4 Optimization (nominally and with disturbances)
Step 3.5 Identification of candidate controlled variables (use active constraint
control)
Step 3.6 Evaluation of loss with constant setpoints for alternative controlled
variables
Step 3.7 Evaluation and selection (including controllability analysis)
Case studies: Tenneessee-Eastman, Propane-propylene splitter, recycle process,
heat-integrated distillation
57
B. Brute-force procedure
• Define optimal operation:
Minimize cost function J
• Each candidate variable c:
With constant setpoints cs
compute loss L for expected
disturbances d and
implementation errors n
• Select variable c with smallest
loss
58
Acceptable loss )
self-optimizing control
Unconstrained degrees of freedom:
C. Optimal measurement combination (Alstad, 2002)
Basis: Want optimal value of c independent of disturbances )
  copt = 0 ¢  d
• Find optimal solution as a function of d: uopt(d), yopt(d)
• Linearize this relationship: yopt = F d
• F – sensitivity matrix
• Want:
• To achieve this for all values of  d:
• Always possible if
• Optimal when we disregard implementation error (n)
59
Alstad-method continued
• To handle implementation error: Use “sensitive” measurements, with
information about all independent variables (u and d)
60
Toy Example
61
Toy Example
62
Toy Example
63
EXAMPLE: Recycle plant (Luyben, Yu, etc.)
5
4
1
Given feedrate F0 and
column pressure:
Dynamic DOFs:
Nm = 5
Column levels:
N0y = 2
Steady-state DOFs: N0 = 5 - 2 = 3
64
2
3
Recycle plant: Optimal operation
mT
1 remaining unconstrained degree of freedom
65
Control of recycle plant:
Conventional structure (“Two-point”: xD)
LC
LC
XC
xD
XC
xB
LC
Control active constraints (Mr=max and xB=0.015) + xD
66
Luyben rule
67
Luyben rule (to avoid snowballing):
“Fix a stream in the recycle loop” (F or D)
Luyben rule: D constant
LC
LC
XC
LC
68
Luyben rule (to avoid snowballing):
“Fix a stream in the recycle loop” (F or D)
A. Singular value rule: Steady-state gain
Conventional:
Looks good
Luyben rule:
Not promising
economically
69
B. “Brute force” loss evaluation:
Disturbance in F0
Luyben rule:
Conventional
70
Loss with nominally optimal setpoints for Mr, xB and c
B. “Brute force” loss evaluation:
Implementation error
Luyben rule:
71
Loss with nominally optimal setpoints for Mr, xB and c
C. Optimal measurement combination
• 1 unconstrained variable (#c = 1)
• 1 (important) disturbance: F0 (#d = 1)
• “Optimal” combination requires 2 “measurements” (#y = #u + #d = 2)
– For example, c = h1 L + h2 F
• BUT: Not much to be gained compared to control of single variable
(e.g. L/F or xD)
72
Conclusion: Control of recycle plant
Active constraint
Mr = Mrmax
Self-optimizing
73
L/F constant: Easier than “two-point” control
Assumption: Minimize energy (V)
Active constraint
xB = xBmin
Recycle systems:
Do not recommend Luyben’s rule of
fixing a flow in each recycle loop
(even to avoid “snowballing”)
74
Summary ”self-optimizing” control
•
Operation of most real system: Constant setpoint policy (c = cs)
–
–
–
–
•
•
•
•
Central bank
Business systems: KPI’s
Biological systems
Chemical processes
Goal: Find controlled variables c such that constant setpoint policy gives
acceptable operation in spite of uncertainty
) Self-optimizing control
Method A: Maximize (G)
Method B: Evaluate loss L = J - Jopt
Method C: Optimal linear measurement combination:
c = H y where HF=0
• More examples later
75
Outline
• About Trondheim and myself
• 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-optimzing 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
76
Step 4. Where set production rate?
•
•
•
•
77
Very important!
Determines structure of remaining inventory (level) control system
Set production rate at (dynamic) bottleneck
Link between Top-down and Bottom-up parts
Production rate set at inlet :
Inventory control in direction of flow
78
Production rate set at outlet:
Inventory control opposite flow
79
Production rate set inside process
80
Definition of bottleneck
A unit (or more precisely, an extensive variable E within this unit)
is a bottleneck (with respect to the flow F) if
- With the flow F as a degree of freedom, the variable E is optimally
at its maximum constraint (i.e., E= Emax at the optimum)
- The flow F is increased by increasing this constraint
(i.e., dF/dEmax > 0 at the optimum).
A variable E is a dynamic( control) bottleneck if in addition
- The optimal value of E is unconstrained when F is fixed at a
sufficiently low value
Otherwise E is a steady-state (design) bottleneck.
81
Reactor-recycle process:
Given feedrate with production rate set at inlet
82
Reactor-recycle process:
Reconfiguration required when reach bottleneck
(max. vapor rate in column)
MAX
83
Reactor-recycle process:
Given feedrate with production rate set at
bottleneck (column)
F0s
84
Outline
• About Trondheim and myself
• 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-optimzing 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
85
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)
86
Outline
•
•
•
About Trondheim and myself
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-optimzing control)
Step 4: Where set production rate?
II Bottom Up
• Step 5: Regulatory control: What more to control ?
– Bonus: A little about tuning and “half rule”
• Step 6: Supervisory control
• Step 7: Real-time optimization
•
87
Case studies
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 cv’s, y2)
• Pairing with manipulated variables (mv’s u2)
y1 = c
y2 = ?
88
Example: Distillation
• Primary controlled variable: y1 = c = y,x (compositions top, bottom)
• BUT: Delay in measurement of x + unreliable
• Regulatory control: For “stabilization” need control of:
–
–
–
–
Liquid level condenser (MD) No steady-state effect
Liquid level reboiler (MB)
Pressure (p)
Holdup of light component in column
(temperature profile)
89
ys
y
X
C
Ts
T
TC
Ls
L
90
X
C
FC
z
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:
y2s
New DOF
91
K
u2
G
y1
y
Original DOF
2
Objectives regulatory control layer
•
•
•
•
•
•
•
92
Take care of “fast” control
Simple decentralized (local) PID controllers that can be tuned on-line
Allow for “slow” control in layer above (supervisory control)
Make control problem easy as seen from layer above
Stabilization (mathematical sense)
Local disturbance rejection
“stabilization”
Local linearization (avoid “drift” due to disturbances)
(practical sense)
Implications for selection of y2:
1. Control of y2 “stabilizes the plant”
2. y2 is easy to control (favorable dynamics)
1. “Control of y2 stabilizes the plant”
“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
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“Extended stabilization” (avoid “drift” due to disturbance sensitivity):
• Intuitive: y2 located close to important disturbance
• Or rather: Controllable range for y2 is large compared to sum of
optimal variation and control error
• More exact tool: Partial control analysis
Recall 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
Want small
control error = implementation error n
94
Want large
Partial control analysis
Primary controlled
variable y1 = c
(supervisory control layer)
Local control of y2
using u2
(regulatory control layer)
Setpoint y2s : new DOF
for supervisory control
y1 = P1 u1 + Pr1 (y2s-n2) + Pd1 d
P1 = G11 – G12 G22-1 G21
Pd1 = Gd1 – G12 G22-1 Gd2 - WANT SMALL
Pr1 = G12 G22-1
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2. “y2 is easy to control”
• Main rule: y2 is easy to measure and located close
to manipulated variable u2
• Statics: Want large gain (from u2 to y2)
• Dynamics: Want small effective delay (from u2 to y2)
96
Aside: Effective delay and tunings
• PI-tunings from “SIMC rule”
• Use half rule to obtain first-order model
– Effective delay θ = “True” delay + inverse response time constant + half of
second time constant + all smaller time constants
– Time constant τ1 = original time constant + half of second time constant
97
Example cascade control (PI)
d=6
ys
98
K1
y2s
K2
u2
G2
y2
G1
y1
Example cascade control (PI)
d=6
ys
K1
y2s
K2
Without cascade
With cascade
99
u
G2
y2
G1
y1
Example cascade control
• Inner fast (secondary) loop:
– P or PI-control
– Local disturbance rejection
– Much smaller effective delay (0.2 s)
• Outer slower primary loop:
– Reduced effective delay (2 s instead of 6 s)
• Time scale separation
–
Inner loop can be modelled as gain=1 + 2*effective delay (0.4s)
• Very effective for control of large-scale systems
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Outline
• About Trondheim and myself
• 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-optimzing 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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1
Step 6. Supervisory control layer
• Purpose: Keep primary controlled outputs c=y1 at optimal setpoints cs
• Degrees of freedom: Setpoints y2s in reg.control layer
• Main structural issue: Decentralized or multivariable?
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2
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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3
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
-
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Requires multivariable dynamic model
Tuning may be difficult
Less transparent
“Everything goes down at the same time”
Outline
• About Trondheim and myself
• 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-optimzing 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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5
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 selfoptimizing)
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6
Outline
•
•
•
About Trondheim and myself
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-optimzing 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
•
•
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Conclusion / References
Case studies
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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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), 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
ESCAPE’12 Symposium, Haag, May 2002).
… + more…..
•
See home page of S. Skogestad:
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http://www.chembio.ntnu.no/users/skoge/