Practical plantwide process control
Part 1
Sigurd Skogestad, NTNU
Thailand, April 2014
1
Part 1 (3h): Plantwide control
Introduction to plantwide control (what should we really control?)
Part 1.1 Introduction.
–
–
–
Objective: Put controllers on flow sheet (make P&ID)
Two main objectives for control: Longer-term economics (CV1) and shorter-term stability (CV2)
Regulatory (basic) and supervisory (advanced) control layer
Part 1.2 Optimal operation (economics)
–
–
Active constraints
Selection of economic controlled variables (CV1). Self-optimizing variables.
Part 1.3 -Inventory (level) control structure
–
–
Location of throughput manipulator
Consistency and radiating rule
Part 1.4 Structure of regulatory control layer (PID)
–
–
Selection of controlled variables (CV2) and pairing with manipulated variables (MV2)
Main rule: Control drifting variables and "pair close"
Summary: Sigurd’s rules for plantwide control
2
Part 1.1 Introduction
– Objective: Put controllers on flow sheet (make P&ID)
– Two main objectives for control: Longer-term economics (CV1) and
shorter-term stability (CV2)
– Regulatory (basic) and supervisory (advanced) control layer
3
Why control?
• Operation
Actual value(dynamic)
Steady-state (average)
time
4
In practice never steady-state:
• Feed changes
• Startup
“Disturbances” (d’s)
• Operator changes
• Failures
• …..
- Control is needed to reduce the effect of disturbances
- 30% of investment costs are typically for instrumentation and control
Countermeasures to disturbances (I)
I.
Eliminate/Reduce the disturbance
(a)
Design process so it is insensitive to disturbances
•
Example: Use buffertank to dampen disturbances
Tin
inflow
(b)
outflow
Detect and remove source of disturbances
•
•
5
∞
Tout
“Statistical process control”
Example: Detect and eliminate variations in feed composition
Countermeasures to disturbances (II)
II. Process control
Do something (usually manipulate valve)
to counteract the effect of the disturbances
(a) Manual control: Need operator
(b) Automatic control: Need measurement + automatic valve + computer
Goals automatic control:
• Smaller variations
• more consistent quality
• More optimal
• Smaller losses (environment)
• Lower costs
• More production
Industry: Still large potential for improvements!
6
Classification of variables
d
u
input (MV)
Process
(shower)
y
output (CV)
Independent variables (“the cause”):
(a) Inputs (MV, u): Variables we can adjust (valves)
(b) Disturbances (DV, d): Variables outside our control
Dependent (output) variables (“the effect or result”):
(c)
(d)
7
Primary outputs (CVs, y1): Variables we want to keep at a given
setpoint
Secondary outputs (y2): Extra measurements that we may use to
improve control
Inputs for control (MVs)
• Usually: Inputs (MVs) are valves.
– Physical input is valve position (z), but we often simplify and say that
flow (q) is input
3
p
Valve equation: q[m =s] = Cv f (z) ¢ p=½
8
Idealized view of control
(“PhD control”)
d, ys
= y-ys
Control: Use inputs (MVs, u) to counteract the effect of the disturbances (DVs, d)
such that the outputs (CV=y) are kept close to their setpoints (ys)
9
Practice: Tennessee Eastman challenge
problem (Downs, 1991)
(“PID control”)
10
Where place
TC
PC
LC
CC
x
SRC
??
Notation feedback controllers (P&ID)
T
(measured CV)
Ts
(setpoint CV)
TC
MV (could be valve)
2nd letter:
C: controller
I: indicator (measurement)
T: transmitter (measurement)
11
1st letter: Controlled variable (CV) = What we are trying to control (keep constant)
T: temperature
F: flow
L: level
P: pressure
DP: differential pressure (Δp)
A: Analyzer (composition)
C: composition
X: quality (composition)
H: enthalpy/energy
Example: Level control
Inflow (d)
Hs
H
LC
Outflow (u)
CLASSIFICATION OF VARIABLES:
12
INPUT (u): OUTFLOW (Input for control!)
OUTPUT (y): LEVEL
DISTURBANCE (d): INFLOW
How we design a control system for a
complete chemical plant?
• How do we get from PID control to PhD control?
•
•
•
•
13
Where do we start?
What should we control? and why?
etc.
etc.
Plantwide control =
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 “PhD” control
14
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
15
Main objectives control system
1. Implementation of acceptable (near-optimal) operation
2. Stable operation
ARE THESE OBJECTIVES CONFLICTING?
•
Usually NOT
–
Different time scales
•
–
Stabilization doesn’t “use up” any degrees of freedom
•
•
16
Stabilization fast time scale
Reference value (setpoint) available for layer above
But it “uses up” part of the time window (frequency range)
Part 1.2 Optimal operation (economics)
Example of systems we want to operate optimally
• Process plant
– minimize J=economic cost
• Runner
– minimize J=time
• «Green» process plant
– Minimize J=environmental impact (with given economic cost)
• General multiobjective:
– Min J (scalar cost, often $)
– Subject to satisfying constraints (environment, resources)
17
Process operation: Hierarchical structure
Manager
Process engineer
Operator/RTO
Operator/”Advanced control”/MPC
PID-control
20
u = valves
Translate optimal operation
into simple control objectives:
What should we control?
CV1 = c ? (economics)
CV2 = ? (stabilization)
21
Part 1.2 Optimal operation (economics)
• Goal: Select economic controlled variables (CV1)
– Active constraints
– Self-optimizing variables
22
Outline
• Skogestad procedure for control structure design
I Top Down
• Step S1: Define operational objective (cost) and constraints
• Step S2: Identify degrees of freedom and optimize operation for disturbances
• Step S3: Implementation of optimal operation
– What to control ? (primary CV’s) (self-optimizing control)
• Step S4: Where set the production rate? (Inventory control)
II Bottom Up
• Step S5: Regulatory control: What more to control (secondary CV’s) ?
• Step S6: Supervisory control
• Step S7: Real-time optimization
23
Step S1. Define optimal operation (economics)
• What are we going to use our degrees of freedom (u=MVs)
for?
• Typical cost function*:
J = cost feed + cost energy – value products
•
•
24
*No need to include fixed costs (capital costs, operators, maintainance) at ”our” time
scale (hours)
Note: J=-P where P= Operational profit
Optimal operation distillation column
•
•
Distillation at steady state with given p and F: N=2 DOFs, e.g. L and V (u)
Cost to be minimized (economics)
cost energy (heating+ cooling)
J = - P where P= pD D + pB B – pF F – pVV
value products
•
•
25
cost feed
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 (d)
2) p free (u): pmin · p · pmax
Feed:
1) F given (d)
2) F free (u): F · Fmax
Optimal operation: Minimize J with respect to steady-state DOFs (u)
Step S2. Optimize
(a) Identify degrees of freedom
(b) Optimize for expected disturbances
•
•
•
•
26
Need good steady-state model
Time consuming! But it is offline
Main goal: Identify ACTIVE CONSTRAINTSs
A good engineer can often guess the active constraints
Steady-state DOFs
Step S2a: Degrees of freedom (DOFs)
for operation
NOT as simple as one may think!
To find all operational (dynamic) degrees of freedom:
• Count valves! (Nvalves)
• “Valves” also includes adjustable compressor power, etc.
Anything we can manipulate!
BUT: not all these have a (steady-state) effect on the economics
27
Steady-state DOFs
Steady-state degrees of freedom (DOFs)
IMPORTANT!
DETERMINES THE NUMBER OF VARIABLES TO CONTROL!
• No. of primary CVs = No. of steady-state DOFs
Methods to obtain no. of steady-state degrees of freedom (Nss):
1. Equation-counting
•
•
Nss = no. of variables – no. of equations/specifications
Very difficult in practice
2. Valve-counting (easier!)
•
•
Nss = Nvalves – N0ss – Nspecs
N0ss = variables with no steady-state effect
• Inputs/MVs with no steady-state effect (e.g. extra bypass)
• Outputs/CVs with no steady-state effect that need to be controlled (e.g., liquid
levels)
3. Potential number for some units (useful for checking!)
4. Correct answer: Will eventually find it when we perform optimization
28
CV = controlled variable
Steady-state DOFs
Typical Distillation column
4
5
3
1
4 DOFs:
With given feed and pressure:
NEED TO IDENTIFY 2 more CV’s
- Typical: Top and btm composition
6
2
29
Nvalves = 6 , N0y = 2* ,
NDOF,SS = 6 -2 = 4 (including feed and pressure as DOFs)
*N0y : no. controlled variables (liquid levels) with no steady-state effect
Steady-state DOFs
Steady-state degrees of freedom (Nss):
3. Potential number for some process units
•
•
•
•
•
•
•
•
•
•
30
•
•
•
•
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/speed)
adiabatic flash tank: 0*
liquid phase reactor: 1 (holdup reactant)
gas phase reactor: 0*
heat exchanger: 1 (bypass or flow)
column (e.g. distillation) excluding heat exchangers: 0* + no. of sidestreams
pressure* : add 1DOF at each extra place you set pressure (using an extra
valve, compressor or pump), e.g. in adiabatic flash tank, gas phase reactor or
absorption column
*Pressure is normally assumed to be given by the surrounding process and is then not a degree of freedom
Ref: Araujo, Govatsmark and Skogestad (2007)
Extension to closed cycles: Jensen and Skogestad (2009)
Real number may be less, for example, if there is no bypass valve
Steady-state DOFs
Distillation column (with feed and pressure as DOFs)
split
“Potential number”,
31
Nss= 0 (column distillation) + 1 (feed) + 2*1 (heat exchangers) + 1 (split) = 4
With given feed and pressure: N’ss = 4 – 2 = 2
Step S2b: Optimize for expected disturbances
•
What are the optimal values for our degrees of freedom u (MVs)?
J = cost feed + cost energy – value products
•
Minimize J with respect to u for given disturbance d (usually steady-state):
minu J(u,x,d)
subject to:
Model equations (e,g, Hysys):
Operational constraints:
f(u,x,d) = 0
g(u,x,d) < 0
OFTEN VERY TIME CONSUMING
– Commercial simulators (Aspen, Unisim/Hysys) are set up in “design mode” and
often work poorly in “operation (rating) mode”.
– Optimization methods in commercial simulators often poor
• We use Matlab or even Excel “on top”
32
…. BUT A GOOD ENGINEER CAN OFTEN GUESS THE
SOLUTION (active constraints)
Step S3: Implementation of optimal
operation
• Have found the optimal way of operation.
How should it be implemented?
• What to control ? (primary CV’s).
1.Active constraints
2.Self-optimizing variables (for
unconstrained degrees of freedom)
33
Optimal operation - Runner
Optimal operation of runner
– Cost to be minimized, J=T
– One degree of freedom (u=power)
– What should we control?
34
Optimal operation - Runner
1. Optimal operation of Sprinter
– 100m. J=T
– Active constraint control:
• Maximum speed (”no thinking required”)
• CV = power (at max)
35
Optimal operation - Runner
2. Optimal operation of Marathon runner
• 40 km. J=T
• What should we control? CV=?
• Unconstrained optimum
J=T
uopt
36
u=power
Optimal operation - Runner
Self-optimizing control: Marathon (40 km)
• Any self-optimizing variable (to control at
constant setpoint)?
•
•
•
•
37
c1 = distance to leader of race
c2 = speed
c3 = heart rate
c4 = level of lactate in muscles
Optimal operation - Runner
J=T
Conclusion Marathon runner
copt c=heart rate
select one measurement
c = heart rate
38
• CV = heart rate is good “self-optimizing” variable
• Simple and robust implementation
• Disturbances are indirectly handled by keeping a constant heart rate
• May have infrequent adjustment of setpoint (cs)
Selection of CV1
Expected active constraints distillation
•
•
Both products (D,B) generally have purity specs
Valuable product: Purity spec. always active
–
Reason: Amount of valuable product (D or B) should
always be maximized
• Avoid product “give-away” (“Sell water as methanol”)
• Also saves energy
methanol
+ water
valuable
product
methanol
+ max. 0.5%
water
Control implications:
1.
2.
39
ALWAYS Control valuable product at spec. (active
constraint).
May overpurify (not control) cheap product
cheap product
(byproduct)
water
+ max. 2%
methanol
Example with Quiz:
Optimal operation of two distillation columns
in series
40
QUIZ 1
Operation of Distillation columns in series
With given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column)
N=41
αAB=1.33
F ~ 1.2mol/s
pF=1 $/mol
> 95% A
pD1=1 $/mol
< 4 mol/s
N=41
αBC=1.
5
> 95% B
pD2=2 $/mol
< 2.4 mol/s
> 95% C
pB2=1 $/mol
Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2
Energy price: pV=0-0.2 $/mol (varies)
41
DOF = Degree Of Freedom
Ref.: M.G. Jacobsen and S. Skogestad (2011)
QUIZ: What are the expected active constraints?
1. Always. 2. For low energy prices.
SOLUTION QUIZ 1
Operation of Distillation columns in series
With given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column)
N=41
αAB=1.33
F ~ 1.2mol/s
pF=1 $/mol
> 95% A
pD1=1 $/mol
N=41
αBC=1.
5
> 95% B
pD2=2 $/mol
1.
xB = 95% B
Spec. valuable product (B): Always active!
Why? “Avoid product
Hm….? give-away”
< 4 mol/s
< 2.4 mol/s
2. Cheap energy: V1=4 mol/s, V2=2.4 mol/s
> 95% C
Max. column capacity constraints active!
pB2=1 $/mol
Why? Overpurify A & C to recover more B
Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2
Energy price: pV=0-0.2 $/mol (varies)
42
DOF = Degree Of Freedom
Ref.: M.G. Jacobsen and S. Skogestad (2011)
QUIZ: What are the expected active constraints?
1. Always. 2. For low energy prices.
QUIZ 2
Control of Distillation columns in series
PC
PC
LC
LC
Given
LC
43
Red: Basic regulatory loops
LC
QUIZ. Assume low energy prices (pV=0.01 $/mol).
How should we control the columns?
HINT: CONTROL ACTIVE CONSTRAINTS
SOLUTION QUIZ 2
Control of Distillation columns in series
PC
PC
LC
LC
xB
1 unconstrained DOF (L1):
Use for what?? CV=?
Given
CC
xBS=95%
•Not: CV= xA in D1! (why? xA should vary with F!)
•Maybe: constant L1? (CV=L1)
Hm…….
•Better: CV= xA in B1?
Self-optimizing?
HINT: CONTROL
MAX V1 ACTIVE CONSTRAINTS! MAX V2
General for remaining unconstrained DOFs:
LOOK FOR “SELF-OPTIMIZING” CVs = Variables we can keep constant
LC
WILL GET BACK TO THIS!LC
44
Red: Basic regulatory loops
QUIZ. Assume low energy prices (pV=0.01 $/mol).
How should we control the columns?
HINT: CONTROL ACTIVE CONSTRAINTS
Comment: Distillation column control in
practice
1. Add stabilizing temperature loops
– In this case: use reflux (L) as MV because boilup (V) may
saturate
– T1s and T2s then replace L1 and L2 as DOFs.
2. Replace V1=max and V2=max by dpmax-controllers
(assuming max. load is limited by flooding)
• See next slide
45
Comment: In practice
Control of Distillation columns in series
PC
PC
LC
LC
xB
T1
TC
T1s
T2
TC
T2s
CC
Given
MAX V1
LC
46
MAX V2
LC
xBS=95%
CV = Active constraint
More on: Active output constraints
Need back-off
c ≥ cconstraint
J
Loss
Jopt
Back-off
c
a)
If constraint can be violated dynamically (only average matters)
•
b)
Required Back-off = “measurement bias” (steady-state measurement error for c)
If constraint cannot be violated dynamically (“hard constraint”)
•
Required Back-off = “measurement bias” + maximum dynamic control error
Want tight control of hard output constraints to reduce the
back-off. “Squeeze and shift”-rule
47
CV = Active constraint
Hard Constraints: «SQUEEZE AND SHIFT»
COST FUNCTION
N Histogram
LEVEL 0 / LEVEL 1
2
Sigma 1 -- Sigma 2
Sigma 2
OFF
SPEC
LEVEL 2
Q1 -- Q2
W2
1.5
DELTA COST (W2-W1)
W1
1
Sigma 1
0.5
Rule for control of hard output constraints:
• “Squeeze and shift”!
• Reduce variance (“Squeeze”) and “shift”
setpoint cs to reduce backoff
SQUEEZE
Q2
0
48
0
© Richalet
50
100
150
Q1
200
SHIFT
QUALITY
250
300
350
400
450
CV = Active constraint
Example. Optimal operation = max. throughput.
Want tight bottleneck control to reduce backoff!
Back-off
= Lost
production
Time
49
CV = Active constraint
Example back-off.
xB = purity product > 95% (min.)
D1
xB
• D1 directly to customer (hard constraint)
–
–
–
–
–
•
D1 to large mixing tank (soft constraint)
xB
±2%
Measurement error (bias): 1%
Backoff = 1%
Setpoint xBs= 95 + 1% = 96% (to be safe)
Do not need to include control error because it averages out in tank
8
–
–
–
–
50
Measurement error (bias): 1%
Control error (variation due to poor control): 2%
Backoff = 1% + 2% = 3%
Setpoint xBs= 95 + 3% = 98% (to be safe)
Can reduce backoff with better control (“squeeze and shift”)
xB,product
Unconstrained variables
More on: WHAT ARE GOOD “SELFOPTIMIZING” VARIABLES?
• Intuition: “Dominant variables” (Shinnar)
• More precisely
1. Optimal value of CV is constant
2. CV is “sensitive” to MV (large gain)
51
Unconstrained optimum
GOOD “SELF-OPTIMIZING” CV=c
1. Optimal value copt is constant (independent of disturbance d):
2. c is “sensitive” to MV=u (to reduce effect of measurement noise)
Equivalently: Optimum should be flat
Good
52
Good
BAD
Example.
Control of Distillation columns. Cheap energy
PC
PC
LC
LC
xB
Overpurified
CC
xBS=95%
Given
MAX V1
LC
MAX V2
LC
Overpurified
1 unconstrained DOF (L1): What is a good CV?
53
•Not: CV= xB in D1! (why? Overpurified, so xB,opt increases with F)
•Maybe: constant L1? (CV=L1)
•Better: CV= xA in B1? Self-optimizing?
Overpurified: To avoid loss of valuable product B
More on: Optimal operation
minimize J = cost feed + cost energy – value products
Two main cases (modes) depending on marked conditions:
Mode 1. Given feedrate
Mode 2. Maximum production
54
Mode 1. Given feedrate
Amount of products is then usually indirectly given and
J = cost feed– value products + cost energy
Often constant
Optimal operation is then usually unconstrained
“maximize efficiency (energy)”
Control:
• Operate at optimal trade-off
• NOT obvious what to control
• CV = Self-optimizing variable
J=
energy
55
copt
c
Mode 2. Maximum production
J = cost feed + cost energy – value products
• Assume feedrate is degree of freedom
• Assume products much more valuable than feed
• Optimal operation is then to maximize product rate
Control:
• Focus on tight control of bottleneck
• “Obvious what to control”
• CV = ACTIVE CONSTRAINT
J
Infeasible
region
56
cmax
c
Case study
Control structure design using self-optimizing control for
economically optimal CO2 recovery*
Step S1. Objective function= J = energy cost + cost (tax) of released CO2 to air
4 equality and 2 inequality constraints:
1.
2.
3.
4.
5.
6.
stripper top pressure
condenser temperature
pump pressure of recycle amine
cooler temperature
CO2 recovery ≥ 80%
Reboiler duty < 1393 kW (nominal +20%)
Step S2.
(a)
10 degrees of freedom: 8 valves + 2 pumps
4 levels without steady state effect:
absorber, stripper (2), make-up tank
Disturbances: flue gas flowrate, CO2 composition
in flue gas + active constraints
(b) Optimization using Unisim steady-state simulator.
Mode I (nominal feedrate): No inequality constraints active
Unconstrained degrees of freedom = 10 – 4 – 4 = 2
Step S3 (Identify CVs).
1. Control the 4 equality constraints
2. Identify 2 self-optimizing CVs (Use Exact Local method and select CV set with minimum loss)
57
*M. Panahi and S. Skogestad, ``Economically efficient operation of CO2 capturing process, Part I: Self-optimizing procedure for selecting the
best controlled variables'', Chemical Engineering and Processing, 50, 247-253 (2011).
Exact local method* for finding
2 self-optimizing CVs
The set with the minimum worst case loss is the best
1
max. Loss= σ(M) 2
2
1/2
y -1
M=J uu (HG ) H [FWd Wny ]
F=G y J -1uu J ud -G dy
Juu and F, the optimal sensitivity of the measurements with respect to
disturbances, are obtained numerically
Δyopt.
F=
Δd
58
* 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)
Identify 2 self-optimizing CVs
39 candidate CVs
- 15 possible tray temperature in absorber
- 20 possible tray temperature in stripper
- CO2 recovery in absorber and CO2 content at the bottom of stripper
- Recycle amine flowrate and reboiler duty
Use a bidirectional branch and bound algorithm* for finding the
best CVs
Best self-optimizing CV set in region I:
•
•
c1 = CO2 recovery (95.26%)
c2 = Temperature tray no. 16 in stripper
These CVs are not necessarily the best if new constraints are met
59
* V. Kariwala and Y. Cao. Bidirectional Branch and Bound for Controlled Variable Selection, Part II: Exact
Local Method for Self-Optimizing Control, Computers & Chemical Engineering, 33(2009), 1402-1412.
Proposed control structure with given
nominal flue gas flowrate (mode I)
60
Mode II: large feedrates of flue gas (+30%)
Feedrate
flue gas
(kmol/hr)
Self-optimizing CVs in region I
CO2 recovery
%
Temperature
tray no. 16
°C
Reboiler
duty
(kW)
Cost
(USD/ton)
Optimal nominal point
219.3
95.26
106.9
1161
2.49
+5% feedrate
230.3
95.26
106.9
1222
2.49
+10% feedrate
241.2
95.26
106.9
1279
2.49
+15% feedrate
252.2
95.26
106.9
1339
2.49
+19.38%, when reboiler
duty saturates
261.8
95.26
106.9
1393
(+20%)
2.50
+30% feedrate
(reoptimized)
285.1
91.60
103.3
1393
2.65
region I
region II
max
Saturation of reboiler duty; one unconstrained degree of freedom left
Use Maximum gain rule to find the best CV among 37 candidates :
• Temp. on tray no. 13 in the stripper: largest scaled gain, but tray 16 also OK
61
Proposed control structure with large flue
gas flowrate (mode II)
max
62
Switching policies CO2 plant
(”supervisory control”)
• Assume operating in region I (unconstrained)
– with CV=CO2-recovery=95.26%
• When reach maximum Q: Switch to Q=Qmax (Region II) (obvious)
– CO2-recovery will then drop below 95.26%
• When CO2-recovery exceeds 95.26%: Switch back to region I !!!
63
Conclusion optimal operation
ALWAYS:
1. Control active constraints and control them tightly!!
– Good times: Maximize throughput -> tight control of bottleneck
2. Identify “self-optimizing” CVs for remaining unconstrained degrees of freedom
•
Use offline analysis to find expected operating regions and prepare control
system for this!
– One control policy when prices are low (nominal, unconstrained optimum)
– Another when prices are high (constrained optimum = bottleneck)
ONLY if necessary: consider RTO on top of this
64
Part 1.3 -Inventory (level) control structure
– Location of throughput manipulator
– Consistency and radiating rule
65
Outline
• Skogestad procedure for control structure design
I Top Down
• Step S1: Define operational objective (cost) and constraints
• Step S2: Identify degrees of freedom and optimize operation for disturbances
• Step S3: Implementation of optimal operation
– What to control ? (primary CV’s)
– Control Active constraints + self-optimizing variables
• Step S4: Where set the production rate? (Inventory control)
II Bottom Up
• Step S5: Regulatory control: What more to control (secondary CV’s) ?
• Step S6: Supervisory control
• Step S7: Real-time optimization
66
Step S4. Where set production rate?
• Very important decision that determines the structure of the rest of the
inventory control system!
• May also have important economic implications
• Link between Top-down (economics) and Bottom-up (stabilization)
parts
– Inventory control is the most important part of stabilizing control
• “Throughput manipulator” (TPM)
= MV for controlling throughput (production rate, network flow)
• Where set the production rate = Where locate the TPM?
– Traditionally: At the feed
– For maximum production (with small backoff): At the bottleneck
67
TPM (Throughput manipulator)
•
•
Definition 1. TPM = MV used to control throughput (CV)
Definition 2 (Aske and Skogestad, 2009). A TPM is a degree of freedom that
affects the network flow and which is not directly or indirectly determined by
the control of the individual units, including their inventory control.
–
–
The TPM is the “gas pedal” of the process
Value of TPM: Usually set by the operator (manual control)
•
–
The TPM is usually a flow (or closely related to a flow), e.g. main feedrate, but not always.
•
•
•
•
–
parallel units or splits into alternative processing routes
multiple feeds that do not need to be set in a fixed ratio
If we consider only part of the plant then the TPM may be outside our control.
•
68
It can be a setpoint to another control loop
Reactor temperature can be a TPM, because it changes the reactor conversion,
Pressure of gas product can be a TPM, because it changes the gas product flowrate
Fuel cell: Load (current I) is usually the TPM
Usually, only one TPM for a plant, but there can be more if there are
•
•
–
Operators are skeptical of giving up this MV to the control system (e.g. MPC)
throughput is then a disturbance
TPM and link to inventory control
•
Liquid inventory: Level control (LC)
– Sometimes pressure control (PC)
•
•
69
Gas inventory: Pressure control (PC)
Component inventory: Composition control (CC, XC, AC)
Production rate set at inlet :
Inventory control in direction of flow*
TPM
* Required to get “local-consistent” inventory control
70
Production rate set at outlet:
Inventory control opposite flow*
TPM
* Required to get “local-consistent” inventory control
71
Production rate set inside process*
TPM
* Required to get “local-consistent” inventory control
72
General: “Need radiating inventory
control around TPM” (Georgakis)
73
Consistency of inventory control
•
Consistency (required property):
An inventory control system is said to be consistent if the steadystate mass balances (total, components and phases) are satisfied
for any part of the process, including the individual units and the
overall plant.
74
QUIZ 1
CONSISTENT?
75
Local-consistency rule
Rule 1. Local-consistency requires that
1. The total inventory (mass) of any part of the process must be locally
regulated by its in- or outflows, which implies that at least one flow in or
out of any part of the process must depend on the inventory inside that
part of the process.
2. For systems with several components, the inventory of each component of
any part of the process must be locally regulated by its in- or outflows or
by chemical reaction.
3. For systems with several phases, the inventory of each phase of any part
of the process must be locally regulated by its in- or outflows or by phase
transition.
76
Proof: Mass balances
Note: Without the word “local” one gets the more general consistency rule
QUIZ 1
CONSISTENT?
77
Local concistency requirement ->
“Radiation rule “(Georgakis)
78
Flow split: May give extra DOF
TPM
TPM
Split: Extra DOF (FC)
79
Flash: No extra DOF
QUIZ 2
Consistent?
Local-consistent?
Note: Local-consistent is
more strict as it implies
consistent
80
QUIZ 3
Closed system: Must
leave one inventory
uncontrolled
81
QUIZ 4
OK? (Where is production set?
TPM1
TPM2
82
NO. Two TPMs (consider overall liquid balance).
Solution: Interchange LC and FC on last tank
Example: Separator control
Alternative TPM locations
Compressor could be replaced by valve if p1>pG
83
Alt.1
Alt.3
84
Alt.2
Alt.4
Similar to original but
NOT CONSISTENT
(PC not direction of flow)
Example: Solid oxide fuel cell
xH2??
xCH4,s
CC
PC
CH4
H2O
(in ratio with CH4 feed
to reduce C and CO formation)
Air
CH4 + H2O = CO + 3H2
CO + H2O = CO2 + H2
2H2 + O2- → 2H2O + 2eSolid oxide electrolyte
O2-
e-
TPM = current I [A] = disturbance
O2 + 4e- → 2O2-
(excess O2)
TC
PC
Ts = 1070 K
(active constraint)
85
PC
TC
86
LOCATION OF SENSORS
• Location flow sensor (before or after valve or pump): Does not matter
from consistency point of view
– Locate to get best flow measurement
• Before pump: Beware of cavitation
• After pump: Beware of noisy measurement
• Location of pressure sensor (before or after valve, pump or
compressor): Important from consistency point of view
87
QUIZ 4
OK? (Where is production set?
TPM1
TPM2
88
NO. Two TPMs (consider overall liquid balance).
Solution: Interchange LC and FC on last tank
Where should we place TPM?
•
•
TPM = MV used to control throughput
Traditionally: TPM = Main feed valve (or pump/compressor)
–
Gives inventory control “in direction of flow”
Consider moving TPM if:
1.
There is an important CV that could otherwise not be well controlled
– Dynamic reasons
– Special case: Max. production important: Locate TPM at process bottleneck* !
•
•
2.
TPM can then be used to achieve tight bottleneck control (= achieve max. production)
Economics: Max. production is very favorable in “sellers marked”
If placing it at the feed may yield infeasible operation (“overfeeding”)
–
If “snowballing” is a problem (accumulation in recycle loop), then consider placing TPM
inside recycle loop
BUT: Avoid a variable that may (optimally) saturate as TPM (unless it is at bottleneck)
–
Reason: To keep controlling CV=throughput, we would need to reconfigure (move TPM)**
*Bottleneck: Last constraint to become active as we increase throughput -> TPM must be used for bottleneck control
89
**Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally)
saturate with CV that may be given up”
QUIZ. Distillation. OK?
LV-configuration
TPM
90
DB-configuration OK???
TPM
91
DB-configuration: Level control NOT consistent by
itself, but can still work* if we add one (or
preferably two) composition/temperature loops
cc
TPM
cc
92
*But DB-configuration is not recommended!
QUIZ
*
**
* Keep p ¸ pmin
** Keep valve fully open
93
94
QUIZ
95
LOCATION OF SENSORS
• Location flow sensor (before or after valve or pump): Does not matter
from consistency point of view
– Locate to get best flow measurement
• Before pump: Beware of cavitation
• After pump: Beware of noise
• Etc.
• Location of pressure sensor (before or after valve, pump or
compressor): Important from consistency point of view
96
Often optimal: Locate TPM at bottleneck!
• "A bottleneck is a unit where we reach a constraints which makes
further increase in throughput infeasible"
• If feed is cheap and available: Located TPM at bottleneck (dynamic
reasons)
• If the flow for some time is not at its maximum through the
bottleneck, then this loss can never be recovered.
97
Single-loop alternatives for bottleneck control
Traditional: Manual control of feed rate
Bottleneck.
Want max
flow here
TPM
Alt.1. Feedrate controls bottleneck flow (“long loop”…):
FC
Fmax
TPM
Alt. 2: Feedrate controls lost task (another “long loop”…):
Fmax
TPM
Alt. 3: Reconfigure all upstream inventory loops:
Fmax
98
TPM
May move TPM to inside recycle loop to
avoid snowballing
Example: Eastman esterification process
Alcohol recycle
Reach max mass transfer
rate: R increases sharply
(“snowballing”)
Ester product
Alcohol + water + extractive agent (e)
99
First improvement: Located closer to bottleneck
10
0
Final improvement: Located “at” bottleneck + TPM
is inside “snowballing” loop
Follows Luyben’s law 1 to avoid snowballing(modified): “Avoid having all
streams in a recycle system on inventory control”
10
1
Where should we place TPM?
•
•
TPM = MV used to control throughput
Traditionally: TPM = Main feed valve (or pump/compressor)
–
Operators like it. Gives inventory control “in direction of flow”
Consider moving TPM if:
1.
There is an important CV that could otherwise not be well controlled
•
–
Special case: Max. production important: Locate TPM at process bottleneck* !
•
•
2.
Dynamic reasons
Because max. production is very favorable in “sellers marked”
TPM can then be used to achieve tight bottleneck control (= achieve max. flow)
If placing it at the feed may yield infeasible operation (“overfeeding”)
–
If “snowballing” is a problem (accumulation in recycle loop), then consider placing TPM
inside recycle loop
BUT: Avoid a variable that may (optimally) saturate as TPM (unless it is at bottleneck)
–
Reason: To keep controlling CV=throughput, we would need to reconfigure (move TPM)**
*Bottleneck: Last constraint to become active as we increase throughput -> TPM must be used for bottleneck control
10
2
**Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally)
saturate with CV that may be given up”
Moving TPM
A purely top-down approach: Start by
controlling all active constaints at max.
throughput (may give moving TPM)
Economic Plantwide Control Over a Wide Throughput Range: A Systematic
Design Procedure
Rahul Jagtap, Nitin Kaistha*and Sigurd Skogestad
Step 0:
Step 1:
Obtain active constraint regions for the wide throughput range
Pair loops for tight control of economic CVs at maximum throughput
– Most important point economically
– Most active constraints
Step 2: Design the inventory (regulatory) control system
Step 3: Design loops for ‘taking up’ additional economic CV control at lower
throughputs along with appropriate throughput manipulation strategy
10
3
Warning: May get complicated, but good economically because of tight control of active constraints
PC
X
B
A
FC
A, B Recycle
PC
LC
FC
LC
LVLRxrMAXLC
HS3
CCB
xBRxr
C
Opt
FC
CCD
RC
A+ B C
B+CD
0.02%
TC
SP1 > SP2 > SP3
HS2
Stri
ppe
r
V1MAX
SP3
LS1
LC3
TRxrOpt
TRxrMAX
LS2
SP2
LC2
LC1
Colu
mn
FC
SP1
TC
165 °C
CCB
V2MAX TPM for < max
throughput
FC
LC
Figure 5. Plantwide control structure for maximum throughput operation of recycle process (Case Study I)
10
4
0.98%
TC
D
Conclusion TPM (production rate
manipulator)
• Think carefully about where to place it!
• Difficult to undo later
10
5
Part 1.4 Structure of regulatory control
layer (PID)
Part 1.4 Structure of regulatory control layer (PID)
– Selection of controlled variables (CV2) and pairing with manipulated
variables (MV2)
– Main rule: Control drifting variables and "pair close"
Summary: Sigurd’s rules for plantwide control
10
6
Outline
• Skogestad procedure for control structure design
I Top Down
• Step S1: Define operational objective (cost) and constraints
• Step S2: Identify degrees of freedom and optimize operation for disturbances
• Step S3: Implementation of optimal operation
– What to control ? (primary CV’s) (self-optimizing control)
• Step S4: Where set the production rate? (Inventory control)
II Bottom Up
• Step S5: Regulatory control: What more to control (secondary CV’s) ?
– Distillation example
• Step S6: Supervisory control
• Step S7: Real-time optimization
10
7
Regulatory layer
II. Bottom-up
• Determine secondary controlled variables (CV2) and
structure (configuration) of control system (pairing, CV2MV2)
• A good control configuration is insensitive to parameter
changes
10
8
Regulatory layer
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 decisions:
• What more should we control?
(secondary cv’s, CV2, use of extra
measurements)
• Pairing with manipulated variables
(mv’s u2)
CV1
CV2 = ?
10
9
Regulatory layer
Objectives regulatory control layer
1.
2.
3.
4.
5.
6.
7.
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”
–
11
0
“stabilization” (practical sense)
8. Allow for “slow” control in layer above (supervisory control)
9. Make control problem easy as seen from layer above
10. Use “easy” and “robust” measurements (pressure, temperature)
11. Simple structure
12. Contribute to overall economic objective (“indirect” control)
13. Should not need to be changed during operation
Regulatory layer
Stabilizing control: Use inputs MV2=u2 to control
“drifting” variables CV2
CV2s
K
u2
G
CV1
Primary CV
CV2
Secondary CV
(control for
dynamic reasons)
Key decision: Choice of CV2 (controlled variable)
Also important: Choice of MV2=u2 (“pairing”)
Process control: Typical «drifting» variables (CV2) are
• Liquid inventories (level)
• Vapor inventories (pressure)
• Some temperatures (reactor, distillation column profile)
11
1
Regulatory layer
Degrees of freedom unchanged
• No degrees of freedom lost as setpoints y2s replace inputs u2 as new
degrees of freedom for control of y1
Cascade control:
CV2s
New DOF
11
2
K
u2
G
CV1
CV2
Original DOF
Regulatory layer
Example: Exothermic reactor (unstable)
Active constraints (economics):
Product composition c + level (max)
• u = cooling flow (q)
• CV1 = composition (c)
• CV2 = temperature (T)
feed
CV1s
CC
CV2s
TC
CV1=c
LC
CV2=T
u
11
3
Ls=max
product
cooling
Regulatory layer
Details Step 5 (Structure regulatory control layer)
(a) What to control (CV2)?
1. Control CV2 that “stabilizes the plant” (stops drifting)
2. Select CV2 which is easy to control (favorable dynamics)
• In addition, active constraints (CV1) that require tight control
(small backoff) may be assigned to the regulatory layer.*
11
4
*Comment: usually not necessary with tight control of unconstrained CVs because
optimum is usually relatively flat
Regulatory layer
“Control CV2 that stabilizes the plant (stops drifting)”
In practice, control:
1. Levels (inventory liquid)
2. Pressures (inventory gas/vapor) (note: some pressures may be left
floating)
3. Inventories of components that may accumulate/deplete inside plant
•
•
•
E.g., amine/water depletes in recycle loop in CO2 capture plant
E.g., butanol accumulates in methanol-water distillation column
E.g., inert N2 accumulates in ammonia reactor recycle
4. Reactor temperature
5. Distillation column profile (one temperature inside column)
• Stripper/absorber profile does not generally need to be stabilized
11
5
Regulatory layer
Details Step 5b….
(b)
Identify pairings =
Identify MVs (u2) to control CV2, taking into account:
11
6
•
Want “local consistency” for the inventory control
– Implies radiating inventory control around given flow
•
Avoid selecting as MVs in the regulatory layer, variables that may
optimally saturate at steady-state (active constraint on some region),
because this would require either
– reassigning the regulatory loop (complication penalty), or
– requiring back-off for the MV variable (economic penalty)
•
Want tight control of important active constraints (to avoid back-off)
•
General rule: ”pair close” (see next slide)
Regulatory layer
Step 5b…. Main rule: “Pair close”
The response (from input to output) should be fast, large and in one direction.
Avoid dead time and inverse responses!
11
7
Regulatory layer
Sigurd’s pairing rule: “Pair MV that may
(optimally) saturate with CV that may be
given up”
•
Main reason: Minimizes need for reassigning loops
. loop
LV
Ts
TC
TC
(a) Normal: Control T using V
•
•
•
11
8
TS
(b) If V may saturate: Use L
Important: Always feasible (and optimal) to give up a CV when optimal MV saturation occurs.
–
Proof (DOF analysis): When one MV disappears (saturates), then we have one less optimal CV.
Failing to follow this rule: Need some “fix” when MV saturates to remain optimal, like
–
reconfiguration (logic)
–
backoff (loss of optimality)
BUT: Rule may be in conflict with other criteria
–
Dynamics (“pair close” rule)
–
Interactions (“avoid negative steady-state RGA” rule)
–
If conflict: Use reconfiguration (logic) or go for multivariable constraint control (MPC which may provide “built-in” logic)
Normal: Control T using V
•
. loop
LV
Ts
TC
TC
11
9
TS
Regulatory layer
Why simplified configurations?
Why control layers?
Why not one “big” multivariable controller?
• Fundamental: Save on modelling effort
• Other:
–
–
–
–
–
–
12
0
easy to understand
easy to tune and retune
insensitive to model uncertainty
possible to design for failure tolerance
fewer links
reduced computation load
Hierarchical/cascade 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:
1. 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
2. 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
12
1
Cascade control
distillation
ys
y
With flow loop +
T-loop in top
X
C
Ts
T
TC
Ls
L
12
2
X
C
FC
z
QUIZ: What are the benefits of adding a flow
controller (inner cascade)?
qs
Extra measurement y2 = q
1.
12
3
z
Counteracts nonlinearity in valve, f(z)
•
2.
q
With fast flow control we can assume q = qs
Eliminates effect of disturbances in p1 and p2
Summary: Sigurd’s plantwide control rules
Rules for CV-selection:
1. Control active constraints
–
Purity constraint on expensive product is always active (overpurification gives loss):
2. Unconstrained degrees of freedom (if any): Control “self-optimizing” variables (c).
•
•
The ideal variable is the gradient of J with respect to the inputs (Ju = dJ/du), which always should be zero, independent of disturbances d, but this variable is rarely
available
–
Exception (is available!): Parallel systems (stream split, multiple feed streams/manifold) with given throughput (or given total gas flow, etc.)
–
Should have equal marginal costs Jiu = dJi/du, so Ju = J1u - J2u, etc.
–
Heat exchanger splits: equal Jächke temperatures, JT1 = (T1 – Th1)^2/(T1-T0)
In practice, one prefers to control single variables, c=Hy (where y are all available measurements and H is a selection matrix), which are easy to measure and control, and which
have the following properties:
•
Optimal value for c is almost constant (independent of disturbances): Want small magnitude of dcopt(d)/dd.
•
Variable c is sensitive to changes in input: Want large magnitude of gain=dc/du (this is to reduce effect of measurement error and noise).
–
If the economic loss with single variables is too large, then one may use measurement combinations, c=Hy (where H is a “full” matrix).
3. Unconstrained degrees of freedom: NEVER try to control a variable that reaches max or min at the optimum (in particular, never control J)
–
Surprisingly, this is a very common mistake, even (especially?) with control experts
Rules for inventory control:
1. Use Radiation rule (PC, LC, FC ++)
2. Avoid having all flows in a recycle system on inventory control (this is a restatement of Luyben’s rule of “fixing a flow inside a recycle system” to avoid snowballing)
–
A special case is a closed system
Rules for pairing:
1. General: “Pair close” (large gain and small effective time delay)
2. CV1: Sigurd’s pairing rule: “Pair MV that may (optimally) saturate with CV that may be given up”
3. CV2 (stabilizing loop): Avoid MV that may saturate
12
4
Part 1 (3h): Plantwide control
Introduction to plantwide control (what should we really control?)
Part 1.1 Introduction.
–
–
–
Objective: Put controllers on flow sheet (make P&ID)
Two main objectives for control: Longer-term economics (CV1) and shorter-term stability (CV2)
Regulatory (basic) and supervisory (advanced) control layer
Part 1.2 Optimal operation (economics)
–
–
Active constraints
Selection of economic controlled variables (CV1). Self-optimizing variables.
Part 1.3 -Inventory (level) control structure
–
–
Location of throughput manipulator
Consistency and radiating rule
Part 1.4 Structure of regulatory control layer (PID)
–
–
Selection of controlled variables (CV2) and pairing with manipulated variables (MV2)
Main rule: Control drifting variables and "pair close"
Summary: Sigurd’s rules for plantwide control
12
5
Plantwide control. Main 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 (2012).
• More information:
http://www.nt.ntnu.no/users/skoge/plantwide
12
6
All papers available at: http://www.nt.ntnu.no/users/skoge/