CHAPTER 21: Multiloop Control Performance When I complete this chapter, I want to be able to do the following. • Distinguish favorable and unfavorable interaction • Balance controllability, integrity and dynamic performance • Apply two methods for decoupling • Properly select applications for decoupling
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CHAPTER 21: Multiloop Control Performance · 2019-10-23 · CHAPTER 21: Multiloop Control Performance When I complete this chapter, I want to be able to do the following. • Distinguish
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CHAPTER 21: Multiloop Control Performance
When I complete this chapter, I want to be able to do the following.
• Distinguish favorable and unfavorable interaction
• Balance controllability, integrity and dynamic performance
• Apply two methods for decoupling
• Properly select applications for decoupling
Outline of the lesson.
• Some observations on multiloop design performance
• The RDG, Relative Disturbance Gain
• Controllability and interaction
• Disturbance directionality
• Decoupling
CHAPTER 21: Multiloop Control Performance
REQUIRED: DOF, Controllability, Operating Window
HIGHLY DESIRED
• Integrity - Performance is “acceptable after one or more controllers become inactive
• Control performance
- CVs achieve zero offset and low deviations from SP- MVs have acceptable dynamic variability
• Robustness - Performance (not just stability) is achieved for a range of plant dynamics
• Range - Strong effect to compensate large disturbances
MULTILOOP CONTROL PERFORMANCE
Let’s learn how to achieve thesegood properties
MULTILOOP CONTROL PERFORMANCE
Motivating Example
No. 1 - Blending
FA, xA
FS, xAS = 0FM, xAM
Must retune when flow controller is in manual!
Table 20-4. Tuning for the blending system with dilute product (XXAM=0.05, 8=0.95)
Tuning term AXAM-FA controller (slow loop)
FM-FS controller (fast loop)
Single-loop Multiloop Single-loop Multiloop
Kc (kg/min/wgt fraction) 105. 100 1.0 1.0
TI (sec) 38. 38 2.6 2.6
Table 20-5. Tuning for the blending system with dilute product (XXAM=0.05, 8=0.05)
Tuning term AXAM-FS Pairing (slow loop)
FM-FA Pairing (fast loop)
Single-loop Multiloop Single-loop Multiloop
Kc (kg/min/wgt fraction) -2000. -100 1.0 1.0
TI (sec) 38. 38 2.6 2.6
The design with RGA nearer 1.0is better
MULTILOOP CONTROL PERFORMANCE
Motivating Example No. 2 - Distillation SP ResponseFR → XD
FRB → XB
FD → XD
FRB → XB
0 50 100 150 2000.98
0.982
0.984
0.986
0.988IAE = 0.26687 IS E = 0.00052456
XD
, lig
ht k
ey
0 50 100 150 2000.02
0.021
0.022
0.023
0.024IAE = 0.25454 IS E = 0.0004554
XB
, lig
ht k
ey
0 50 100 150 2008.5
8.6
8.7
8.8
8.9
9S AM = 0.31512 S S M = 0.011905
Time
Ref
lux
flow
0 50 100 150 20013.5
13.6
13.7
13.8
13.9
14S AM = 0.28826 S S M = 0.00064734
Time
Reb
oile
d va
por
0 50 100 150 2000.98
0.982
0.984
0.986
0.988IAE = 0.059056 IS E = 0.00017124
XD
, lig
ht k
ey
0 50 100 150 2000.019
0.02
0.021
0.022
0.023IAE = 0.045707 IS E = 8.4564e-005
XB
, lig
ht k
ey
0 50 100 150 2008.46
8.48
8.5
8.52
8.54S AM = 0.10303 S S M = 0.0093095
Time
Ref
lux
flow
0 50 100 150 20013.5
13.6
13.7
13.8
13.9
14S AM = 0.55128 S S M = 0.017408
Time
Reb
oile
d va
por
RGA = 6.09 RGA = 0.39
For set point
response, RGA
closer to 1.0 is better
MULTILOOP CONTROL PERFORMANCE
Motivating Example No. 3 - Distillation disturb. ResponseFR → XD
FRB → XBFD → XD
FRB → XB
0 50 100 150 200
0.975
0.98
IAE = 0.14463 IS E = 0.00051677
XD
, lig
ht k
ey
0 50 100 150 2000
0.005
0.01
0.015
0.02
0.025IAE = 0.32334 IS E = 0.0038309
XB
, lig
ht k
ey
0 50 100 150 2008.5
8.55
8.6
8.65
8.7S AM = 0.21116 S S M = 0.0020517
Time
Ref
lux
flow
0 50 100 150 20013.1
13.2
13.3
13.4
13.5
13.6S AM = 0.38988 S S M = 0.0085339
Time
Reb
oile
d va
por
RGA = 6.09
RGA = 0.39
0 50 100 150 2000.95
0.96
0.97
0.98
0.99IAE = 0.45265 IS E = 0.0070806
XD
, lig
ht k
ey
0 50 100 150 2000
0.005
0.01
0.015
0.02
0.025
0.03IAE = 0.31352 IS E = 0.0027774
XB
, lig
ht k
ey
0 50 100 150 2008
8.1
8.2
8.3
8.4
8.5
8.6S AM = 0.51504 S S M = 0.011985
Time
Ref
lux
flow
0 50 100 150 20011
11.5
12
12.5
13
13.5
14S AM = 4.0285 S S M = 0.6871
Time
Reb
oile
d va
por
For set point
response, RGA
farther from 1.0is better
MULTILOOP CONTROL PERFORMANCE
• Conclusion from examples - RGA Alone does not provide sufficient information for control design
• Key missing information is disturbance type
• Key factor is the DISTURBANCE DIRECTION
Disturbances in this direction are easily corrected.
Disturbances in this direction are difficult to correct.
MULTILOOP CONTROL PERFORMANCE
Short-cut Measure of Multiloop Control Performance
• We want to predict the performance using limited information and calculations
• We would like to have the following features
- Dimensionless
- Based on process characteristics
- Related to the disturbances type
Let’s recall if the RGAhad these features
MULTILOOP CONTROL PERFORMANCE
∫ ∫=∞ ∞
0 0dttEfRDGdttE SLtuneML )( )(
Single-loop performance (dead times, large disturbances, etc. are bad)
Tune Factor
Change in tuning for multi-loop
Relative Disturbance Gain• dimensionless• only s-s gains• can be +/- and > or < 1.0• different for each
disturbance• Usually the dominant term
for interaction
MULTILOOP CONTROL PERFORMANCE
∫ ∫=∞ ∞
0 0dttEfRDGdttE SLtuneML )( )(
cp
ID
KKTK
MLIc
SLIc
TKT
K
−
− 221
122
22112112
11
1KKKK
KKKK d
d
What is this term?
What unique information is here?
What is the typical range?
Relative disturbance gain
MULTILOOP CONTROL PERFORMANCE
Process Example: Binary Distillation with XD=.98, XB = 0.02
1. Calculate the RGA, RDG, ftune, and Ratio of integral errors for both loop pairings
2. Select best loop pairings
FR → XD
FRB → XBFD → XD
FRB → XB
Energy Balance:
Material Balance:
MULTILOOP CONTROL PERFORMANCE
0 50 100 150 2000.97
0.975
0.98
0.985IAE = 0.14463 IS E = 0.00051677
CV 1
0 50 100 150 2000
0.005
0.01
0.015
0.02
0.025IAE = 0.32334 IS E = 0.0038309
CV 2
0 50 100 150 2008.5
8.55
8.6
8.65
8.7S AM = 0.21116 S S M = 0.0020517
Time
MV 1
0 50 100 150 20013.1
13.2
13.3
13.4
13.5
13.6S AM = 0.38988 S S M = 0.0085339
Time
MV 2
Distillation tower (R,V) with both controllers in automatic for feed composition disturbance
Good performance in spite of the large RGA
XD XB
MULTILOOP CONTROL PERFORMANCE
0 50 100 150 200
0.97
0.98
0.99IAE = 0.3252 IS E = 0.0027029
CV 1
0 50 100 150 200-0.01
0
0.01
0.02IAE = 2.0211 IS E = 0.030442
CV 2
0 50 100 150 2008.5
8.6
8.7
8.8
8.9
9S AM = 0.38091 S S M = 0.0057519
Time
MV 1
0 50 100 150 20012.5
13
13.5
14
14.5
15S AM = 0 S S M = 0
Time
MV 2
Distillation tower (R,V) with only XD controller in automatic for feed composition disturbance
Favorable interaction results in small XB deviation although it is not controlled!
No control!
XD XB
0 50 100 150 2000.9785
0.979
0.9795
0.98
0.9805
0.981IAE = 0.035341 IS E = 3.4646e-005
CV 1
0 50 100 150 2000.017
0.018
0.019
0.02
0.021IAE = 0.055842 IS E = 8.7178e-005
CV 2
0 50 100 150 2008.52
8.54
8.56
8.58S AM = 0.042228 S S M = 7.8417e-005
Time
MV 1
0 50 100 150 20012.5
13
13.5
14
14.5
15S AM = 0 S S M = 0
Time
MV 2
Distillation Tower (R,V) with only XD controller in automatic and disturbance through FR model
MULTILOOP CONTROL PERFORMANCE
Example is change in reflux subcooling.
Good performance in spite of the large RGA
No control!
XD XB
MULTILOOP CONTROL PERFORMANCE
∫ ∫=∞ ∞
0 0dttEfRDGdttE SLtuneML )( )(
PRELIMINARY LOOP PAIRING GUIDELINE
Pair loops with good single-loop performance and favorable interaction, as indicated by a small |RDG|.
Small = good SL performance
Small = favorable interaction
MULTILOOP CONTROL PERFORMANCE
TAKING ADVANTAGE OF THE DYNAMICS
If unfavorable interaction exists in the best loop pairing, the effects of interaction can be reduced by tight tuning of the important loop and loose tuning of the less important loops.
FR → XD
FRB → XB
RGA = 6.090 50 100 150 200
0.98
0.982
0.984
0.986
0.988IAE = 0.09672 IS E = 0.00015157
XD
, lig
ht k
ey
0 50 100 150 2000.02
0.022
0.024
0.026
0.028
0.03IAE = 0.55824 IS E = 0.0021608
XB
, lig
ht k
ey
0 50 100 150 2008.5
8.6
8.7
8.8
8.9
9S AM = 0.57349 S S M = 0.098745
Time
Ref
lux
flow
0 50 100 150 20013.5
13.6
13.7
13.8
13.9
14S AM = 0.27914 S S M = 0.00064532
Time
Reb
oile
d va
por
Tightlytuned
Looselytuned
MULTILOOP CONTROL PERFORMANCE
TAKING ADVANTAGE OF THE DYNAMICS
Seek MV-CV pairings that provide fast feedback control for the more important loops. This tends to match the dynamic performance with the control objectives.
Evaluate the loop pairing for this process example, which supplies gas to a consumer from two sources.
PC
AC
E-1
P-1
P-2
V-1
vaporizer
gas
gas
A = composition
MULTILOOP CONTROL PERFORMANCE
PROVIDING LARGE RANGE (OPERATING WINDOW)
• For most important CVs, select an MV with large range.- If other loops are in manual, the important loop retains large operating window.
• Provide “extra” MV using split range capabilities.
AC
AC Discuss the range available when
1. Both loops are in automatic.
2. Only one loop is in automatic.
MULTILOOP CONTROL PERFORMANCE
PROVIDING INTEGRITY
• Favor loop pairings with positive relative gains.
- Only use negative RGA if very advantageous dynamics- Use zero RGA very carefully for dynamic advantage
• If non-positive RGA used, add monitor to alarm operator when other loop is inactive
• Consider the effects of RGA on tuning. Avoid high multiloop gains that lead to unstable single-loop systems.
MULTILOOP CONTROL PERFORMANCE
RETAINING CONTROLLABILITY
Do not implement a loop that eliminates the causal relationship of another loop.
T
A
Reactant
Solvent
Coolant
• Evaluate the design, specifically the control of the concentration in the reactor
• Suggest an alternative design
MULTILOOP CONTROL PERFORMANCE
RETAINING CONTROLLABILITY
Do not control the same variable with two loops with the same set point.
PC
Flows into the pipe
Flows exiting the pipe
PC
• What problems could occur if the two PCs had the same set point?
• Why would we use different set points?
• Would the system function with different set points?
MULTILOOP CONTROL PERFORMANCE
REDUCING EFFECTS OF DISTURBANCES
Implement loops that reduce the effects of disturbances before they affect the key controlled variables.
T
A
Reactant
Solvent
Coolant
• How does this design satisfy the rule above.
• Suggest additional methods for reducing the effects of disturbances
MULTILOOP CONTROL PERFORMANCE
REDUCING THE EFFECTS OF UNFAVORABLE INTERACTION USING DECOUPLING
• Retains the single-loop control algorithms
• Reduces (eliminates) the effects of interaction
• Three approaches
- Implicit decoupling: Calculated MVs
- Implicit decoupling: Calculated CVs
- Explicit decoupling: Controller compensation
MULTILOOP CONTROL PERFORMANCE
IMPLICIT DECOUPLING: CALCULATED MVs
323213
11121
21
FMVF)FF(dt
dF
AMVAFF
Fdt
dA
F
A
−=−+=
−=−+
=
τ
τ
• How can we adjust these calculated variables?
• Are there any special tuning guidelines?
MULTILOOP CONTROL PERFORMANCE
IMPLICIT DECOUPLING: CALCULATED CVs
)FF()LL(K)FF(dt
)LL(dA
)FF()FF(dt
)LL(dA
'''''in
'in
''
'''in
'in
''
21212121
212121
2 −−−+−=−
+−+=+
• How can we control these calculated variables?
• Are there any special tuning guidelines?
MULTILOOP CONTROL PERFORMANCE
+-+
+
+ +-
+
Gc1(s)
Gc2(s)
G11(s)
G21(s)
G12(s)
G22(s)
Gd2(s)
Gd1(s)
D(s)
CV1(s)
CV2(s)
MV2(s)
MV1(s)
SP1(s)
SP2(s)
GD21(s)
GD12(s)
+
+
REDUCING THE EFFECTS OF UNFAVORABLE INTERACTION USING EXPLICIT
DECOUPLING
• Compensates for the effects of interaction
MULTILOOP CONTROL PERFORMANCE
Decoupling - Perfect decoupling compensates for interactions
)()(
)(sGsG
sGii
ijDij −=One design approach:
+-+
+
+ +-
+
Gc1(s)
Gc2(s)
G11(s)/λ11
G22(s)/λ22
Gd2(s)
Gd1(s)
D(s)
CV1(s)
CV2(s)
SP1(s)
SP2(s)
MULTILOOP CONTROL PERFORMANCE
Decoupling - Deciding when to decouple
(RDG)(ftune) Interpretation Decision< 1 Favorable interaction Do not decouple≈ 1 No significant
differenceDo not decouple
> 1 Unfavorable interaction Decouple(see next item)
MULTILOOP CONTROL PERFORMANCE
FR → XD
FRB → XB RDG Tuning factor(with KcML =(Kc)SL/λ) ∫
∫=∫∫
SL
ML
Dec
ML
EE
EE
XD -0.50 1.55 -0.77
XB 1.2 1.55 1.85
Which decoupling do you recommend?
MULTILOOP CONTROL PERFORMANCE
Simulation confirms that top-to-bottom decoupling improves XB control performance.
|RDG*ftune | > 1.0
improvement
MULTILOOP CONTROL PERFORMANCE
Simulation confirms that bottom-to-top decoupling does not improve XD control performance.
|RDG*ftune | < 1.0
No improvement(a bit worse)
MULTILOOP CONTROL PERFORMANCE
Decoupling - A large relative gain indicates extreme sensitivity to modelling errors can occur
∫∫
−
−
dt|E|
dt|E|
ewayDecoupl
ewayDecoupl
1
2
(Worst case mismatch)
MULTILOOP CONTROL PERFORMANCE
Decoupler with no errors; excellent performance!
Decoupler with 15% gain errors, unstable!
Decoupler performance can be very sensitive to gain errors. If possible, use process knowledge in determining plant gains, Kij.
MULTILOOP CONTROL PERFORMANCE
Decoupling
• Because the closed-loop system changes, the controller must be retuned by approximately the relative gain, (Kc)dec ≈ λ (Kc)SL .
• When a valve saturates, the “other” loops need to be retuned again!
• The behavior with integral windup is complex.
• Why not use MPC?
MULTILOOP CONTROL PERFORMANCE
CONCLUSIONS
• CONTROL PERFORMANCE DEPENDS STRONGLY ON THE DISTURBANCE
- Multiloop systems have directions that are easy/difficult to achieve
- Multiloop performance can be worse or better than SL
• SHORT-CUT METHOD IS AVAILABLE TO EVALUATE MULTILOOP PERFORMANCE
- RDG uses steady-state gains
- Large value is BAD; small value might be good (careful of +/- cancellation)
MULTILOOP CONTROL PERFORMANCE
Small RGA Large RGASmall RDGFavorableinteraction
Large RDGUnfavorableinteraction
Complete the following table with recommendations for control design