CHAPTER 21: Multiloop Control Performance · 2019-10-23 · CHAPTER 21: Multiloop Control...

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


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


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


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


• 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.


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


∫ ∫=∞ ∞

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


∫ ∫=∞ ∞


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


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:


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


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


Example is change in reflux subcooling.

Good performance in spite of the large RGA

No control!

XD XB


∫ ∫=∞ ∞


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


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


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


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.


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.


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


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?


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


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


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?


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?


+-+

+

+ +-

+

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


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)


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)


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?


Simulation confirms that top-to-bottom decoupling improves XB control performance.

|RDG*ftune | > 1.0

improvement


Simulation confirms that bottom-to-top decoupling does not improve XD control performance.

|RDG*ftune | < 1.0

No improvement(a bit worse)


Decoupling - A large relative gain indicates extreme sensitivity to modelling errors can occur

∫∫

−

−

dt|E|

dt|E|

ewayDecoupl

ewayDecoupl

1

2

(Worst case mismatch)


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.


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?


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)


Small RGA Large RGASmall RDGFavorableinteraction

Large RDGUnfavorableinteraction

Complete the following table with recommendations for control design

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CHAPTER 21: Multiloop Control Performance · 2019-10-23 · CHAPTER 21: Multiloop Control...

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