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Enhanced Single-Loop Control Strategies(Advanced Control)

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Cascade Control Time-Delay Compensation Inferential Control Selective and Override Control

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Cascade Control• A disadvantage of conventional feedback control is that

corrective action for disturbance does not begin until after the controlled variables deviates from the set-point.

Disturbance: Oil flow rateCold oil temperature satisfactory response

Disturbance: Fuel gas supply pressure(Fuel gas flow) sluggish response

Example: Furnace temperature control

Conventional feedback control

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• Feedforward control: disturbances have to be measured and a model is required to calculate the controller output

• Cascade control: use a secondary measurement and a secondary feedback controller

Another Example: Temperature control of tanks in series

How to improve control performance ?

Disturbance

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• Cascade control: a primary control loop (TT1 and TC1) and a secondary control loop (TT2 and TC2)

Set-point

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Cascade Control• Distinguishing features:1. Two FB controllers but only a single control valve

(two controlled variables, two sensors, and one manipulated variable).

2. Output signal of the "master" controller is the set-point for “slave" controller.

3. Two FB control loops are "nested" with the "slave" (or "secondary") control loop inside the "master" (or "primary") control loop.

• Terminology:slave vs. master

secondary vs. primaryinner vs. outer

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Primary (outer)control loop

Secondary (inner)Control loop

Mastercontroller

Slavecontroller

A Furnace Cascade Temperature Control

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Block Diagram of Cascade Control System

1

2

1

2

= hot oil temperature= fuel gas pressure= cold oil temperature

(or cold oil flow rate)= supply pressure of gas fuel

YYD

D

1 1

2 2

1 1

2 2

= measured value of = measured value of = set point for

= set point for

m

m

sp

sp

Y YY YY Y

Y Y

(Furnace Example)

1 : primary loop2 : secondary loop

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Design Considerations for Cascade Control• For a cascade control system to function properly, the

secondary control loop must response faster than the primary loop.

• The secondary controller is normally a P or PI controller. The primary controller is usually PI or PID.

• First, design Gc2 for inner loop. (inside-out)

2 22

2 2 2 21

c v p

sp c v p m

G G GYY G G G G

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1 21

2 2 2 2 1 2 2 1 1(16 5)

1

p d

c v p m c c v p p m

G GD G G G G G G G G G GY

1 2 2 21

1 2 2 2 1 2 2 1 1

1(16 8)

1d c v p m

c v p m c c v p p m

G G G G G

D G G G G G G G G G GY

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Example Consider the block diagram with the following transfer functions:

1 2

1 22 1

5 4 11 4 1 2 1

11 0.05 0.23 1

v p p

m md d

G G Gs s s

G G G Gs

Great improvement

D1 step response

Primary loop: PISecondary loop: P

Slight improvement

D2 step response

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• The presence of time delay in a process limits the performance of a conventional feedback control system.– A time delay will adversely affects closed-loop stability.

Time Delay Compensation (Smith Predictor)

Example 16.2Compare the set-point responses for a second-order process with a time delay and without the delay. The transfer function is

Assume . Use the following PI controllers.

For , .

For

(the controller gain must be reduced to meet stability requirements)

( )

5 1 3 1

s

peG s

s s

1m vG G

0, 3.02cK 6.5 I

2, , 7.1.23 0. IcK

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Closed-loop set-point responses

• The response of the closed-loop system will be sluggish compared to that of the control loop with no time delay. (not only 2 min.)

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For this ideal case the controller responds to the error signal that would occur if no time delay were present.

Model

If the process model is perfect and the disturbance is zero, then 1 1 2 16 19spE E Y Y Y Y Y '

2Y Y 1 16 20spE' Y Y

Block Diagram of Smith Predictor

* - sG = G eWithout time delay

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* - sG = G G e

Assuming there is no model error the inner loop has the effective transfer function

16 211 * 1

cc

sc

GPGE G G e

'

,G G

Equivalent Structure for Smith Predictor

cG '

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For no model error:

By contrast, for conventional feedback control

1 1 1

* s * sc c c

* s * *sp c c c

G G e G G e G GYY G G e G G G G

*

* 16 231 1

sc c

ssp c c

G G G G eYY G G G G e

The Smith predictor has the advantage of eliminating the time delay from the characteristic equation. Unfortunately, this advantage is lost if the process model is inaccurate.

(It can still provide improvement if the model parameters are within about of the actual values)30%

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Closed-loop set-point responsesSmith predictor (SP) has the same controller settings with conventional feedback PI controller. ( )

• The responses are identical, except for the initial time delay.

SP ( )2

3.02cK 6.5 I

PI ( )0

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How about the disturbance response?

• The Smith predictor generally is beneficial for handling disturbance. However, under certain conditions, a conventional PI controller can provide better regulatory control than SP.

1 1

1

d* s

c

*c

G G G eYD G G

2

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• Problem: Controlled variable cannot be measured or has large sampling period.

• Possible solutions:1. Control a related variable (e.g., temperature instead

of composition).2. Inferential control: Control is based on an estimate

of the controlled variable.• The estimate is based on available measurements.

– Examples: empirical relation, neural network• Modern term: soft sensor

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Measured Variables

Soft sensor block diagram

( Note: X and/or Y can be used for control )

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Selective Control & Override Control

• For every controlled variable, it is very desirable that there be at least one manipulated variable.

• But for some applications,

NC > NMwhere:

NC = number of controlled variables

NM = number of manipulated variables

• Solution: Use a selective control system or an override.

C MN N

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• Low selector:

• High selector:

• Median selector:• The output, Z, is the median of an odd number of inputs

• Selectors are used to improve the control performance as well asto protect equipment from unsafe operating conditions.

Selectors

(useful when redundant sensors are used to measure a single process variable)

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• multiple measurements• one controller• one final control element

Example: High Selector Control System

Control of a reactor hotspot temperature

Determine the hotspot temperature

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Overrides• An override is a special case of a selective control system• One of the inputs is a numerical value, a limit.• Used when it is desirable to limit the value of a signal (e.g.,

a controller output).

Temperature control of a heater

for safety

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2 measurements, 2 controllers, 1 final control element

A selective control system to handle a sand/water slurry(regulate the level and exit flow rate)

Keep flow rate aboveits minimum valueFC

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Block Diagram for the Selective Control Loop

faster

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Split-Range Control• Multiple final control elements or multiple controllers

Reactor temperature control (both heating and cooling are used)