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Enhanced Single-Loop Control Strategies

1. Cascade control

2. Time-delay compensation

3. Inferential control

4. Selective and override control

5. Nonlinear control6. Adaptive control

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Example: Cascade Control

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Cascade Control

Distinguishing features:

1. Two FB controllers but only a single control

valve (or other final control element).

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. primary

inner vs. outer

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1

2

1

2

1

2

= hot oil temperature

= fuel gas pressure

= cold oil temperature (or cold oil flow rate)

= supply pressure of gas fuel

= measured value of hot oil temperature

= measured value of fuel gas temm

m

Y

Y

D

D

Y

Y

1 1

2 2

perature

= set point for

= set point for

sp

sp

Y Y

Y Y

Chapter16

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 G

D G G G G G G G G G G

Y

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Example 16.1

Consider the block diagram in Fig. 16.4 with the following

transfer functions:

1 2

1 22 1

5 41

1 4 1 2 1

11 0.05 0.2

3 1

v p p

m md d

G G Gs s s

G G G Gs

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Example 16.2Compare the set-point responses for a second-order process with a time delay

(min) and without the delay. The transfer function is

Assume and time constants in minutes. Use the following PI

controllers. For min, while for min the controller

gain must be reduced to meet stability requirements

16 18( ) 5 1 3 1

s

p

e

G s s s

1m vG G

0, 13.02 6.5cK and 2 11.23, 7.0min .cK

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

1 16 20spE' Y Y

For this ideal case the controller responds to the error signal that would occur if not time

were present. Assuming there is not model error the inner loop has the effective

transfer function ,G G

16 21

1 * 1

cs

c

GPG

E G G e

'

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For no model error:

By contrast, for conventional feedback control

* - sG = G G e

1 1

1 1

cc * s

c

* sc c

* s *sp c c

GG

G G e

G G e G GY

Y G G e G G

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*

16 231 *

sc

ssp c

G G eY

Y G G e

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Inferential Control

Problem:Controlled variable cannot be measured or haslarge 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, Kalman filter

Modern term:soft sensor

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Inferential Control with Fast and Slow

Measured Variables

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Selective Control Systems & Overrides

For every controlled variable, it is very desirable thatthere be at least one manipulated variable.

But for some applications,

NC > NMwhere:

NC = number of controlled variables

NM

= number of manipulated variables

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Solution: Use aselective control systemor an override.

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Low selector:

High selector:

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Median selector:

The output, Z, is the median of an odd number of inputs

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multiple measurements

one controller

one final control element

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Example: High Selector Control System

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2 measurements, 2 controllers,

1 final control element

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Overrides

An overrideis a special case of a selective controlsystem

One of the inputs is a numerical value, a limit.

Used when it is desirable to limit the value of asignal (e.g., a controller output).

Override alternative for the sand/water slurryexample?

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Nonlinear Control Strategies

Most physical processes are nonlinear to some degree. Some are very

nonlinear.

Examples: pH, high purity distillation columns, chemical reactions

with large heats of reaction.

However, linear control strategies (e.g., PID) can be effective if:

1. The nonlinearities are rather mild.

or,

2. A highly nonlinear process usually operates over a narrow range of

conditions.

For very nonlinear strategies, a nonlinear control strategy can provide

significantly better control.

Two general classes of nonlinear control:1. Enhancements of conventional, linear, feedback control

2. Model-based control strategies

Reference: Henson & Seborg (Ed.), 1997 book.

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Enhancements of Conventional Feedback Control

We will consider three enhancements of conventional feedback control:

1. Nonlinear modifications of PID control

2. Nonlinear transformations of input or output variables

3. Controller parameter scheduling such asgain scheduling.

Nonlinear Modifications of PID Control:

0 (1 ( ) ) (16-26)c cK K a | e t | Chapt

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Kc0and a are constants, and e(t) is the error signal (e = ysp- y).

Also called, error squared controller.

Question: Why not use

Example: level control in surge vessels.

One Example: nonlinear controller gain

2 ( ) instead of ( ) ( )u e t u | e t | e t ?

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Nonlinear Transformations of Variables

Objective:Make the closed-loop system as linear as possible. (Why?)

Typical approach:transform an input or an output.

Example:logarithmic transformation of a product composition in a high

purity distillation column. (cf. McCabe-Thiele diagram)

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wherex*Ddenotes the transformed distillate composition.

Related approach:Define uoryto be combinations of several

variables, based on physical considerations.

Example: Continuous pH neutralization

CVs: pHand liquid level, h

MVs: acid and base flow rates, qAand qB

Conventional approach: single-loop controllers forpH and h.

Better approach: control pH by adjusting the ratio, qA/ qB, andcontrol hby adjusting their sum. Thus,

u1 = qA/ qB and u2 =qA/ qB

1(16-27)

1

* DD

Dsp

xx log

x

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Gain Scheduling

Objective:Make the closed-loop system as linear as possible.

Basic Idea:Adjust the controller gain based on current measurements of

a scheduling variable, e.g., u, y,or some other variable.

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Note: Requires knowledge about how the process gain changes with this

measured variable.

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Examples of Gain Scheduling

Example 1. Titration curve for a strong acid-strong base neutralization.

Example 2.Once through boiler

The open-loop step response are shown in Fig. 16.18 for two

different feedwater flow rates.

Fig. 16.18 Open-loop responses.

Proposed control strategy: Vary controller setting with w, the fraction of

full-scale (100%) flow.

(16-30)c c I I D D

K wK , / w, / w,

Compare with the IMC controller settings for Model H in Table 12.1:

1 2( ) , , ,1 2 2

2

s

c I D

c

KeG s K

s K

Model H :

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Adaptive Control

A general control strategy for control problems where the process or

operating conditions can change significantly and unpredictably.

Example:Catalyst decay, equipment fouling

Many different types of adaptive control strategies have been proposed.

Self-Tuning Control (STC):A very well-known strategy and probably the most widely used adaptive

control strategy.

Basic idea:STC is a model-based approach. As process conditions change,

update the model parameters by using least squares estimation and recent u&

ydata. Note:For predictable or measurable changes, use gain scheduling

instead of adaptive control

Reason: Gain scheduling is much easier to implement and less trouble

prone.

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Block Diagram for Self-Tuning Control