Control System Instrumentation

Standard Instrument Signals

• Pneumatic (air pressure): 3 – 15 psig

• Electrical: 4 – 20 mA

• I/P or E/P transducer

• Figure 9.3 illustrates the general configuration of a measurement transducer; it typically consists of a sensing element combined with a driving element (transmitter).

• Since about 1960, electronic instrumentation has come into widespread use.

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Transducers and Transmitters

Sensors

The book briefly discusses commonly used sensors for the most important process variables. (See text.)

Transmitters

• A transmitter usually converts the sensor output to a signal level appropriate for input to a controller, such as 4 to 20 mA.

• Transmitters are generally designed to be direct acting.

• In addition, most commercial transmitters have an adjustable input range (or span).

• For example, a temperature transmitter might be adjusted so that the input range of a platinum resistance element (the sensor) is 50 to 150 °C.

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Range and Scale Factor

range 50 to 150

20 4scale factor 0.16 mA /

150 500.16m

C

C

G s

Transfer Function – Nonlinear Case

nominal

mm m

dTG s K

dT

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Measurement / Transmission Lags

• Temperature sensor

make as small as possible (location, materials for thermowell)

• Pneumatic transmission lines

usually pure time delay, measure experimentally (no time delays for electronic lines); less common today compared to electronic transmissions.

( ) 1

( ) 1m s s

mm s s

T s m C

T s s U A

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m

Transmitter/Controller

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May need additional transducers for Gm if its output is in mA or psi. In the above case, Gc is dimensionless (volts/volts).

Measurement Errors

• Systematic errors– Drift: slowly changing instrument output when

input is constant.– Nonlinearity– Hysteresis or backlash– Dead band– Dynamic error

• Random errors

Figure 9.15 Nonideal instrument behavior: (a) hysteresis, (b) dead band.

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Precision, Resolution, Accuracy and Repeatability

• Precision can be interpreted as the number of significant digits in measurement, but more accurately it refers to the least significant digit which contains valid information, e.g., 0.01 in the present case. Therefore, 0.33 is more precise than 0.3.

• Resolution is defined as the smallest change in the input that will result in a significant change in the transducer output.

• Repeatability is +/- 0.02 in the present case.• Accuracy is 0.39-0.25=0.14, i.e., maximum error.

Final Control Elements

• The most-common manipulated variables to be adjusted are: (1) energy flow rates, and (2) material flow rates.

• Type (1): transducer + heating element

• Type (2): transducer + control valve (pump drive, screw conveyer, blower, etc.)

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Control Valve Characteristics (Inherent)

Design equation for liquids

: flow rate, gpm

: valve coefficient, valve size

: valve lift, 0 1 (fraction open of the valve)

: pressure drop across valve

: specific gravity

vv

s

v v

v

s

Pq C f

g

q

C C

P

g

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1

(1) Quick Opening (square root trim)

(2) Linear Trim

(3) Equal Percentage

20-50

/Note that ln

f

f

f R

R

df dff R

d

1

ln constant

Note also that 0 0.05 inaccurate!

fR

d

f R

Pressure Drop Across Control Valve Installed On-Line

In practical applications, one must take other flow obstructions into account for actual valve performance.

Design Guideline

Since and

for ease of control high

for low cost low

1 1 to at design flow rate

3 4

s v

v

v

vd

P P P

P

P

Pq

P

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Design Calculation for a Linear Valve

pick 0.5

200127

0.5 10

select 4-in valve according to catalog

dv

v

s

qC

P

g

Rangeability (Turn-Down Ratio)

maximum controllable flow level flow at 95% lift

minimum controllable flow level flow at 5% lift

rangeability=19 for linear valves

rangeability=34 for equal-percentage valves (R=50)

rangeability=3 for q

uick-opening valves

Example

2

If the flow rate is reduced to 25% of the design level,

5030 1.9 (psi)

200

40 1.9 38.1 (psi)

500.06 (almost closed)

127 38.1

he

v

v

s

P

P

qf

PC

g

Installed Valve Characteristics

• Desired behavior: the flow rate is a linear function of valve lift.

• Let us assume that the control valve has linear trim and it is necessary to increase the flow rate. If p through exchanger did not change, then valve would behave linearly (true for low flow rates), since it takes most of p . For higher flow rates, p through exchanger will be important, changing effective valve characteristics (valve must open more than expected nonlinear behavior).

Linear Valve Behavior

2

2

0.52

0.52

0.5 200 gpm 127

30200

40 30200

127 40 30200

127

(calculated previously)

40 30200

d v

he

v

vv

s

q C

qP

qP

P qq C

g

q

q

Equal-Percentage Valve Characteristics

1

max

1 1 2

0.521

0.52

50 50

=1 1.1 1.1 200 220

220115

/ 50 40 30 1.1

115 50 40 30200

11 ln

ln 50 115 40 30 /

Assume

As

200

sume d

v

v s

R f

q q

qC

f P g

qq

q

q

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Control Valve Transfer Function

gpm gpmor

p

1

where

si %C

O

vv

v

v

t

KG s

s

qK

p

q

p