Practical Use of Straight line Theory

1
Practical Use of Straight line Theory

• Prepared by
• Bernie Lafferty Bsc(Hons) GIMA Mathematical
  Sciences

2
Typical Reservoir Site
The Industrial standard output for an
Instruments low - high range is 4mA - 20 mA DC
(Direct Current )
An ultrasonic level probe measures the level of
the reservoir and displays it on an instrument
panel at site. ( Range typically 0 - 5 metres )
Valid range for instrument
3
Interface to Telemetry
Telemetry Unit Conversion
The Industrial standard output is 4mA - 20 mA DC
4mA
20mA
819
4095
lt 819 means bad value instrument fault
The output from the Instrument (4mA-20mA DC) is
fed into the Telemetry Unit and then converted
using Analogue to Digital conversion into a count
value between 0 - 4095.
Valid Instrument Range 4mA-20mA
Bad value Instrument Faulty !
Fixed for all analogues no matter the Instrument
scaling
4
Scanner Radio Communications
The Count value ( between 0 - 4095 ) which
represents the DC current value ( 0 - 20 mA )
which in turn represents the value on
the instrument at site is then transmitted to
Scottish Water Control Centre.
Communications types are

• Satellite
• Scanning Radio
• Private Wire (BT)
• PSTN (dial-up BT)

0 - 4095
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Scottish Water Control Centre
The count value (between 0 - 4095) is received at
Master Station at the Water Control Centre and
using Digital to Analogue conversion is
converted back into the original analogue value
and then displayed on computer screens.
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Summary of Process
Mathematics Summary
Instrument Conversion
Standard Telemetry Conversion
Master Station Conversion
half scale
Fixed graph for all analogues
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Overview Multi-Analogues
Instrument
Control Centre
Telemetry Outstation
Range 0- 5 m
Range 0- 5 m
Level meter
Computer Screen
PH meter
0 - 14 PH
0 - 14 PH
Probes
4mA-20mA
Value between 0-4095
Flow meter
4mA-20mA
Value between 0-4095
0 - 100 l/s
0 - 100 l/s
4mA-20mA
Value between 0-4095
l/s litres per second m metres
Graph 2
Graph 1
Graph 3
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Mathematical Overview
Level meter
PH meter
Flow meter
Range 0- 5 m
Range 0 - 100 l/s
Range 0 - 14 PH
Typical value on Instrument
3.75
7
25
Graph 1 / equation 1
y0.0032x 0.04
y0.001143x 0.04
y0.00016x 0.04
y16mA
y12mA
y8mA
DC current value on Graph
y0.0000048842x
y0.0000048842x
y0.0000048842x
Graph 2 / equation 2
y3276
y2457
y1638
Count value on Graph
Graph 3 / equation 3
y0.001526x - 1.25
y0.004274x - 3.5
y0.031x - 25
y3.75
y7
y25
Analogue value on Graph

• Notes
• Gradients are less than 1 ( this will stop
  errors being compounded )
• Equation 2 is FIXED no matter the instrument
  scaling due to the
• Industrial Standard Output for instruments (
  4mA-20mA )

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Graphical Example
Level meter Range 0 - 5 m present value 3.75
Value on Computer Screen
3.75 m