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Advanced Plant Automation Individual Assignment 2011/12

Ian Burton

EPS4

Contents

1. Introduction…………………………………………………………………………………………………………..2-2

2.

Volume Calculations………………………………………………………………………………………………3-7

2.1. Volume of vessel at any height…………………………………………………………………………..3

2.2. Volume of liquid below the lower limit………………………………………………………………5

2.3. Volume of liquid above the higher level…………………………………………………………….6

2.4. Volume of usable liquid………………………………………………………………………………….....7

2.5. Total mass of usable liquid……………………………………………………………………………......7

3. Linear Scaling……………………………………………………………………………………………………….8-11

3.1. Input analogue to digital converter…………………………………………………………………….8

3.2. Output digital to analogue meter……………………………………………………………………….8

3.3. Graphical linear scale…………………………………………………………………………………………9

3.4. Linear Scale Equation……………………………………………………………………………………….10

3.6. Height Factor……………………………………………………………………………………………………10

4. Programming……………………………………………………………………………………………………11-21

4.1. OB1………………………………………………………………………………………………………………….114.2. FC40…………………………………………………………………………………………………………………13

4.3. Vat-1………………………………………………………………………………………………………………..21

5. Testing……………………………………………………………………………………………………………….22-24

5.1. Program results………………………………………………………………………………………………..22

5.2. Calculated Results…………………………………………………………………………………………….23

6. Conclusion…………………………………………………………………………………………………………25-25

7. Appendix…………………………………………………………………………………………………………………26




Ian Burton

EPS4

1.Introduction

As part of the module for Advanced Plant Automation it is required for each student to

complete an individual assignment that involves all the learning outcomes covered in the

module during the semester.

The project that has to be completed involves creating a program using the Simatic software

by Siemens to represent the outlined process. The program to be designed will calculate the

volume of a certain liquid in the vessel shape given and the formula for the volume value

must be explained in full.

It may be assumed that the analogue to digital converter has a resolution of eight bits and

the sensor is calibrated to give 0 to 10 volts between the empty bottom of the vessel and

the top.As well as the volume calculation, the weight of the substance must be calculated

with the given density value. Once all calculations have been done the program must be

represented as a single function block that may be called in OB1.

To display that the program is functioning as it should, outputs will be used to show when

the vessel given is one third, two thirds and full.

The tank level must be displayed by means of a moving coil of 0 to 5V connected to the

analogue output. The 0V in this case will represent the specified low level of the vessel and

the 5V will represent the specified highest point of the vessel. It may be assumed that for

the digital to analogue meter that it has a resolution of twelve bits. Linear scaling will have

to be done to ensure the counts and volume ratios produce the required output.

The diagrams below show the vessel that the program has to be developed for.

3.25M

0.25M

L = 6M

B = 6M

A = 5M




Ian Burton

EPS4

2.VolumeCalculations

This chapter will cover all the calculations based around the volume of the vessel. These

calculations will be required to be done a function block may be created. It must be noted

that the counts coming in from the analogue to digital converter will be the height the

sensor is reading. The calculations will all be done in meters unless otherwise specified.

2.1. Volume of Vessel at Any Height

The shape of the vessel that the program must be created for is called a triangular prism.

The volume of the triangular prism whose length is “L” meters, and whose triangular cross

section has a base of “A” units and height of “H” units has a volume given by:

= 12 × × ×

To be able to use the equation shown above for the total volume of the triangular prism the

perpendicular height must be determined as this is the only unknown. This may be

completed as shown below.

The height may be calculated using the theorem of Pythagoras. By halving the length of “A”

the height “H” may be calculated as follows:

=

− 12

A = 5M

B = 6M

H




Ian Burton

EPS4

= 6 − 12 5

= 36 − 6.25

= 5.45435

Having the height calculated, the total volume of the triangular prism may be found but the

problem that has to be solved is that the equation stated above is for the total volume of

the triangular prism but if the height that is detected by the sensor changes frequently then

the basic equation will not do. This is due to the fact that the side named “A” will vary in

length depending on the height detected. Therefore a formula for the side “A” using the

height “H” at any time and a constant must be created to allow the volume to be calculated

at any height of liquid in the vessel. This calculation is performed below.

The angle θ shown in the diagram above will have to be determined as this will be constant

for any height “H”. The side “B” is given as 6m and the height “H” for the triangular prism

was calculated previously and thus the angle θ may be calculated using the right angled

triangle from the above diagram.

=

= 5.4546

= 5.4546

= 65.368° 1.14

A = 5M

B = 6M

H = 5.454M

θ




Ian Burton

EPS4

Now that the angle θ has been calculated a general formula for the length of “A” may be

determined so with any height the formula will give the volume of liquid in the triangular

prism. This calculation is detailed below and the calculation is done using the angle in

radians.

=

= 2 × tan (1.14)

The multiplication by two must be added to the equation because previously the triangle

was halved to make the right angled triangle needed to form the required values. Now all

the parameters required to generate a formula for the volume of the triangular prism have

been calculated and the finalised formula is shown below for any height detected by the

sensor.

= 12 × 2 ×

tan (1.14) × ×

The total volume of the triangular prism is shown below.

= 5.454tan (1.14) × 6 × 5.454

= 82.03

2.2. Volume of Liquid below the Lower Limit

This volume may be calculated using the volume formula derived previously for the

triangular prism but with the height value changed. The height of the complete vessel was

calculated to be 5.454m and the height of the lower limit is 0.25m. Knowing this the height

that must be added to the volume formula to calculate the lower limit volume will be the

total height subtracting the lower limit height. This volume will then have to be subtracted

from the total volume to produce the volume of the lower limit below the valve.




Ian Burton

EPS4

(r) = () − 12 × 2 × 5.204

tan (1.14) × 6 × 5.204

() = 82.03 − 74.68

() = 7.35

2.3. Volume of Liquid above the Higher Level

The volume of the triangular prism above the higher level may to be calculated using the

derived formula. Here the height will be the total height of the triangular prism subtracting

the height of the higher level as shown in the diagram below.

The volume of the triangular prism above the higher limit is calculated below.

(ℎℎ) = 12 × 2 × 2.204

tan (1.14) × 6 × 2.204

(ℎℎ) = 13.39

H = 5.454

H = 5.454-0.25

= 5.204m

Lower Limit

0.25m

H = 5.454-3.25

= 2.204m

High Limit = 0.25m




Ian Burton

EPS4

2.4. Volume of Usable Liquid

The volume of the total usable volume of liquid may now be calculated as follows:

= () − (ℎℎ) − ()

= 82.03 − 13.39 − 7.35

= 61.29

2.5. Total Mass of Usable Liquid

The total mass of the liquid in the triangular prism vessel is calculated just for the usable

volume amount. This is done by using the specified density ratings given in the project brief.

Material

Type Liquid

Name Liquid Argon

Density 1390 kg/m3

= () ×

= 61.29× 1390

= 85193.1




Ian Burton

EPS4

3. Linear Scaling

3.1. Input Analogue to Digital Converter

The analogue to digital converter used for this project is to be assumed to have a resolution

of 8 bits. The input counts have to be calculated for the total triangular prism and for the

higher level and lower level points of the vessel. This is detailed below:

= 2 − 1 = 255

= ×

ℎ

ℎ

= 255 × 3.255.454

= 151.95

= × ℎ ℎ

= 255 × 0.25

5.454

= 11.68

These calculated count values are for the input analogue to digital converter. The same

must be done for the calculation of the output resolution to be able to determine the

output representation of the level in the tank using the coil meter.

3.2. Output Digital to Analogue Meter

The digital to analogue meter used for the project is said to be assumed to have a resolution

of 12 bits. The output resolution calculation is calculated below.

= 2 − 1 = 4095




Ian Burton

EPS4

Using the output resolution calculated, this will represent the input resolution at the higher

level point and 0 will represent the input counts at the lower level of the triangular prism

vessel. This is explained more in depth in the graphical linear scale representation section.

3.3. Graphical Linear Scale

The Linear scaling graph shown above details the input counts against the output counts.

The next step is to derive the equation for this graph that will determine the output counts

in relation to input counts which can be converted to a volume figure.




Ian Burton

EPS4

3.4. Linear Scale Equation

= +

= − −

= 151.95 − 11.684095 − 0

= 0.0342

For the equation of the line shown above, the slope “m” is now known and the constant “C”

is the value where the line meets the Y axis which in this case is 11.68 counts. Therefore the

output counts value may be determined for any input counts. This is shown below.

For an input of 140 counts the output counts is:

= +

140 = 0.0342 + 11.68

= 3752.05

3.6. Height Factor

The height factor to be calculated will determine the number of counts that will represent

the height. This is done to allow the height to be determined at any count value and allow

further calculations to be made.

ℎ = ℎ

= 2555.454 = 46.7547

Slope Calculation:




Ian Burton

EPS4

4. Programming

The programme created in FC1, OB1 and the vat table are described step by step in this

chapter. The programme in FC1 uses all the formulas calculated previous in the report and

performs them in FC1. OB1 allows the inputs used by FC1 to be varied depending on the

dimensions of the vessel and produces outputs based on the calculations performed and the

input counts read by the PLC.

4.1. OB1

In the organization block OB1 the function FC40 has been created. This block allows allows

all the inputs to be varied depending on the dimensions of the triangular prism vessel used.

The outputs can be seen here when the PLC is running. The functon has been created so

that no matter what size the triangular prism used is the inputs may be changed and the

programme will perform all the required calculations. This is one of the benefits of this

programme design that it will facilitate and traingular prism dimensions of if the valve

height were to be changed.




Ian Burton

EPS4

Inputs

Height Counts: This is the counts that represent the height that the sensor reads.

Input Resolution: This is the resolution calculated for the input analogue to digital converter.

This may be changed if there was a different input resolution to be added.

Height of the Tank: This is the total height of the tank given in meters. This may be changed

if a vessel of different height were to be used.

Length of Side B: This is the length of the side labelled “B” on the project description. This

side of the vessel may be varied if a different vessel were to be used.

Length of Side L: This is the total length of the triangular prism vessel given in meters. This

may be varied for different vessel dimensions.

Upper Level Height: This is the height of the vessel specified in the project description that

is the highest limit for usable liquid. This value may be changed if a different height was

needed.

Lower Level Height: This is the lowest height of the vessel for usable liquid in the vessel. Any

liquid below this height is not usable. This value may be varied depending on the required

valve height.

Output Resolution: this is the calculated resolution for the output digital to analogue meter.

This resolution may be changed according to the output devices resolution.

Argon Density: This is the density of the liquid argon that is the liquid being used for this

particular project. This density may be changed depending on the material stored in the

tank.




Ian Burton

EPS4

Outputs

Total Volume of the Vessel: This is the total volume of the vessel calculated by the

developed program given in meters cubed.

Total Usable Volume: This is the calculated usable volume of the vessel given in meters

cubed.

Output Counts: This is the output counts given after scaling has taken place.

Density of Usable Liquid: This is the weight of the usable liquid once the volume has beendetermined. This value is given in kilograms.

4.2. FC40

The first process in the function FC1 is to convert the height counts that are read by the PLC

to a real number. This is done to allow all the calculation in the process to be performed.

The heights come in and moved to an integer. This this integer is converted to a double

integer. This double integer is then converted to a a real format.

Network two calculates the height factor as done in part 3.6. This height factor is calculated

by using the input resoultion and divides it by the height of the tank to produce the height

factor that will be used in equation further in the programme.




Ian Burton

EPS4

Network three calculates the angle that will be constant for the triangular prism shape. This

is done to allow the volume calculation for any size triangular prism vessel to be calculated.

First the height of the tank is divided by the length of the side labelled “B”. Then using this

output answer the next block calculates the inverse SIN of it which then produces the

constant angle. This calculation is done in part 2.1 of the report.

The height counts that were converted to a real number and dividing this by the height

factor calculated previous. This calculation ten produces the output height counts.

Network five calculates the height counts the sensor actually observes. This is due to the

sensor being above the tank and thus the output height counts calculated previously must

be subtracted from the total height of the vessel to produce the height the sensor

determines.




Ian Burton

EPS4

Network six is the beginning of the formula for the volume calculation. The first step is to

calculate the TAN of the constant angle calculated in network three. The first block in the

network does this and gives out the constant TAN of the angle. The next block divides the

height the sensor determines by the TAN of the constant angle to produce an answer that

will be multiplied by other factors in the next network.

Network seven uses the previous networks answer, multiplies it by the height the sensor

determines and then produces another answer. This answer is then multiplied by the length

of the vessel which is an input which may be changed depending on the size of the vessel

being used. These calculations produce the total volume above the liquid in the vessel as the

height is what the sensor determines which is the height of the volume above the liquid in

the tank.

Network eight calculates the total volume of the vessel without the volume above the liquid

in the tank. This is done by using the total volume of the tank calculated in the next network

and subtracting the volume above the liquid. This will produce the total volume minus the

volume above the liquid.

tan (1.14)

tan (1.14) × ×




Ian Burton

EPS4

Network nine calculates the maximum volume of the vessel. This is done by taking the full

height and dividing it by the TAN of the constant angle which produces an answer called a

factor. This factor is multiplied by the height of the tank then the length of the vessel to

produce the maximum volume of the vessel.

Network ten calculates the height the sensor reads that refers to the upper level height. This

is done by taking the total tank height and subtracting the upper level height which is a

constant input and produces the height to the upper level. Using this answer the same steps

are used in the previous networks to calculate the volume of the tank above the upper level

limit.

Network eleven finishes off the calculation of the volume above the upper level limit. The

output volume is the total volume subtracting the volume above the upper level height.




Ian Burton

EPS4

Network twelve is created to calculate the volume below the lower level height. This is done

by first subtracting the constant lower level height from the total height of the vessel. This

gives the height the sensor reads to the lower level height from the top of the tank. This

new height is used in the calculation of the volume as done in the previous two networks.

Network thirteen finishes off the calculation of the volume up to the lower level height. This

is done by subtracting the total volume above the lower limit from the total volume of the

vessel to give the total volume below the lower level limit.

Network fourteen calculates the total volume of usable liquid in the vessel. This is done by

subtracting the volume up to the lower level height from the volume up to the upper level

height which will produce the total volume of usable liquid for a triangular prism vessel.




Ian Burton

EPS4

Network fifteen calculates the total usable volume for any dimensioned triangular vessel.

This is done by using the volume of the vessel calculated earlier for the volume of the vessel

without the volume above the upper level height and subtracting the volume of the area of

below the lower level height of the vessel.

Network sixteen calculates the scaling of the output for the usable volume of the vessel. The

first block produces the volume of the usable liquid in the vessel. This is the divided by the

output resolution and then multiplied by the output resolution to produce the output value

of usable volume of liquid.

Network seventeen calculates the output counts for any input counts so that the volume of

the vessel may be acuratly scaled to produce the requied output for the input height counts.




Ian Burton

EPS4

Network 18 produces the output counts that will be shown in the outputs of OB1.

Network 19 begins the calculation for the weight of the liquid in the vessel. The first block

uses the constant input value of the density of argon and multiplies it by the usable volume

in the vessel to produce the maximum density of the usable volume. The next blocks and

network twenty scale the density for the weight of the usable liquid in the triangular vessel.

Network 21 uses a compare block to show when the volume of liquid in the tank is more

than one third full the output Q1.0 will come on to verify this. This is done by calculating one




Ian Burton

EPS4

third of the usable volume in the vessel and using the compare to determine if the volume is

greater than this value.

Network twenty two uses the same basis as the previous block but in this case the output

Q0.2 will light up when two thirds of the usable liquid is in the vessel.

Network twenty three determines when the volume of the useable liquid is full. The output

Q0.3 will light once the volume is filled.




Ian Burton

EPS4

4.3. VAT_1

The vat table shown above was created to allow the simulation of the programme to

happen. The input counts may be inserted manually to witness the results. In other words

VAT_1 simulates a PLC with the FC40 programme. This table was used to perform the tests

in the next chapter to verify the programme functions as outlined in the project brief.

The VAT-1 screen also shows when the outputs come on representing when the tank is at

various fill levels.




Ian Burton

EPS4

5. Testing

Testing of the created program has been done by using the program to determine the

outputs at empty, one third, two thirds and full levels. To determine are these values are

the required outputs calculations for the same input values has been done to compare the

values.

5.2. Program Results

The tables below show the outputs from the program with the specified fill limits.

Vessel EmptyInput Counts 12

Total Volume of Vessel 7.52 m3

Total Usable Volume 0.19 m3

Output Counts 12.7

Weight of Usable Liquid 264.87 kg

Vessel 1/3 FullInput Counts 58



Output Counts 1711



Total Volume of Vessel 53.51m3


Output Counts 3079





Ian Burton

EPS4

Vessel Full

Input Counts 152



Output Counts 4077


5.3. Calculated Results

The tables shown below are the calculated results found for the various fill levels.

Vessel Empty

Input Counts 11.68

Total Volume of Vessel 0 m3

Total Usable Volume 0 m3

Output Counts 0

Weight of Usable Liquid 0 kg

Vessel 1/3 Full

Input Counts 58



Output Counts 1365





Output Counts 2730





Ian Burton

EPS4

Vessel Full

Input Counts 151.95



Output Counts 4095





Ian Burton

EPS4

6. Conclusion

The program created for this project has been developed to cater for any tank that is a

triangular prism shape but it may be any dimensions. This is an advantage as the program

will cover a vast number of situations such as the lower level height of the valve changing

which means only the new value of height has to be inserted for this.

Upon first inspection of the completed program it was concluded the program functions as

required by the project brief and covers the requirement set out.

Testing of the program has shown that for all the various fill levels the outputs are what are

expected of the program. There are slight variations between the program outputs and the

calculated outputs and this is due to the way in which the program functions. There have

been decimal points left out in the program to allow it to function while in the hand

calculations there were no decimal points left out and thus there are very slight differences

which can be seen in the test tables in chapter five.

Understanding the project and what was required posed some bit of misunderstanding but

taking the time to think about what was required and how to set about getting the results

proved to be the most important part as a logical thinking approach was needed to have any

idea of concluding this project.

The project completes the project brief in all topics that were required to be done.




7.Appendix

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