Date: 120123
M atem atica
Matematica/Abstracts
Translation of scientific
knowledge from
text/mathematics to (computer)
code without any compromises
according;
flow,energy,thermodynamics.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
1
Date: 120123
Matematica/customers
AGA; Measurement of gasflows
(O2, N2, GNG…).
Söderenergi; Calculation of energy
production in powerplants.
Siemens; Design of flow meters
and calculations.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
2
Date: 120123
Matematica/History
Founded >25 years ago by Stefan
Rudbäck, civ ing (m Sc).
First customers;Johnson mek
verkstads AB , production of
standard flowmeters (ex orifice
plates), and AGA (gas production).
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
3
Date: 110506
2.1 Matematica Ex 1
Natural/Bio Gas flow calculation
system with <0.7% unc (of actual
flow) with Matematica.Lib hp tech.
(or 0.4% with Matematica.Lib dpns
tech).
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
4
Matematica dpns tech
total system unc<0.4%
Matematica hp tech
sys unc<0.7%
Fig showing
Real unc of installed
natural gas flow meters
in Sverige compared
with matematica
hp and dpns tech
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
5
1. Complete Matematica hp system for natural gas in Nynäshamn
Gas Chromatograph, GC
kg/h
kg
MW
MWh
T
P
dp
Gas flow
Tube
Orifice plate
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
6
1.2 Software/Matematica high prec system for natural gas
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
7
Matematica/Ex_2
Steam
Matematica dpns tech
total system unc<0.4%
Matematica hp tech
sys unc<0.7%
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
Fig;Shows real
error of installed
steam flow meters
in Sweden compared
with Matematica
hp and dpns tech
8
Difference btw different flow calculation
methods for an application
gasexpansion
flow=k1*sqrt(dp)
flow=k2*sqrt(dp)
flow=matematica algorim*k2*sqrt(dp)
Sharp (laminar) flow profile
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
9
Date: 120123
M atem atica
Matematica/Example_2
If You want the massflow in a system with a
magnetic volume-flowmeter You have to do the
following calculation;
flow(kg/h)=flow(m3/h)*density(kg/m3).
Simplified first order code often calculates
density linear as a function of temperature. This
can lead to an error of several %!
Matematica Lib calculates density with 0.01%
uncertainty including pressure
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
10
Date: 120123
How can this be realized?
In 3 steps;
1. The knowledge/math is ”on the shelf”.
2. Computers like PC/control system are
also ”on the shelf”.
3. The knowledge/math are moved from
the bookshelf to the computers without
compromises.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
11
Date: 120123
Why? Because calculation
errors often result in;
1. Waste.
2. Poor quality.
3. The production cannot be
developed in an optimal way.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
12
Date: 120123
How?
With software from Matematica
for
1.the desk/Processline and
2.the production line/
Matematica_Lib with or
without hard/soft package
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
13
Date: 120123
1.Processline
The software which makes new
software/function blocks for control
systems. Processline is the tool you need
to design your production site as good as
possible at your desk.
Output from Processline as
standardized code will save time and
errors for You.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
14
copyright (c) 2011 Stefan Rudbäck,
Processline
example
Matematica,+46
708387910, of MMI/Steam
15
copyright (c) 2011 Stefan Rudbäck,
Processline
example of MMI/
Matematica,+46 708387910,
16
Date: 120123
Ex; With Processline You can:
1.Identify flow calculation errors.
2.Eliminate the errors with better code.
3.Automatic generate the code with a click on
Processline Kodfabriken/Bigblock Tag
4.Build a ”blindtarm” (dead end) that works
side by side with the old code (if any).
5.Put the new code to work when it’s proven
stable.
Point 1-5 can reduce calculation errors from
sometimes >10 to < 0.01%.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
17
Input area
spec of flowmeter
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
18
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
19
Generate standardized code with a click
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
20
Date: 120123 3.Generate standardized control system code with
Processline/kodfabriken/Bigblock, exemple GNG.
KODFABRIKEN/Bigblock;Production of standardized
control system code, IEC61131.
1.Calculation error<=0,0% of calculated flow
q_pol_mat_PT
For;10224 <q_pol_mat_PT< 102242
2280,00 <P(kPaA)< 4640,00
30,0000 <T(C)< 40,0000
Scaling; 20 mA from dp-cell= 18.9786 kPa= 20 mA
to control system
Copyright (c) 2009 Matematica,
mail@matematica.se, +46-(0)708-387910
Here follows parameters (In/Out), varibles
(internal) and code for ABB Industrial IT
for ex ControlBuilder
och AC800M.
copyright (c) 2011 Stefan Rudbäck,
21
Matematica,+46 708387910,
Date: 120123 3.Generate standardized control system code with
Processline/kodfabriken/Bigblock, exemple GNG.
Ex; Create a function block flow and then copy
in 3 steps 1.parameters, 2.variables and 3.code
from the report area of Processline with Ctrl-C
and paste it into the ABB function block flow
(mode structured text) with Ctrl-V
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
22
Date: 120123 3.Generate standardized control system code with
Processline/kodfabriken/Bigblock, exemple GNG.
2.Parameters (in and out signals);
P
real
in
22.8000
BarA
T
real
in
40.0000
C
density
real
out
kg/m3
dpcell
real
in
kPa,=signal from
dp-cell, linear or square root calculated
dp_max
real
in
18.9786
kPa=20 mA
dp_rot
bool
in
0
0=linear/1=square
root calculating dp-cell
q_pol_mat_PT
real
out
kg/h,PT
compensated & matematica algorithm calculated
flow,use this signal
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
23
Date: 120123 3.Generate standardized control system code with
Processline/kodfabriken/Bigblock, exemple GNG.
3.Variables (internal signals);
q_pol_mat
real
q_rot_mat
real
fmat
dp
real
real
fdens_mat
kvot
real
PkPa
real
Tmax
real
Tmin
real
Pmax
real
Pmin
real
kompminmax
kompmaxmax
kompminmin
kompmaxmin
kg/h,matematica algorithm
calculated flow, not to be used
kg/h,square root calculated
flow, not to be used
kPa,=calc dp = dpcell at
linear dp-cell
real
real
real
real
real
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
24
Date: 120123 3.Generate standardized control system code with
Processline/kodfabriken/Bigblock, exemple GNG.
4.Code as structured text ST
*)
kompminmin:=1.0;
kompmaxmin:=1.0;
kompminmax:=1.0;
kompmaxmax:=1.0;
PkPa:=P*100.000;
Tmax:=40.0000;
Tmin:=30.0000;
Pmax:=4640.00;
Pmin:=2280.00;
kompminmax:=1.00281;
kompmaxmax:=1.00273;
kompminmin:=0.99747;
kompmaxmin:=0.99730;
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
25
Date: 120123 3.Generate standardized control system code with
Processline/kodfabriken/Bigblock, exemple GNG.
kvot:=(kompminmin*(Tmax-T)*(PmaxPkPa)+kompmaxmin*(T-Tmin)*(PmaxPkPa)+kompminmax*(Tmax-T)*(PkPa-Pmin)
+kompmaxmax*(T-Tmin)*(PkPa-Pmin))
/(Tmax-Tmin)/(Pmax-Pmin);
fdens_mat:=sqrt(PkPa/3460.00*308.150/(T+273.15)*kvot*1.546346);
dp:=dpcell;
if dp_rot then
dp:=dpcell*dpcell/dp_max/dp_max*dp_max;
end_if;
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
26
Date: 120123 3.Generate standardized control system code with
Processline/kodfabriken/Bigblock, exemple GNG.
q_rot_mat:=23469.2*Sqrt(dp);
fmat:=(1-0.34445E12*expt(q_rot_mat,2)*2280.00/(P*100.000))/0.99640
*(1+5.64794/expt(q_rot_mat,0.75))/1.00099;
q_pol_mat:=q_rot_mat*fmat;
q_pol_mat_PT:=q_pol_mat*fdens_mat;
density:=PkPa/3460.00*308.150/(T+273.15)*kvot*28.8451;
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
27
4. Build a ”blindtarm” ”dead end” to be
debugged or compared with old code (if exists).
After 1 week/month/year put the new code
into action!
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
28
Date: 120123
2.1 Matematica.Lib.
The function library that uses
scientific state of the art knowledge
without compromises.
Ex: Stem Power/energy calculation
with Matematica.Lib can reduce the
calc error from typical 5% to<0.3%
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
29
Power/energy calc with
Matematica.Lib
general function blocks
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
30
Part_1
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
31
Part_2
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
32
Date: 120123
2.2 Matematica.Lib.
Double precision non stop technology.
Specify your demands for;
Production reliability
and
Production precision
and Matematica will meet those demands
(Ex; see below)
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
33
Date: 120123
Ex 1; Detection and elimination of flow profile errors from
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
34
tion factor for
r flow=0,77889
Date: 120123
gnal from
Double precision non
technology.
eter=100
ted flow=77,889
Ex 1; Dp1dim_fpdc_
1. Detects and corre
rection factor for
flow profile changes
ated flow
laminar-transient-tu
without any addition
ction factor for
error
lent flow=1,0062
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
35
Simplified Graphics showing flow profile uncertainty in the transient area
100 % turbulent flow profile
Transient area
=both turbulent
and laminar flow
possible
Double precision non stop technology.
Ex 1; Dp1dim_fpdc_flow.
1. Detects and corrects
flow profile changes;
laminar-transient-turbulent
without any additional
error
100 %
2000
laminar flow profile
10000
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
Reynolds number
36
Simplified Graphics showing flowsignal from US-Mag
with and without correction
US/Mag flow signal with Dp1dim_fpdc_flow Calibrated flow
signal
Transient area
US/Mag
=both turbulent
flow signal
and laminar flow
without
possible
Matematica
Unknown
flow signal
Double precision non stop technology.
Reynolds
number
10000
Dp1dim_fpdc_flow function block
eliminates flow signal errors from
1 dim flowmeters calibrated for 1
Reynolds number ex 100000.
Reynolds
number
2000
Real flow
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
37
Double precision non stop technology.
Horrible downsizing with additional costs
and errors not necessary any more
Tube
Mag/US
Tube
Mag/US
with Matematica
dpns software
FORGET THIS HORRIBLE INSTALLATION
NEW INSTALLATION
with
Matematica
with
Matematica
Dp1dim_fpdc_flow
software
Tube
Dp1dim_fpdc_flow
software
=no additional costs
and errors
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
38
Double precision non stop technology.
Ex 2; Dpns statistical calc of best possible value
Meausure of 4 temps in a tube
Failure of transmitter 4 = no problem
(compare with simple calc (1+2+3+10)/4=4>>2.146)
T_avg
Signal
unlikely
value
T1 T2 T3
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
39
T4
Let T4_stat_proc_value control the wheight factor wf4
(T4_proc=wf4*T4_stat_proc and so on for 1,2,3)
=(1+2+3)/3
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
40
Matematica.Lib.dpns block under normal conditions
T_avg
T1 T2 T3 T4
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
41
Example; Improvement of a Power/energy calc system with
Matematica.Lib function blocks double precision non stop (dpns)
and flow profile block dp_flow.
TF1
TF2
TF3
TF4
TR1
TR2
TR3
TR4
Matematica.Lib
dpns
Forward temp
Power/energy
Matematica.Lib
Power/energy
calculation system
(see page 28-30)
dpns
Return temp
q1
q2
Dp1dim_fpdc_flow
q3
q4
Dp1dim_fpdc_flow
Dp1dim_fpdc_flow
dpns
Return flow
double
precision
non stop
technology
Dp1dim_fpdc_flow
and more/less transmitters
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
42
With Matematica
double precision non stop technology
the following is possible;
-The measurement uncertainty can be reduced to a limit defined by the user
(to a certain limit).
-The reliability can be improved to a limit defined by the user.
(transmitter failure will be non-stop handled by the system)
-Transmitters can be simplified.
It’s often better with multiple simple (cheap) transmitters than 1 advanced
(expensive). Failures will be non-stop handled.
-Safety system operating parallell with the production system can be
eliminated. Failures will be non-stop handled.
-Real transmitter errors will be calculated.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
43
Exemple of Matematica.Lib funktion blocks
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
44
Example of
Matematica.Lib
function blocks
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
45
Matematica.Lib
in list form
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
46
Matematica.Lib
in list form 2
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
47
Matematica.Lib steam MMI
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
48
Matematica high precision calculation system for GNG flow in a pipe. Output kg
Measured values from transmitters
temp
dp
pressure
Gas
comp
from GC
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
49
Matematica high precision measurement and calculation system for GNG. System
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
50
Matematica:Lib Natural Gas GNG
density calculation
Code based on ISO 12213 <0.1% uncerta
>1400 statements of code in GNGdens fu
block Siemens PCS 7 /ABB CB
General and precise
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
51
Matematica:Lib Naturgas GNG flow calculation
Code based on ISO 5167 = 0.5% uncertainty >4
statements of code in ISO_5167 function block
(orifice plates, venturis and nozzles)
Siemens PCS 7/ABB CB
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
52
Matematica:Lib
Naturgas GNG totalization of power to
energy with function block Totalizer_3 .
Code developed by Matematica with 84 digits
without underflow.
May summarize in 100 years with 1 ms sampling
<0.0001% underflow.
Totalizer_3 function block appr. 800 statements of
code Siemens PCS 7/ABB CB
General copyright
and precise
(c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
53
Date: 120123
Matematica
How can Your organisation and
Matematica cooperate
in the future?
There are (at least)
4 possibilities;
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
54
Date: 120123
Matematica-Your organisation
coop 1.
Start point; Consult basis.
Matematica
designes/calculates/generates
control system code with
Processline.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
55
Date: 120123
Matematica-Your organisation
coop 2.
Developed coop;
Licens agreement for
Processline.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
56
Date: 120123
Matematica-Your organisation
coop 3.
Developed coop;
Simulation licens
(Windows) for
Matematica.Lib.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
57
Date: 120123
Matematica-Your organisation
coop 4. Developed coop;
Simulation and onlinelicense (Windows and
Siemens/ABB) for
Matematica.Lib.
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
58
Date: 120123
At last;
I hope some of my soft or hard
packages can help Your organisation to
better business in the future. Do not
hesitate to contact me for a discussion
of the first step in a future cooperation.
Regards
Stefan Rudbäck, Man dir, civ ing, M Sc
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
59
Contact;
Matematica
Stefan Rudbäck, civ ing
mail@matematica.se
www.matematica.se
+46(0)708387910
skype; stefan.rudback
copyright (c) 2011 Stefan Rudbäck,
Matematica,+46 708387910,
60