Trigonometric Functions - ABB SM2000 User Manual Supplement

...2 MATH CONFIGURATION
2.9 Standard Functions
The following examples, using preset functions available on the
Math Pad, are included for easier reference.

2.9.1 Trigonometric Functions

Three trigonometric functions, Sin(x), Cos(x) and Tan(x) return
the Sine, Cosine and tangent of the variable x.
Note. The variable x must be specified in Radians,
where 1° = π/180 Radians.
For example, to find the Sine of 90°, first convert
degrees to radians:
90° = (90 x π) / 180 = π/2 ≈ 1.571Radians
The equation is entered as Sin(1.571)
2.9.2 Statistical Functions – Table 2.5 & Fig. 2.5
Statistical functions can be used to calculate the average, rolling
average and standard deviation of an analog variable.
n I s a t n a t n e o u s A v g ) (
S a m p e l s A v e a r g e
N . o V a u l e V a u l e S a
–
1 4 0
–
2 8 0
3 7 0 –
–
4 5 0
5 6 0 6 0 1
6 3 0
7 4 0
8 1 0 0
9 1 2 0
1 0 1 1 0 8 0 6
Table 2.5 Sample Statistical Calculations
Average and
Rolling average
Samples 1 to 5
Rolling Rolling
average – average –
Samples Samples
°C
2 to 6 3 to 7
140
120
100
80
60
40
20
1 2 3 4 5
Sample number
Fig. 2.5 Samples Included
8
R A v ) ( S
R o l l n i g S a t
A v e a r g e D e i v
m p e l s V a u l e S a m p e l s
– – –
– – –
– – –
– – –
o t 5 6 0 1 o t 5 2
5 8 2 o t 6 1
5 0 3 o t 7 1
5 6 4 o t 8 1
7 0 5 o t 9 1
o t 1 0 8 0 6 o t 1 0 3
Average and
rolling average
Samples 6 to 10
Standard
Devation –
samples 6
to 10
6 7 8 9 10
2.9.3 Logarithmic Functions
The logarithmic functions Log(x), Ln(x) and e
scale process inputs.
– the output of vacuum gauges follow a logarithmic
Example
curve and this must be linearized, therefore the antilog of the
input must be derived :
Linear Vacuum = k.10(Vacuum Gauge Output)
2.9.4 Relative Humidity – Fig. 2.6
Relative humidity is calculated using the following formula:
RH = 100
Where
VPSw = Saturation Vapour Pressure at Wet Bulb
VPSd
D ) (
Td
n d a d r
t a o i n Tc
P
A
–
RH
–
–
A relative humidity calculation requires two inputs, one from a
–
wet bulb sensor and one from a dry bulb sensor. Both of these
0 8 . inputs are incorporated into the equation as analog.
8 3 .
RH tables are based on the use of an aspirated psychrometer
2 9 .
having an air velocity of at least 11.5 feet per second or 3.5
7 1 .
meters per second across the bulb sensors.
2 9 .
Inputs used for wet and dry bulb measurement must be in the
1 0 .
ranges 0 to 100ºC or 32 to 212ºF. The result must be set to 0 to
100.0% RH.
(VPSw – AP(Td – Tw)
VPSd
Temperature
= Saturation Vapour Pressure at Dry Bulb
Temperature
= Dry Bulb Temperature
= Wet Bulb Temperature
= Total Atmospheric Pressure (1000 mbar)
= Psychometric Constant (6.66 x 10
= % of Relative Humidity
x
can be used to
–4
)