Controller  Noise
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Related Links: Noise Class
NOTE this page is only valid for SysCAD 9.3 or later versions. For Help for SysCAD 9.2, see Controller  Noise (SysCAD 9.2)
Contents
General Description
 This unit operation is used to simulate process noise. It can be used to add disturbance to Feeders, pipe outlet capacity and other writeable variables.
 The Noise Control model is an orphan model, i.e it cannot be connected to any other unit operation.
 The noise model is for dynamic simulation only with the purpose of adding disturbance to the model.
Diagram
The diagram shows the default drawing of the Noise control unit.
Inputs and Outputs
There are no connections to this unit.
Model Theory
In SysCAD 9.3 Build 136 or earlier, the random number generator used for these probability functions is from Numerical Recipes in C.
In SysCAD 9.3 Build 137 or later, the random number generator used for all probability functions is from the C++ standard library (http://www.cplusplus.com/reference/random/).
The Probability Density functions used for the Noise generation are shown in the following headings. In all cases the following convention is used:
 [math]\mu[/math] = Mean Value
 [math]\sigma[/math] = Standard Deviation
Gaussian
The Probability Density Function P(t):
 [math] P(t) = \frac{1}{\sigma \sqrt{2π}}e^{\dfrac{(t\mu)^2}{2\sigma^2}} [/math]
 where [math] \sigma \gt 0 [/math]
Flat
The Probability Density Function P(t):
 [math] P(t) = 0 [/math]
 where [math]t \lt \mu  m[/math] or [math]t \gt \mu + m[/math]
 [math] P(t) = \frac{1}{2\sigma} [/math]
 where [math]\mu  m ≤ t ≤ \mu + m[/math] and [math] m ≥ 0 [/math]
 and [math] m [/math] = maximum deviation
Poisson
The Probability Density Function P(t):
 [math] P(t) = \frac{\mu^t}{t!}\ e^{\mu}[/math]
 where [math]e[/math] = the base of the natural logarithm system (2.71828...) and [math] \mu \gt 0 [/math]
Gamma
The Probability Density Function (P(t)):
 [math]P(t) = \frac{1}{\Gamma(\alpha)\ \beta^{\alpha}}\ t^{\alpha1}\ e^{t/\beta}[/math]
 where [math] \alpha ≥ 0.5 [/math] and [math] \beta \gt 0 [/math]
Note: The Chisquared distribution is a special case of the Gamma distribution with [math]\alpha = n/2 [/math] and [math] \beta = 2 [/math], where [math]n[/math] = degrees of freedom
Weibull
The Probability Density Function (P(t)):
 [math]P(t) = \alpha^{\beta}\ \beta\ t^{\beta1}\ e^{(t/\alpha)^\beta}[/math]
 where [math]t = \alpha (\ln(U))^{1/\beta}[/math] and [math] \alpha ≥ 0.04 [/math] and [math] \beta ≥ 0.01 [/math]
 [math]U[/math] is a randomly generated number between 0 and 1
Bernoulli
Only available in SysCAD 9.3 Build 137 or later.
The Probability Density Function (P(t)):
 [math]P(t) = p^{t}\ (1p)^{1t} [/math]
 where [math] 0 ≤ p ≤ 1 [/math]
Binomial
Only available in SysCAD 9.3 Build 137 or later.
The Probability Density Function (P(t)):
 [math]P(t) = \binom{n}{t} p^{t}\ (1p)^{nt} [/math]
 where [math]n[/math] is a positive integer, [math]\binom{n}{t} = \frac{n!}{t!(nt)!}[/math] and [math] 0 \lt p ≤ 1 [/math]
Geometric
Only available in SysCAD 9.3 Build 137 or later.
The Probability Density Function (P(t)):
 [math]P(t) = p\ (1p)^{t} [/math]
 where [math] 0 \lt p ≤ 1 [/math]
Exponential
Only available in SysCAD 9.3 Build 137 or later.
The Probability Density Function (P(t)):
 [math]P(t) = \mu\ e^{\mu\ t} [/math]
 where [math] \mu \gt 0 [/math]
Extreme Value
Only available in SysCAD 9.3 Build 137 or later.
The Probability Density Function (P(t)):
 [math]P(t) = \frac{1}{\beta}\ z(t)\ e^{z(t)} [/math]
 where [math]z(t) = e^{(\alphat)/\beta} [/math] and [math] \beta \gt 0 [/math]
Log Normal
Only available in SysCAD 9.3 Build 137 or later.
The Probability Density Function (P(t)):
 [math]P(t) = \frac{1}{s\ t\ \sqrt{2π}}\ e^{(\ln tm)^2/2s^2} [/math]
 where [math] 0 \lt s ≤ 50.70 [/math]
Cauchy
Only available in SysCAD 9.3 Build 137 or later.
The Probability Density Function (P(t)):
 [math]P(t) = \frac{1}{π\ \beta\ \left [1+\left (\frac{t\alpha}{\beta} \right )^2 \right ]} [/math]
 where [math] \beta \gt 0 [/math]
Fisher F
Only available in SysCAD 9.3 Build 137 or later.
The Probability Density Function (P(t)):
 [math]P(t) = \frac{Γ \left (\frac{m+n}{2} \right )}{Γ\left (\frac{m}{2}\right )\ Γ\left (\frac{n}{2}\right )}\ \frac{\left (\frac{m\ t}{n} \right )^{(m/2)}}{t\ \left (1+\frac{m\ t}{n} \right )^{(m+n)/2}} [/math]
 where [math] 1 ≤ m ≤ 100 [/math] and [math] n ≥ 1 [/math]
Student t
Only available in SysCAD 9.3 Build 137 or later.
The Probability Density Function (P(t)):
 [math]P(t) = \frac{1}{\sqrt{n\ π}}\ \frac{Γ\left (\frac{n+1}{2} \right )}{Γ\left (\frac{n}{2} \right )}\ \left (1+\frac{t^2}{n} \right )^{(n+1)/2} [/math]
 where [math] n ≥ 0.25 [/math]
References
 Press W.H, Teukolsky S.A, Vetterling W.T, Flannery B.P Numerical Recipes in C (2nd Edition) Cambridge University Press 1992.
 Sanders D.H Statistics A Fresh Approach McGrawHill 1990.
 http://www.cplusplus.com/reference/random/ and related links describing each distribution.
Data Sections
The default sections and variable names are described in detail in the following tables. The default Noise Controller access window consists of 2 sections. This number may increase or decrease, based on user configuration.
Summary of Data Sections
 NoiseCon tab  Contains a summary of all of the individual Noise Controls contained in the unit.
 NC Tabs tab  This page contains all of the information for each individual Noise Controls, starting at 1 for the first Noise Controls.
 Info tab  Contains general settings for the unit and allows the user to include documentation about the unit and create Hyperlinks to external documents.
NoiseCon
Unit Type: NoiseCon  The first tab page in the access window will have this name.
Tag / Symbol  Input/ Calc  Description 
Requirements  
On  Tick Box  The Overall Noise Control unit will be enabled or disabled using this box. This means that all of the independent Noise controllers in the unit will be disabled. 
The following message and field is visible when upgrading the project with existing noise controllers from SysCAD 9.2 (or earlier) to SysCAD 9.3. Change numbering to start from 1 instead of 0. NB this affects Tags.  
ChangeNumbering  Button  Update Numbering to Start from 1 instead of 0. Only visible if the noise controller was added in SysCAD 9.2 or earlier version. NB: this may affect external tag references such as reports, please adjust the external references appropriately if updating the controller numbering. 
ShowCnv  Tick Box  With this option selected, SysCAD will display engineering units for the Output tag. Note that these will only be displayed after SysCAD has completed at least one step. 
Count  Input  The number of independent Noise controllers required. This may be any number from 1 upwards. The user may also change this number at any time. The unit will always add new noise controllers after existing ones. User may delete individual Noise using the 'Delete Me' button under the individual noise controller blocks. 
FreqMethod  Each Step  The noise controller output value will be set every step. 
Steps Period  The frequency of setting the noise controller output value is based on steps.  
Time Period  The frequency of setting the noise controller output value is based on simulated time period.  
StepsPeriod  Input  Only visible only if FreqMethod is set to Steps Period. The number of steps which must pass before the noise controller output value is set. 
StepsOffSet  Input  Only visible only if FreqMethod is set to Steps Period. Number of steps delay before the first noise controller output value is set. 
StepsPassed  Display  Only visible only if FreqMethod is set to Steps Period. The number of steps that have passed since the last output value set. 
TimePeriod  Input  Only visible only if FreqMethod is set to Time Period. The amount of simulated time must pass before the noise controller output value is set. 
TimeOffSet  Input  Only visible only if FreqMethod is set to Time Period. Simulated time delay before the first noise controller output value is set. 
TimePassed  Display  Only visible only if FreqMethod is set to Time Period. The amount of simulated time that has passed since the last output value set. 
SetAtStartUp  Tick Box  With this option selected, the noise controller output value will be set during Startup step. 
SetTagAlways  Tick Box  Only visible only if FreqMethod is set to Steps Period or Time Period. With this option selected, the noise controller output value will be set every step. 
Check Tags  Button  SysCAD will perform a check on the validity of the tags and functions used in the noise controllers. 
Summary shows a summary table with the following values for each individual noise controller in the unit.  
NC  Display  The Noise Controller number 
Action  On  The random number generator is on and the controller will be setting the output tag at the specified frequency. 
Off  The random number generator is off and the controller will NOT be setting the output tag.  
Manual (User)  The random number generator is off but the controller will be setting the output tag to the User value (ManualOutput) at the specified frequency.  
Manual (Mean)  The random number generator is off but the controller will be setting the output tag to the mean value at the specified frequency.  
Output  Display  The output value for the individual Noise Controller. 
DevFrac  Display  The deviation fraction, when compared with mean value; for each individual Noise Controller. 
OutputUnitTag  Display  The output tag for each individual Noise Controller. 
NC1: Individual Noise Controller Data Fields
Noise Controller is displayed on the NCx pages. Each page displays four Noise Controllers.
Tag / Symbol  Input/ Calc  Description 
Cfg.[NC number]  
Action  On  The random number generator is on and the controller will be setting the output tag at the specified frequency. 
Off  The random number generator is off and the controller will NOT be setting the output tag.  
Manual (User)  The random number generator is off but the controller will be setting the output tag to the User value (ManualOutput) at the specified frequency.  
Manual (Mean)  The random number generator is off but the controller will be setting the output tag to the mean value at the specified frequency.  
Name  Input  The user may give the Noise Controller a name that describes the control, such Feed_Variation. 
Type  Gaussian  Distribution method as described in the Model Theory above. 68.27% of the numbers generated will be between (Mean  StdDev) and (Mean + StdDev). 
Flat  Distribution method as described in the Model Theory above.  
Poisson  Distribution method as described in the Model Theory above.  
Gamma  Distribution method as described in the Model Theory above.  
Weibull  Distribution method as described in the Model Theory above.  
Bernoulli  Distribution method as described in the Model Theory above.  
Binomial  Distribution method as described in the Model Theory above.  
Geometric  Distribution method as described in the Model Theory above.  
Exponential  Distribution method as described in the Model Theory above.  
ExtremeValue  Distribution method as described in the Model Theory above.  
LogNormal  Distribution method as described in the Model Theory above.  
Cauchy  Distribution method as described in the Model Theory above.  
Fisher_F  Distribution method as described in the Model Theory above.  
Student_t  Distribution method as described in the Model Theory above.  
ManualOutput  Value  Only visible when Action is set to Manual (User). The output tag will be set to this value instead of a randomly generated number. 
StdDevInput  Only visible if Type = Gaussian or Flat  
Value  The user specifies the Standard Deviation value.  
Fraction  The user specifies the Standard Deviation as a fraction of the Mean value.  
Mean  Input  Only visible if Type = Gaussian, Flat, Poisson or Exponential. The mean value around which the random number must be generated. 
StdDev  Input/Calc  Only visible if Type = Gaussian. The standard deviation around the mean value. 
StdDevFrac  Input/Calc  Only visible if Type = Gaussian. The standard deviation expressed as a fraction of the mean value. 
MaxDev  Input/Calc  Only visible if Type = Flat. The maximum deviation around the mean value. 
MaxDevFrac  Input/Calc  Only visible if Type = Flat. The maximum deviation expressed as a fraction of the mean value. 
Alpha  Input  Only visible if Type = Gamma, Weibull, ExtremeValue or Cauchy. The alpha parameter as described in the Model Theory above. 
Beta  Input  Only visible if Type = Gamma, Weibull, ExtremeValue or Cauchy. The beta parameter as described in the Model Theory above. 
n  Input  Only visible if Type = Binomial, Fisher_F or Student_t. The n parameter as described in the Model Theory above. 
p  Input  Only visible if Type = Bernoulli, Binomial or Geometric. The probability (of success) parameter as described in the Model Theory above. 
m  Input  Only visible if Type = LogNormal or Fisher_F. The m parameter as described in the Model Theory above. 
s  Input  Only visible if Type = LogNormal. The s parameter as described in the Model Theory above. 
OutputTag  Input  This is the Tag that will be set. This tag must be copied from the relevant unit. For example: Plant_Feed.QmReqd (t/h), Feed_Water.T_Reqd (C) or P_001.Qm_Capacity (kg/h). Note 1: Only input data fields (i.e. white) can be used here. Note 2: This field is optional. 
OutputUnitTag  Display  The Unit Operation Tag. For example: If the Output Tag is Plant_Feed.QmReqd (t/h), then the OutputUnitTag is Plant_Feed. 
OutputValue / Output  Calc  The output value. 
Dev  Calc  The deviation value: (output  mean). 
DevFrac  Calc  The deviation fraction: (output  mean)/mean. 
Delete  Button  This allows the user to Delete the current individual noise controller. Please note that there is no 'Undo'! 
MoveUp  Button  This allows the user to increase the Priority of the current individual noise controller. For example, if the current noise controller is number 3, the user can change it to 2 or 1 by clicking on this button once or twice. 
MoveDown  Button  This allows the user to decrease the Priority of the current individual noise controller. For example, if there are 3 noise controller in the unit and the current noise controller is number 1, the user can change it to 2 or 3 by clicking on this button once or twice. 
Adding this Model to a Project
Insert into Configuration file
Sort either by DLL or Group.

DLL: 
ControlDyn.dll 
→ 
Units/Links 
→ 
Control 2: Noise 
or 
Group: 
General 
→ 
Units/Links 
→ 
Control 2: Noise 
See Project Configuration for more information on adding models to the configuration file.
Insert into Project

Insert Unit 
→ 
Control 2 
→ 
Noise 
See Insert Unit for general information on inserting units.