SShapedPositive

Symmettric S-shaped curve with positive slope around origin (0,0)

Diagram

Information

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The SShapedPositive lookup-function is a point symmetric, s-shaped growth function with respect to the origin (0,0) that has a positive slope. The curve has two parameters: An upperBound (lowerBound = -upperBound) and a slope s which is given as a positive number.

The output y is obtained by the following formula:

y = upperBound * (s^u - 1)/(s^u +1)

Graph of the Lookup-Function for Different Slopes (`upperBound` = 1)

Parameters (6)

convertInput	Value: false Type: Boolean Description: = true, if the input value is a rate or time variable that needs to be converted
inputIsRate	Value: false Type: Boolean Description: = true, if the input is given in units of time, otherwise it is assumed to be a rate
convertOutput	Value: false Type: Boolean Description: = true, if the output value is a rate or time variable that needs to be converted
outputIsRate	Value: false Type: Boolean Description: = true, if the output is given in units of time, otherwise it is assumed to be a rate
upperBound	Value: 1 Type: Real Description: Upper asymptote (upperBound > 0)
s	Value: 2 Type: Real Description: Slope controls gradient of curve (s > 1)

Connectors (4)

	y	Type: RealOutput Description: Output signal
	u	Type: RealInput Description: Input
	u_c	Type: RealOutput Description: Input after conversion
	y_c	Type: RealOutput Description: Output before conversion

Components (7)

	modelSettings	Type: ModelSettings Description: Setting important global variables within a model
	rateConversionIn	Type: RateConversion Description: Convert the input (rate) to another time base
	noConversionIn	Type: PassThrough Description: Use input as is
	timeConversionIn	Type: TimeConversion Description: Convert the input to another time base
	noConversionOut	Type: PassThrough Description: Use output as is
	rateConversionOut	Type: RateConversion Description: Convert the output (rate) to 1/s
	timeConversionOut	Type: TimeConversion Description: Convert the output to seconds