SoftMin

Gradual approach of a ceiling that cannot be exceeded

Diagram

Information

The output y is obtained by applying a factor in the interval [0,1] to the maximum output u_max (the ceiling). It effectively calculates a smooth minimum with regard to the inputs u and u_max:

The following graph shows the results for u_max = 1.0 and k ∈ {10,5,3,2}:

Graph for u_max = 1.0
Graph.svg

When the intended output u is a small fraction of the maximum output u_max (ceiling) the actual output y will be equal to the intended output. As u approaches the ceiling the limitations will have a gradual effect so that less than the intended output is returned. Eventually the output will be identical to the maximum value.

Notes

  • The basic structure matches the one given by Jim Hines [6, pp. 95-97] in that the ratio u : u_max is used as input to the smooth minimum; John Sterman [3, pp. 711-713] uses the ratio u_max : u instead.

  • The typical use case for this component is the determination of a production start rate given capacity restrictions. Since production will most often be treated as an aggregate process for many different variants of a basic product, the capacity restriction will likely be felt before the aggregate capacity limit is reached.

  • The soft minimum is a special case of the generalized f-mean.

See also

SoftMax

Parameters (4)

k

Value: 4.7

Type: Real

Description: Parameter to control the closeness to a hard minimum

useMinOperator

Value: false

Type: Boolean

Description: = true, if a regular 'hard' minimum is to be used

clipNegativeOutput

Value: true

Type: Boolean

Description: = true, if output can never be less than zero

strict

Value: true

Type: Boolean

Description: = true, if strict limits with noEvent(..) (clippedOutput.strict)

Connectors (3)

y

Type: RealOutput

u

Type: RealInput

Description: Input

u_max

Type: RealInput

Description: The ceiling

Components (13)

hardMin

Type: Min

Description: Hard min operator

clippedOutput

Type: ZeroIfNegative

unclippedOutput

Type: PassThrough

expMaxUtil

Type: Exp

scaledMaxUtil

Type: Gain

scaledInput

Type: Gain

expInput

Type: Exp

sumExp

Type: Add_2

logSum

Type: Log

adjustmentFactor

Type: Gain

softMin

Type: Product_2

maxUtilization

Type: ConstantConverter

Description: Maximum utilization

utilization

Type: Division_Guarded

Description: Fraction of the maximum

Revisions

  • Introduced in v2.0.0.