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

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

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)

• Introduced in v2.0.0.