modelSoftMin

Gradual approach of a ceiling that cannot be exceeded

Extends from Interfaces.PartialConverters.SISO (Converter with single input and single output).

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`

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.

Parameters

Type	Name	Default	Description
Real	k	4.7	Parameter to control the closeness to a hard minimum
Structural Parameters
Boolean	useMinOperator	false	= true, if a regular 'hard' minimum is to be used
Boolean	clipNegativeOutput	true	= true, if output can never be less than zero
Advanced
Boolean	strict	true	= true, if strict limits with noEvent(..) (clippedOutput.strict)

Connectors

Type	Name	Default	Description
Connectors.RealInput	u (from SISO)		Input
Interfaces.Connectors.RealInput	u_max		The ceiling

Components

Type	Name	Default	Description
RealOutput	y (from SO)

Revisions

Introduced in v2.0.0.