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A smooth is an exponential information delay. It is typically used to model time lags in forming an expectation or in perceiving some information. A smooth of order n is modeled as a cascade of n first-order exponential smooth components, where the output of a preceding component is the input for its successor. The delay time for each smooth in the cascade will be delayTime/n.

Notes

• The delayTime given (either as constant parameter or continuous signal) will effectively be clipped to a minimum value of n × modelSettings.dt. The delay time for any first-order smooth in the cascade can thus never become smalle than dt, which denotes the minimum process time anywhere in the model.


• In the system dynamics community a smooth is an information delay (as opposed to a material delay) [1, Appendices E and H]. Information delays model the process of updating information to the actual value. Since the technical procedure is called exponential smoothing, the name smooth has prevailed.


• Mathematically a cascade of first-order exponential delays can be modeled as a convolution of exponential delays giving an Erlang distribution; see Sterman [3, pp. 462-476] for more details.


• The parameter init in the Advanced tab allows to select →InitializationOptions:
  
  • FixedValue (default) will use the parameter initialValue to determine the initial output y.
  
  
  • SteadyState will set the initial output y equal to the initial input u.
  
  
  • Free there will be no initial equation and thus the solver is free to find an initial output using initialValue as an initial guess.

See also

Smooth, AsymmetricSmoothN