DelayFixed

Pipeline information delay without awareness

Diagram

Information

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The real output y is the real input u delayed by a fixed delay time which can be constant (delayTime) or variable (u_delayTime) during the simulation.

y[t] = u[t - delayTime]

The input signal is thus effectively shifted forward in time.

During an initial period (at most as long as the initial delayTime or the maximumDelayTime when the delay time can vary over time), we need to provide information about the historical input u (e.g., the input before the start time of the simulation). The historical input can either be given by a constant value (either the initialValue or the initial input u) or by a function of time (usually a TableFunction), that will take the output connector y_lookupTime as input and then provide the relevant historical input via the input connector u_history.

Notes

The behavior for DelayInformation and DelayFixed are quite similiar, but there is a subtle difference:

The DelayInformation models the delay in perceiving information where the recipient is aware of the delay time and thus will disregard informatiion that is older than the one he already has.

In the case of a DelayFixed we will strictly delay any information given the actual delay time at any point in time and thus may receive information that is actually older than previous information when the delay time increases.

Since information is stored within the component, a rectangle is used for the component to be reminiscent of a stock.

The DelayFixed is an information delay, that is used to model delays in updating beliefs and perceptions; unlike a material delay matter is not conserved [20].

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.

Parameters (6)

delayTime	Value: 1 Type: Time (s) Description: Constant delay time (optional)
maximumDelayTime	Value: 50 Type: Time (s) Description: Maximal value allowed for delay time (needed for variable delay time)
initialValue	Value: 0 Type: Real Description: Initial constant output, if no exogenous history is given
hasConstantDelayTime	Value: true Type: Boolean Description: = true, if the delay time is given by the parameter 'delayTime'
hasExogenousHistory	Value: false Type: Boolean Description: = true, if the input 'u_history' gives the output for an initial period, otherwise the initial output will remain constant until delayTime is reached
init	Value: modelSettings.init Type: InitializationOptions Description: Provide InitializationOptions (Free, FixedValue, SteadyState)

Connectors (5)

	u	Type: RealInput Description: Input
	y	Type: RealOutput Description: Output signal
	u_history	Type: RealInput Description: Historical input to be used in an initial period (up to maximumDelaytime)
	y_lookupTime	Type: RealOutput Description: Time for looking up historical input
	u_delayTime	Type: RealInput Description: Delay time input

Components (13)

	modelSettings	Type: ModelSettings Description: Setting important global variables within a model
	historyHorizon	Type: Add_2 Description: The modelStartTime plus the actual delayTime
	parStartTime	Type: ConstantConverterTime Description: The model's start time
	parDelayTime	Type: ConstantConverterTime Description: Constant delay time (optional)
	parInitialOutput	Type: ConstantConverter Description: Initial output if not history is given
	clippedDelayTime	Type: Clip Description: DelayTime has to be in the interval (dt, maximumDelayTime)
	delayedInput	Type: VariableDelay Description: Delay block with variable DelayTime
	history	Type: PassThrough Description: Output is identical to input
	clock	Type: TimeInput Description: Provide time since start time (=0)
	historyNeededQ	Type: Less Description: Is historical trajectory needed for output?
	switchedOutput	Type: Switch Description: Either return historical value or delayed input
	delayedInputConstant	Type: FixedDelay Description: Delayed input with constant delay time
	lookupTime	Type: Gap Description: Time that needs to be looked up in historical input data