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Models with Time Delays

Systems with input, output, transport, and internal delays

Use the InputDelay, OutputDelay, and ioDelay properties of dynamic system models to represent time delays. See Time Delays in Linear Systems.


padePadé approximation of model with time delays
absorbDelayReplace time delays by poles at z = 0 or phase shift
thiranGenerate fractional delay filter based on Thiran approximation
hasdelayTrue for linear model with time delays
hasInternalDelayDetermine if model has internal delays
totaldelayTotal combined I/O delays for LTI model
delayssCreate state-space models with delayed inputs, outputs, and states
setDelayModelConstruct state-space model with internal delays
getDelayModelState-space representation of internal delays


Time-Delay Basics

Specifying Time Delays

This example shows how the Control System Toolbox™ lets you represent, manipulate, and analyze any LTI model with a finite number of delays.

Model Time Delays

Time Delays in Linear Systems

Represent input and output delays, transport delays, or internal delays in dynamic system models.

Closing Feedback Loops with Time Delays

Interconnecting models that have time delays can give rise to internal delays.

Internal Delays

Internal delays can model feedback loops with delays.

Convert Time Delay in Discrete-Time Model to Factors of 1/z

Incorporate input, output, or transport delays as factors of 1/z in a discrete-time model.

Frequency Response Data (FRD) Model with Time Delay

Absorbing time delays into frequency response data can cause undesirable phase wrapping at high frequencies.

Approximate Time Delays

Time-Delay Approximation

Approximate time delays with all-pass filters for control-design techniques that cannot handle time delays directly.

Time-Delay Approximation in Continuous-Time Open-Loop Model

Use the Padé approximation to approximate time delays in continuous-time models.

Time-Delay Approximation in Continuous-Time Closed-Loop Model

Approximate delays in a continuous-time closed-loop system with internal delays.

Approximate Different Delays with Different Approximation Orders

You can use different approximation orders to model different types of delays, such as internal and output delays.