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.

Functions

`pade`	Padé approximation of models with time delay
`absorbDelay`	Replace time delays by poles at z = 0 or phase shift
`thiran`	Generate fractional delay filter based on Thiran approximation
`hasdelay`	True for linear model with time delays
`hasInternalDelay`	Determine if model has internal delays
`totaldelay`	Total combined I/O delays for LTI model
`delayss`	Create state-space models with delayed inputs, outputs, and states
`setDelayModel`	Construct state-space model with internal delays
`getDelayModel`	State-space representation of internal delays

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.

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.

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.