Models with Time Delays
ioDelay properties of dynamic system models to represent time
Time Delays in Linear Systems.
|Padé approximation of model with time delays|
|Replace time delays by poles at z = 0 or phase shift|
|Generate fractional delay filter based on Thiran approximation|
|True for linear model with time delays|
|Determine if model has internal delays|
|Total combined I/O delays for LTI model|
|Create state-space models with delayed inputs, outputs, and states|
|Construct state-space model with internal delays|
|State-space representation of internal 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
Represent input and output delays, transport delays, or internal delays in dynamic system models.
Interconnecting models that have time delays can give rise to internal delays.
Internal delays can model feedback loops with delays.
Incorporate input, output, or transport delays as factors of 1/z in a discrete-time model.
Absorbing time delays into frequency response data can cause undesirable phase wrapping at high frequencies.
Approximate Time Delays
Approximate time delays with all-pass filters for control-design techniques that cannot handle time delays directly.
Use the Padé approximation to approximate time delays in continuous-time models.
Approximate delays in a continuous-time closed-loop system with internal delays.
You can use different approximation orders to model different types of delays, such as internal and output delays.