Models with Time Delays
Systems with input, output, transport, and internal 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|
- 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.