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 |
Topics
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.