getDelayModel
State-space representation of internal delays
Syntax
[H,tau]
= getDelayModel(sys)
[A,B1,B2,C1,C2,D11,D12,D21,D22,E,tau]
= getDelayModel(sys)
Description
[ decomposes a
state-space model H,tau]
= getDelayModel(sys)sys with internal delays into
a delay-free state-space model, H, and a vector
of internal delays, tau. The relationship among sys, H,
and tau is shown in the following diagram.
[ returns the set
of state-space matrices and internal delay vector, A,B1,B2,C1,C2,D11,D12,D21,D22,E,tau]
= getDelayModel(sys)tau,
that explicitly describe the state-space model sys.
These state-space matrices are defined by the state-space equations:
Continuous-time
sys:Discrete-time
sys:
Input Arguments
|
Any state-space ( |
Output Arguments
|
Delay-free state-space model ( If |
|
Vector of internal delays of If |
|
Set of state-space matrices that, with the internal delay vector For explicit state-space models (E = I,
or If |
Examples
Get Delay-Free State-Space Model and Internal Delay
Decompose the following closed-loop system with internal delay into a delay-free component and a component representing the internal delay.
Create the closed-loop model sys from r to y.
G = tf(1,[1 10],'InputDelay',2.1);
C = pid(0.5,2.3);
sys = feedback(C*G,1);sys is a state-space (ss) model with an internal delay that arises from closing the feedback loop on a plant with an input delay.
Decompose sys into a delay-free state-space model and the value of the internal delay.
[H,tau] = getDelayModel(sys);
Confirm that the internal delay matches the original input delay on the plant.
tau
tau = 2.1000