State-space representation of internal delays
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.
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 = 2.1000
H — Delay-free state-space model
ss object |
sparss object |
Delay-free state-space model, returned as a state-space object of the same type as
H results from decomposing
sys into a delay-free component and a component
exp(-tau*s) that represents all internal delays.
sys has no internal delays,
H is equal
A,B1,B2,C1,C2,D11,D12,D21,D22,E — State-space matrices
For explicit state-space models (E = I or
sys.e = ), the output
sys has no internal delays, the outputs
D22 are all empty
Introduced in R2006a