State-space representation of internal delays
[A,B1,B2,C1,C2,D11,D12,D21,D22,E,tau] = getDelayModel(sys)
[ decomposes a
sys with internal delays into
a delay-free state-space model,
H, and a vector
of internal delays,
tau. The relationship among
tau is shown in the following diagram.
[ returns the set
of state-space matrices and internal delay vector,
that explicitly describe the state-space model
These state-space matrices are defined by the state-space equations:
Any state-space (
Vector of internal delays of
For explicit state-space models (E = I,
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 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