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| R2012a Documentation → Control System Toolbox | |
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[H,tau]
= getDelayModel(sys)
[A,B1,B2,C1,C2,D11,D12,D21,D22,E,tau]
= getDelayModel(sys)
[H,tau] = getDelayModel(sys) decomposes a state-space model 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.
[A,B1,B2,C1,C2,D11,D12,D21,D22,E,tau] = getDelayModel(sys) returns the set of state-space matrices and internal delay vector, 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:
sys |
Any state-space (ss) model. |
H |
Delay-free state-space model (ss). H results from decomposing sys into a delay-free component and a component exp(-tau*s) that represents all internal delays. If sys has no internal delays, H is equal to sys. |
tau |
Vector of internal delays of sys, expressed in the time units of sys. The vector tau results from decomposing sys into a delay-free state-space model H and a component exp(-tau*s) that represents all internal delays. If sys has no internal delays, tau is empty. |
A,B1,B2,C1,C2,D11,D12,D21,D22,E |
Set of state-space matrices that, with the internal delay vector tau, explicitly describe the state-space model sys. For explicit state-space models (E = I, or sys.e = []), the output E = []. If sys has no internal delays, the outputs B2, C2, D12, D21, and D22 are all empty ([]). |
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 arising from the feedback loop.
Decompose sys into a delay-free state-space model and the value of the internal delay.
[H,tau] = getDelayModel(sys);
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