%% 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

% Copyright 2012 The MathWorks, Inc.