Adding a delay in state space form

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I have a control block diagram
The value of tf_b is written as
tf_b=((0.5*s)+1)/(s^2)*(kp + kd*s);
The transport delay block is equivalent to value of . I made a state space form of the above system. It is written as:
I tried adding a delay as shown in the diagram.
sys=ss(A,B,C,D,'InputDelay',theta,'OutputDelay',0);
The simulink model and the state space give different settling times when given as step input. The settling time for the simulink model is 1.82 appoximately and for the state space is 1.97. Is there something I can do to correct this or add a delay properly?

Accepted Answer

Paul
Paul on 1 Jun 2022
The command
sys=ss(A,B,C,D,'InputDelay',theta,'OutputDelay',0);
puts a delay on the input signal, i.e., at the output of the a1input block to the left of the node (assuming that A,B,C,D as written is the state space model for the Simulink block diagram, but with zero transport delay; I did not verify this myself). In other words, the delay is applied to both forward paths, not just the "upper" path.
  5 Comments
Kashish Pilyal
Kashish Pilyal on 2 Jun 2022
Thank you for the help again. I believe this much will have to suffice for now.

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