Transfer function with delay generates weird step response

Hi!

My step response plots have a weird shape as soon as I ad an input delay to the system. I cant figure out why. Depending on the delay it creates all kind of sharp edges.

Any suggestion?

PT1b = tf(10,[3 1],'inputdelay',0.8);
C = pid(0.1,0.1,0.1);
step(feedback(PT1b*C,1))

Answer 1

[Benedikt]

ok, I figured it out. Its not a strange Matlab solver behaviour but it comes from the fact that the closed loop (feedback) actually is a N=2/D=2. This makes no sense in the real world since the controllers D-output goes to infinity for a step input. However it results is a state space model with a direct feet-thru.

PT1b = tf(10,[3 1],'inputdelay',0.5);
C = pid(0.1,0.1,0.1);
feedback(PT1b*C,1)

ans =
 
  A = 
         x1    x2
   x1  -0.5  -0.5
   x2   0.5     0
 
  B = 
         u1
   x1  0.75
   x2     0
 
  C = 
           x1      x2
   y1  0.1667     0.5
 
  D = 
         u1
   y1  0.25
 
  (values computed with all internal delays set to zero)

  Internal delays (seconds): 0.5 
 
Continuous-time state-space model.

A solution for real world is to use a Tf on the D-term of the controller

PT1b = tf(10,[3 1],'inputdelay',0.5);
C = pid(0.1,0.1,0.1 ,0.2);
step(feedback(PT1b*C,1))