Designing a decoupling controller

I have two control loops in simulink that need a decoupler to fix the inverse effect they have on each other.

I have the two transfer functions g(s) to plug between the two loops, but MATLAB 2020b doesn’t have an option for transfer functions in the form Aexp(-Bs), and I can’t find a work around.

If someone can give me any ideas it’d be of great help, thanks!

[Walter Roberson]

exp() is supported for negative constant time s -- exp(-Bs) would be valid for B being a positive constant. It translates into a delay.

s = tf('s');
f = (s^2 - 1)/(s^3 + s - 1)

f =
 
    s^2 - 1
  -----------
  s^3 + s - 1
 
Continuous-time transfer function.

g = (s^2 + 1)/(s^3 + s + 1)

g =
 
    s^2 + 1
  -----------
  s^3 + s + 1
 
Continuous-time transfer function.

step(f)

step(g)

h = f * exp(-5*s) + g * exp(-10*s)

h =
 
  A = 
       x1  x2  x3  x4  x5  x6
   x1   0  -1   1   0   0   0
   x2   1   0   0   0   0   0
   x3   0   1   0   0   0   0
   x4   0   0   0   0  -1  -1
   x5   0   0   0   1   0   0
   x6   0   0   0   0   1   0
 
  B = 
       u1
   x1   2
   x2   0
   x3   0
   x4   2
   x5   0
   x6   0
 
  C = 
         x1    x2    x3    x4    x5    x6
   y1   0.5     0  -0.5   0.5     0   0.5
 
  D = 
       u1
   y1   0
 
  (values computed with all internal delays set to zero)

  Input delays (seconds): 5 
  Internal delays (seconds): 5 
 
Continuous-time state-space model.

step(h)

[mehul kishan]

Hi, thanks for the response. What do you think should I do if B is negative so that I get a positive final output? I’m using the LTI System block i.e. tf(2.2,[1,0],’InputDelay’,-4.3) but it doesn’t work because InputDelay can’t be negative.

Would it perhaps be the same if I use OutputDelay and +4.3?

[Walter Roberson]

https://www.mathworks.com/help/control/ug/specifying-time-delays.html#d123e10765