Initial value for a transfer function

Hello, I'm working on a simulink model of a heat exchanger. I already got the transfer function of my system. It is a second order transfer function. However, i have a slight problem where i should start at 50 at t=0 and end at Tref(value that i want, for example 20). I know that i can convert my transfer function to state-space block where i can define the initial value but it did not work.

In the state-space block I put initial condition to 50. But as you can see in the result, it starts at 0. Thank you to anyone that can help.

So if anyone can help, i really appreciate it.

-Aizat

[Azzi Abdelmalek]

How did you set your initial conditions?

[Aizat BIN AZMI]

I set in the state-space. Initial condition, and i put 50 because i want it starts from 50.

[Azzi Abdelmalek]

What is the value of your vector C, in your state space model?

[Aizat BIN AZMI]

Here is the values of all 4 vectors after I did a conversion of tf2ss.

A1 =

   -0.0071   -0.0000
    1.0000         0

B1 =

     1
     0

C1 =

         0    0.0013

D1 =

     0

Answer 1

[Azzi Abdelmalek]

From your second order state space model,you have

y=C*[x1;x2]

Then if you want to set initial conditions to your states x1 and x2, you should type a vector [x10;x20], then the initials condition for y will be:

y0=C*[x10;x20]

[Azzi Abdelmalek]

For your case, to get 50 as initial conditions for y, set your initial conditions with the vector

[0 50/0.0013]

[Aizat BIN AZMI]

If i may ask, how do you find this value? How by putting vector [0 50/0.0013] as initial value and it works?

[Azzi Abdelmalek]

I already explained it in my answer.

y=C*[x1 x2]

If the initial conditions for your states are x01 and x02 then, the y0 will be

   y0=[0 0.003]*[x01 ; x02]
   y0=0.003*x02

Now if you want

 y0=50,

then

x02=50/0.003

What you have to know is, the initial conditions are for your states x1 and x2.

For the question if it works, you have to tell me

[Aizat BIN AZMI]

It works very well. Thank you so much. I appreciate it.

[Parth Chandak]

How to model the system after you get y and y0? Can you explain that?

clear all
clc

w = 1;
z = 0.2;

x_0 = [1;1];
xdot_0 = [1;5];

num = [0,0,w^2]
den = [1,2*z*w,w^2]

[A,B,C,D] = tf2ss(num,den)
y_0 = C*x_0
ydot_0 = C*xdot_0

sys= ss(A,B,C,D);
H=tf(sys);

stepplot(H)