How to find step response for variable transfer function?

the coefficients of a transfer function are varying, how to find the step response to all the possible transfer functions. transfer function :

step response:

the above figure shows the varying transfer function and step response. I don't know how to get the step response shown in the above diagram for the varying system given. In matlab simulink.

Answer 1

[Sebastian Castro]

Well, first off let's do this with an individual parameter.

% Parameters
K = 1;
T = 1;
L = 1;

% Create the system
s = tf('s');
sys = (K/(T*s + 1))*exp(-L*s)

% Step response
step(sys)

You can instead place this in a big loop for different parameter values. For example:

% Parameters
K = [0.5,1.0,1.5];
T = [0.5,1.0,1.5];
L = [0.5,1.0,1.5];

% Initialize the loop counter
count = 1;

for ii = 1:numel(K)
  for jj = 1:numel(T)
    for kk = 1:numel(L)

        % Create the system (use 3rd dimension to concatenate)
        sys(:,:,count) =  (K(ii)/(T(jj)*s + 1))*exp(-L(kk)*s);
        count = count + 1;

      end
    end
  end

% Step response
step(sys)

By the way, there is a way more elegant/efficient way of expressing parameter variations shown in this documentation link. However, it didn't seem to work because of the exponential portion, which can't accept a realp tunable parameter.

If you want to pursue the above, you may need to do a Pade approximation of that exponential time delay piece first.

- Sebastian

[kintali narendra]

Thanku .I didn't see your answer, I will check and let you know.