Define function for a transfer function

I have a transfer function given by: .

s = tf('s');
sys_closed = 8/(1*s^3+2*s^2+10*s+8);
t = linspace(0,10,400);
y = step(sys_closed,t);
plot(t,y)

Then, for the above transfer function, my coefficients are: a = 1, b = 2, c = 10 and d = 8. I would like to define a function, which returns the values of y for different values of coefficients. To this aim, I defined a function file (named uq_dynamic):

function V = uq_dynamic(X)
a = X(1);
b = X(2);
c = X(3);
d = X(4);
s = tf('s');
sys_closed = d./((a.*(s.^3))+(b.*(s.^2))+(c.*s)+d);
t = linspace(0,10,400);
y = step(sys_closed,t);
V = y;

My main working file requires me to define the transfer function (line 7) in vector notation (since I am coupling Matlab to a third-party toolbox: UQLab). I believe the syntax is incorrect, which returns an error. Could someone please help me to rectify the above transfer function in vector notation/correct syntax. Thank you.

Best,

Vinit

[Paul]

What does "vector notation" mean?

Answer 1

[Divija Aleti]

Hi Vinit,

From my understanding, 'X' is a vector containing 'a', 'b', 'c', 'd' which are scalars. As these are scalars, you do not need to use the dot operator('.') while performing arithmetic operations. Have a look at the following example code where the function is called with X = [1,2,10,8] as the input:

X = [1,2,10,8];
uq_dynamic(X);
function V = uq_dynamic(X)
a = X(1);
b = X(2);
c = X(3);
d = X(4);
s = tf('s');
sys_closed = d/((a*(s^3))+(b*(s^2))+(c*s)+d); %This is the line which differs from your code
t = linspace(0,10,400);
y = step(sys_closed,t);
V = y;
end

This function returns the values of 'y', for different values of 'X'.

Hope this helps!

Regards,

Divija