A transfer function out of a complex function

Hi everyone, got this problem when trying to design a PID controler, so the function is here:

L=(4*exp(-t)+4*t+6)/10

i just can't get it right with all this num and den coefficients since this is a combination of ordinary function and an exponential fucntion. the question is: how do i turn it to a transfer function? got lost really.

Thanks, Sydney.

[Azzi Abdelmalek]

What is L?

[Sydney Flowers]

L is a function which indicates the change of the location of the rotor in time - Z-axis vibration. The function in question is a simplified law, out of which the sin(omega) was taken away and replaced by 1, for i had no idea how to make it in tf, and c and b coefficients were made numeric constants.

Answer 1

[David Sanchez]

substitute in your L function:

exp(x) = 1 + x + (x^2)/4  % Taylor expansion

Operate until you obtain your num and den, then:

my_sys = tf( num, den )

[Azzi Abdelmalek]

what are num and den?

[Sydney Flowers]

numerator and denumenator - coefficient vectors that make up a transfer fucntion.

Answer 2

[Azzi Abdelmalek]

If L is your impulse response, Maybe L is

%L(t)=0.1(4exp(-t)-4t+6)u(t)    % u(t) is a step function

The transfer function of your system is the Laplace transform of your impulse response

%L(p)=0.1*(4*1/(p+1)-4*1/p^2+6/p)
%L(p)=0.4/(p+1)-0.4/p^2+0.6/p=(p^2+0.2p-0.4)/(p^3+p^2)

num=[1 0.2 -0.4]
den=[1 1 0 0]
H=tf(num,den)

[Sydney Flowers]

so the transfer function i get is basically equal to what i had?

[Azzi Abdelmalek]

What do you mean?

[Sydney Flowers]

Does it look this way: my function L -> Laplace transform -> L(p)?

[Azzi Abdelmalek]

Please explain clearly, you've posted a function L(t) which is a temporal function, can you specify if L(t) is a pulse response or a transfer function, and what t represent?

[Sydney Flowers]

L(t) is a function which describes the law according to which the rotor moves in Z-axis. It is the law of the change of the gap between a bearing and a rotor. It was obtained out of the math model, the solution to a differential equasion. Now the goal is to control the gap by means of PID, which i was trying to design in matlab, but faced a problem with turning the function into the transfer function.

[Azzi Abdelmalek]

You did not answer my question, is L(t) a pulse response or what? if not you should explain how this function describe your system, because in your function, there is no neither input signal, neither output.

[Sydney Flowers]

the system is a Z axis one mass attached to the ground with a spring and damper. L(t) is not a pulse response. Again, its a solution to a differential equasion from mx''-c-kx=F(which is a sin-like disturbance)-bx'. Thats it.

[Azzi Abdelmalek]

Ok, in your equation can you specify what represent each parameter or signal

[Sydney Flowers]

having the differential equasion as follows: m*h''-c-k*h=F-b*h', where h is the value of the gap, i obtained the function h(t) = (4*exp(-t)+4*t+6)/10, which is the simplified solution of the equasion. coefficients C of the stiffness of the spring and B of the damper are turned into numeric constants, so they do not appear in the function. that makes h - the gap value and t - time.

[Azzi Abdelmalek]

Do you mean

h: your output signal
m,c,k and F are constant

What about your input signal?

[Sydney Flowers]

F is a disturbing force, so, if i get you right, the input is initial value of the gap h, and omega, on which the F depends. and output is a new value of the gap.