A transfer function out of a complex function

2013 6 5
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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.

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Sydney Flowers
Sydney Flowers 2013-6-5
编辑：Sydney Flowers 2013-6-5
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.

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回答（2 个）

David Sanchez
David Sanchez 2013-6-5

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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 )

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Sydney Flowers
Sydney Flowers 2013-6-5
numerator and denumenator - coefficient vectors that make up a transfer fucntion.

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Azzi Abdelmalek
Azzi Abdelmalek 2013-6-5

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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)

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Sydney Flowers
Sydney Flowers 2013-6-5
so the transfer function i get is basically equal to what i had?
Sydney Flowers
Sydney Flowers 2013-6-5
Does it look this way: my function L -> Laplace transform -> L(p)?
Azzi Abdelmalek
Azzi Abdelmalek 2013-6-5
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
Sydney Flowers 2013-6-5
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
Azzi Abdelmalek 2013-6-5
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
Sydney Flowers 2013-6-5
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
Azzi Abdelmalek 2013-6-5
Ok, in your equation can you specify what represent each parameter or signal
Sydney Flowers
Sydney Flowers 2013-6-5
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
Azzi Abdelmalek 2013-6-5
Do you mean
h: your output signal
m,c,k and F are constant
What about your input signal?
Sydney Flowers
Sydney Flowers 2013-6-5
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.

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