MATLAB: Simulink transfer function with sinusoidal parameters

functionparametersimulinksinusoidaltransfer

I need to design a transfer function in the following form: 1 / (s^2 + K*s) where K is scalar and varies sinusoidal; the denominator should look like [1 K 0].

What would be the way to implement this behavior ?

Thanks

Best Answer

The corresponding equation is

d^2y(t)/dt^2+k.dy(t)/dt+y(t)=x(t)

where

x(t) is the input of your system
y(t) is its output

you have just to replace k by sin(t) using a clock and a sine wave block. and use derivative and integrator block instead of transfer function block to realize your model

or you can do this

from your transfer function

Y(p)(P^2+Kp+1)=X(p)

P^2 Y(p) + K p Y(p)+ 1=X(p)

Y(p)+K Y(p)/p+Y(p)/p^2=X(p)/p^2

this can be represented by

Related Solutions

MATLAB: If i have poles and zeros of a transfer function, how to obtain this transfer function ??

transfer_function = tf( zpk(ListOfZeros, ListOfPoles, ListOfGains))

MATLAB: How to implement an improper transfer function (without delays) in Simulink

The ability to implement an improper transfer function (without delays) is not available in the Transfer Function and LTI System blocks.

To work around this issue, you can implement the transfer function using the Derivative and Integrator blocks.

An example/workaround for improper transfer functions (without delays) is as follows:

Consider the following transfer function:

>> num = [4.03*.064*1.06e-5 .064 4.30];
>> den = [.064*1.06e-5 1];
>> tf(num,den)
ans =
    2.734e-06 s^2 + 0.064 s + 4.3
    -----------------------------
           6.784e-07 s + 1

We can do a partial fraction decomposition:

>> [r,p,k] = residue(num,den);

Now the 3 systems can be implemented in Simulink as:

% SYSTEM 1: Implemented as an "LTI System" block
% https://www.mathworks.com/help/control/ref/ltisystem.html
sys1 = tf(r(1),[1,-p(1)]);  
% SYSTEM 2: Implemented as a gain and a du/dt block
% https://www.mathworks.com/help/simulink/slref/derivative.html 
k(1)*s
% SYSTEM 3: Implemented as a gain block
k(2)

These three systems should be summed in parallel. For instance, a basic setup with a "Step" input may look like:

Best Answer

Related Solutions

MATLAB: If i have poles and zeros of a transfer function, how to obtain this transfer function ??

MATLAB: How to implement an improper transfer function (without delays) in Simulink

Related Question