How to estimate the parameter in a customized transfer function

Hey guys

Currently I'm using system identification toolbox to estimte the transfer function of a set of data. However, I want my transfer function in a particular form:

where and are fitting parameters. Both and are known polynomials (unfortunately I cannot provide any details about them). In this case, this transfer function model cannot be written in a standard form as shown below:

The system identification toolbox seems to require my model to be written in the standard form. Therefore, I'm wondering if there's anyway I can find estimation for and ? Thank you

Answer 1

[Robert U]

Hi Lihao Zheng,

first of all you can convert the two forms from one to another. Second it is possible to define transfer functions in different forms:

s = tf('s');

K0 = 5;
a0 = 10;
p  = 2*s+1;
q  = 3*s^2+2*s+1;

G = K0 / (p/q+a0)

As you can see, Matlab returns G in the polynomial form.

If you convert the transfer functions to one another you will see that

Finding the common devider in the numerator of a(s) leads direktly to K_0 and with that you can calculate {\tilde a_0}.

Kind regards,

Robert

[Lihao Zheng]

Hi, thank you for your response!

Yes, I can indeed convert my G(s) in the form of . If we assume:

and

where p_i and q_i are known coefficient. Since a_o is unknown, the aforementioned b(s) will have the form of:

This form of coefficient is problematic since System identification toolbox does not have model like that.

Answer 2

[Rajiv Singh]

Grey-box identification is an option. You will need to write a function that takes K0 and a0 as inputs, and returns state-space matrices correspinding to your system. See IDGREY, GREYEST, SSDATA. Some examples:

https://www.mathworks.com/help/ident/ug/estimating-coefficients-of-odes-to-fit-given-solution.html

https://www.mathworks.com/help/ident/ug/estimate-complex-conjugate-poles-and-zeros-using-grey-box-model.html