How to get output of 2X2 transfer function for a MIMO system using either "spafdr" or "n4sid" function

I have a mechanical system with 2 inputs and 2 outputs. Currently I use the “spafdr” system id command to get the frequency response and transfer function from each input to each output (total 4 transfer functions).

I need to use either "spafdr" or "n4sid" command to find the 2 by 2 MIMO transfer function in one shot as opposed to map the individual inputs to the individual outputs. 

I haven’t been successful in obtaining the right MIMO transfer function which matches the MIMO transfer function obtained from my first approach of finding them one by one.

I expect output to be of this form 

G=[G11 G12;G21,G22];

Answer 1

[MathWorks Support Team]

The data appears quite clean and benefits from use of periodic excitations. For such data (inputs that are periodic), identification is better performed in frequency domain. I suggest using "ssest" function. This will return a MIMO system in state space.

For example,

>> m=ssest(fft(data_fsm),1:20);

suggests a 4th order model and fits the data >=80 %.

Please refer the documentation below for more information

https://www.mathworks.com/help/releases/R2020a/ident/ref/ssest.html

You can convert this state space system to a transfer function using "ss2tf" function.

>>[b,a] = ss2tf(A,B,C,D,ni)

 returns the transfer function that results when the ni th input of a system with multiple inputs is excited by a unit impulse.

Please refer the link below for more information

https://www.mathworks.com/help/releases/R2020a/matlab/ref/ss2tf.html