Transfer Function Matrix for a MIMO System
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So I have calculated the Transfer Functions for a MIMO system from its state-space model and the system configuration has 3 inputs and 2 outputs. So, I have a total of 6 transfer functions now. I need to concatenate/combine all the Transfer Functions into a single matrix in order to further obtain its Smith Form. But I am unable to figure out how I can combine all the transfer functions into a single matrix to work on it further. Can anybody please help me with it?
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Aman Banthia
on 13 Sep 2023
Hi Akshay,
I understand that you need to concatenate/combine all the Transfer Functions into a single matrix to further obtain its Smith Form.
To combine multiple transfer functions into a single matrix, you can use the concept of a transfer function matrix. Each element of the matrix represents a transfer function between a specific input and output. Here is how you can organize your transfer functions into a matrix:
Let us assume you have a MIMO system with 3 inputs and 2 outputs. You have calculated 6 transfer functions, denoted as G11, G12, G13, G21, G22, and G23. The subscripts represent the input-output relationship, where the first subscript represents the output, and the second subscript represents the input.
To combine these transfer functions into a matrix, you can create a transfer function matrix `G` with dimensions ` [number of outputs, number of inputs] `. In your case, the matrix `G` will have dimensions ` [2, 3]`.
Here is an example code snippet to illustrate the process:
% Define the transfer functions
G11 = tf([1], [1, 2]);
G12 = tf([2], [1, 3]);
G13 = tf([3], [1, 4]);
G21 = tf([4], [1, 5]);
G22 = tf([5], [1, 6]);
G23 = tf([6], [1, 7]);
% Combine the transfer functions into a matrix
G = [G11, G12, G13; G21, G22, G23];
In this example, we have created a transfer function matrix `G` by arranging the individual transfer functions into a 2x3 matrix. Each element of the matrix represents a transfer function between a specific output and input.
Once you have the transfer function matrix `G`, you can further manipulate it or apply operations like obtaining the Smith form or performing other analyses on the MIMO system.
Note: Make sure that the transfer functions you calculate are compatible and have the same input-output dimensions.
Please refer to the following MATLAB Documentation to know more about ‘tf’ function and Concatenating Matrices:
Hope the above solution helps you.
Best Regards,
Aman Banthia
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