MIMO Frequency Response Data Models

This example shows how to create a MIMO frequency-response model using frd.

Frequency response data for a MIMO system includes a vector of complex response data for each of the input/output (I/O) pair of the system. Thus, if you measure the frequency response of each I/O pair of your system at a set of test frequencies, you can use the data to create a frequency response model:

1. Load frequency response data in AnalyzerDataMIMO.mat.

   load AnalyzerDataMIMO H11 H12 H21 H22 freq

   This command loads the data into the MATLAB^® workspace as five column vectors H11, H12, H21, H22, and freq. The vector freq contains 100 test frequencies. The other four vectors contain the corresponding complex-valued frequency response of each I/O pair of a two-input, two-output system.

   Tip

   To inspect these variables, enter:

   whos H11 H12 H21 H22 freq

2. Organize the data into a three-dimensional array.

   Hresp = zeros(2,2,length(freq));
   Hresp(1,1,:) = H11;
   Hresp(1,2,:) = H12;
   Hresp(2,1,:) = H21;
   Hresp(2,2,:) = H22;
   

   The dimensions of Hresp are the number of outputs, number of inputs, and the number of frequencies for which there is response data. Hresp(i,j,:) contains the frequency response from input j to output i.

3. Create a frequency-response model.

   H = frd(Hresp,freq);

H is an frd model object, which is a data container for representing frequency response data.

You can use frd models with many frequency-domain analysis commands. For example, visualize the response of this two-input, two-output system using bode.

Tip

By default, the frd command assumes that the frequencies are in radians/second. To specify different frequency units, use the TimeUnit and FrequencyUnit properties of the frd model object. For example:

H = frd(Hresp,freq,'TimeUnit','min','FrequencyUnit','rad/TimeUnit') 

sets the frequency units to in radians/minute.