fitfrd

Fit frequency response data with state-space model

Syntax

B = fitfrd(A,N)

B = fitfrd(A,N,RD)

B = fitfrd(A,N,RD,WT)

Description

B = fitfrd(A,N) computes a state-space model of order N with a frequency response that approximates the frequency-response model A.

B = fitfrd(A,N,RD) forces the relative degree of B to RD. The relative degree of B is the difference between the number of poles and the number of zeros of B.

B = fitfrd(A,N,RD,WT) uses the magnitude of WT to weight the optimization fit criteria A-B. Use WT to give greater weight to matching the responses of B and A at certain frequencies.

Examples

Fit D-scale Data

Use the fitfrd command to fit D-scale data.

Create D-scale frequency response data from a fifth-order system.

sys = tf([1 2 2],[1 2.5 1.5])*tf(1,[1 0.1]); 
sys = sys*tf([1 3.75 3.5],[1 2.5 13]); 
omeg = logspace(-1,1); 
sysg = frd(sys,omeg); 
bode(sysg,'r-');

You can try to fit the frequency response D-scale data sysg with a first-order system, b1. Similarly, you can fit the D-scale data with a third-order system, b3.

b1 = fitfrd(sysg,1); 
b3 = fitfrd(sysg,3);

Compare the original D-scale data sysg with the frequency responses of the first and third-order models calculated by fitfrd.

b1g = frd(b1,omeg); 
b3g = frd(b3,omeg); 
bode(sysg,'r-',b1g,'k:',b3g,'b-.')
legend('5th order system','1st order fit','3rd order fit','Location','Southwest')

ans = 
  Legend (5th order system, 1st order fit, 3rd order fit) with properties:

         String: {'5th order system'  '1st order fit'  '3rd order fit'}
       Location: 'southwest'
    Orientation: 'vertical'
       FontSize: 8.1000
       Position: [0.1504 0.5945 0.2827 0.1278]
          Units: 'normalized'

  Use GET to show all properties

Input Arguments

A — Frequency response data

frd model

Frequency response data, specified as an frd model. A must be SISO, have a single input with multiple outputs, or have multiple outputs with a single input.

N — Order

nonnegative integer

Order of output model B, specified as a nonnegative integer. Numerical conditioning problems arise if the specified N is higher than required by the dynamics of A.

RD — Relative degree

0 (default) | nonnegative integer | vector

Relative degree, specified as a nonnegative integer or vector. The default value for RD is 0. If A has M inputs, then RD can be a vector of the same size, specifying the relative degree of each channel of B. If RD is a scalar, then it specifies the relative degree for all entries of B. You can specify the default value for RD by setting RD to an empty matrix.

WT — Weight

1 (default) | double | ss model | frd model

Weight, specified as an array, ss model, orfrd model. If WT is a scalar, then it is used to weight all entries of the error criteria (A-B). If WT is a vector, it must be the same size as A, and each individual entry of WT acts as a weighting function on the corresponding entry of (A-B).

Output Arguments

B — Fit for data

ss model

Fit for the input frequency-response data, returned as a state-space (ss) model. B has order N and the same dimensions as A.

Version History

Introduced before R2006a