Fractional order root locus

This function generates the root locus (RL) plot of a fractional order transfer function.

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This function generates the root locus (RL) plot of a fractional order
transfer function (for LTI systems). The first plot is the RL on the
s-plane, and the second plot is the RL on the 1st Riemann sheet of the s-plane
The input is the numerator and denominator polynomial coefficients,
and the fundamental order lambda (i.e. the lowest common denominator of
all the fractional orders on numerator and denominator).
The output returns the figure hundle.
E.g. for the transfer function below:
1.2s^{1.3}+1 1.2s^{13/10}+1
G(s) = ----------------------------- = ----------------------------------
0.8s^{2.6}+s^{1.3}+1 0.8s^{26/10}+s^{13/10}+1
lambda = 10;
num = [1.2 zeros(1,12) 1];
den = [0.8, zeros(1,12), 0.6, zeros(1, 12), 1];
The syntax for calling the function is: [fh1, fh2] = forlocus(num, den, lambda)

Cite As

Zhuo Li (2026). Fractional order root locus (https://uk.mathworks.com/matlabcentral/fileexchange/50458-fractional-order-root-locus), MATLAB Central File Exchange. Retrieved .

General Information

MATLAB Release Compatibility

  • Compatible with any release

Platform Compatibility

  • Windows
  • macOS
  • Linux
Version Published Release Notes Action
1.1.0.0

Corrected an error in the demo code
den = [0.8, zeros(1,22), 0.6, zeros(1, 22), 1]; changed to
den = [0.8, zeros(1,12), 0.6, zeros(1, 12), 1];

1.0.0.0