Root Locus (Graphical Tool)

This is a fun little weekend project I worked on for my Modern Control Theory class.

It is a python implementation of the Root Locus Design Method. The RL plots the location of the roots of the characteristic equation of the closed-loop transfer function as the gain K is varied from 0 to infinity.

Requirements

• Python 2+, 3+
• numpy
• matplotlib
• seaborn (optional)

How To Use

Enter the coefficients of the numerator and denominator of the open loop transfer function as lists num = [] and denum = []. The denominator must have all coefficients entered (even the terms with 0 coefficients) but it doesn't have to be explicitely written out for the numerator.

Now invoke the transfer_function method, compute the roots of the TF using compute_roots, and finally plot with plot_root_locus.

Example

num = [1]
denum = [1, 3, 2, 0]

GH = transfer_function(num, denum)

# create a list of evenly spaced gains
gains = np.linspace(0.0, 10.0, num=500)

roots = compute_roots(GH, gains)
fig, ax = plot_root_locus(gains, roots)
plt.show()

References

• python-control - helped me get a sense of how to go about the problem.
• Bicycle Control Design - great blog post