MediumCalculusca-181

Root Locus Breakaway Point

Problem

For the open-loop transfer function G(s) = K / (s*(s + a)) with a > 0, the root locus branches meet at the breakaway point s = -a/2.

Return [s_break, K_break] where the gain K at that point is |s*(s + a)| evaluated at s_break, equal to a^2 / 4.

Hint

Maximize the gain K(s) = -s*(s + a) along the real axis between the two poles.

case 1

in: [2]

expected: [-1,1]

case 2

in: [4]

expected: [-2,4]

case 3

in: [1]

expected: [-0.5,0.25]

case 4

in: [3]

expected: [-1.5,2.25]

Starter codePython

def root_locus_breakaway(a):
    # Return [s_breakaway, gain]
    # Your code here
    pass

4 test cases · run your code against them in the editor