MediumCalculusca-182

Steady-State Error

Problem

For a unity-feedback loop with the type-0 plant G(s) = k / (s + a), the position error constant is Kp = k / a and the unit-step steady-state error is e_ss = 1 / (1 + Kp).

Given k >= 0 and a > 0, return e_ss.

Hint

The final value theorem evaluates the error transfer function 1/(1 + G(s)) at s = 0.

Test cases

case 1

in: [4,2]

expected: 0.3333333333333333

case 2

in: [0,1]

expected: 1

case 3

in: [1,1]

expected: 0.5

case 4

in: [10,5]

expected: 0.3333333333333333

Starter codePython

def steady_state_step_error(k, a):
    # Your code here
    pass

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