Steady-state error & PID control worksheet with answers

Free printable Steady-state error & PID control worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
R(s)+4(s + 2)s²(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 2)/(s²(s + 10)). Find the acceleration error constant Ka.

G(s) = 4(s + 2)/(s²(s + 10))
Ka =
2.Easy
R(s)+20(s + 1)s(s + 4)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 1)/(s(s + 4)(s + 10)). Find the velocity error constant Kv.

G(s) = 20(s + 1)/(s(s + 4)(s + 10))
Kv =
3.Medium
r(t) = 5 + 3t+4(s + 1)s(s + 2)(s + 4)C(s)−

The input r(t) = 5 + 3t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 4(s + 1)/(s(s + 2)(s + 4)). Find the steady-state error ess.

G(s) = 4(s + 1)/(s(s + 2)(s + 4))r(t) = 5 + 3t
ess =
4.Medium
r(t) = 2t+Ks(s + 1)C(s)−

A unity-feedback loop with G(s) = K/(s(s + 1)) must follow the ramp r(t) = 2t with a steady-state error of 0.1. Find the gain K.

G(s) = K/(s(s + 1))r(t) = 2tess = 0.1
K =
5.Hard
R(s)+K = 105s(s + 10)C(s)−

A proportional controller K = 10 drives the plant G(s) = 5/(s(s + 10)) in a unity-feedback loop. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 5/(s(s + 10))K = 10
ts = s
6.Hard
R(s)+K = 5010s(s + 6)C(s)−

A proportional controller K = 50 drives the plant G(s) = 10/(s(s + 6)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 10/(s(s + 6))K = 50
%OS = %

Answer key

  1. 1. Ka = 0.8
  2. 2. Kv = 0.5
  3. 3. ess = 6
  4. 4. K = 20
  5. 5. ts = 0.8 s
  6. 6. %OS = 65.36 %

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