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)+20s(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20/(s(s + 5)). Find the velocity error constant Kv.

G(s) = 20/(s(s + 5))
Kv =
2.Easy
r(t) = 2+2(s + 2)(s + 4)C(s)−

A step of size 2 is applied to a unity-feedback loop with G(s) = 2/((s + 2)(s + 4)). Find the steady-state error ess.

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

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

G(s) = 2(s + 1)/(s(s + 2))r(t) = 1 + 3t
ess =
4.Medium
r(t) = 0.5t+10s(s + 2)(s + 10)C(s)−

A ramp r(t) = 0.5t is applied to a unity-feedback loop with G(s) = 10/(s(s + 2)(s + 10)). Find the steady-state error ess.

G(s) = 10/(s(s + 2)(s + 10))r(t) = 0.5t
ess =
5.Hard
R(s)+K = 84s(s + 8)C(s)−

A proportional controller K = 8 drives the plant G(s) = 4/(s(s + 8)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 4/(s(s + 8))K = 8
tp = s
6.Hard
R(s)+K = 165s(s + 10)C(s)−

A proportional controller K = 16 drives the plant G(s) = 5/(s(s + 10)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 5/(s(s + 10))K = 16
%OS = %

Answer key

  1. 1. Kv = 4
  2. 2. ess = 1.6
  3. 3. ess = 3
  4. 4. ess = 1
  5. 5. tp = 0.7854 s
  6. 6. %OS = 12.03 %

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