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)+50(s + 1)s(s + 1)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 50(s + 1)/(s(s + 1)(s + 10)). Find the velocity error constant Kv.

G(s) = 50(s + 1)/(s(s + 1)(s + 10))
Kv =
2.Easy
r(t) = 5+4(s + 2)(s + 2)(s + 5)C(s)−

A step of size 5 is applied to a unity-feedback loop with G(s) = 4(s + 2)/((s + 2)(s + 5)). Find the steady-state error ess.

G(s) = 4(s + 2)/((s + 2)(s + 5))r(t) = 5·u(t)
ess =
3.Medium
r(t) = 5t+20s(s + 5)C(s)−

A ramp r(t) = 5t is applied to a unity-feedback loop with G(s) = 20/(s(s + 5)). Find the steady-state error ess.

G(s) = 20/(s(s + 5))r(t) = 5t
ess =
4.Medium
r(t) = 10 + 0.5t+4s(s + 2)(s + 4)C(s)−

The input r(t) = 10 + 0.5t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 4/(s(s + 2)(s + 4)). Find the steady-state error ess.

G(s) = 4/(s(s + 2)(s + 4))r(t) = 10 + 0.5t
ess =
5.Hard
R(s)+K = 82s(s + 4)C(s)−

A proportional controller K = 8 drives the plant G(s) = 2/(s(s + 4)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 2/(s(s + 4))K = 8
tp = s
6.Hard
R(s)+K = 501s(s + 10)C(s)−

A proportional controller K = 50 drives the plant G(s) = 1/(s(s + 10)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 1/(s(s + 10))K = 50
%OS = %

Answer key

  1. 1. Kv = 5
  2. 2. ess = 2.778
  3. 3. ess = 1.25
  4. 4. ess = 1
  5. 5. tp = 0.9069 s
  6. 6. %OS = 4.321 %

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