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)+2(s + 1)s(s + 4)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2(s + 1)/(s(s + 4)). Find the velocity error constant Kv.

G(s) = 2(s + 1)/(s(s + 4))
Kv =
2.Easy
R(s)+5(s + 4)s²(s + 4)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 5(s + 4)/(s²(s + 4)). Find the acceleration error constant Ka.

G(s) = 5(s + 4)/(s²(s + 4))
Ka =
3.Medium
r(t) = 1t+4s(s + 2)C(s)−

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

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

A ramp r(t) = 5t is applied to a unity-feedback loop with G(s) = 10(s + 2)/(s(s + 1)(s + 2)). Find the steady-state error ess.

G(s) = 10(s + 2)/(s(s + 1)(s + 2))r(t) = 5t
ess =
5.Hard
R(s)+K = 402s(s + 10)C(s)−

A proportional controller K = 40 drives the plant G(s) = 2/(s(s + 10)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 2/(s(s + 10))K = 40
tp = s
6.Hard
R(s)+K = 44s(s + 5)C(s)−

A proportional controller K = 4 drives the plant G(s) = 4/(s(s + 5)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 4/(s(s + 5))K = 4
tp = s

Answer key

  1. 1. Kv = 0.5
  2. 2. Ka = 5
  3. 3. ess = 0.5
  4. 4. ess = 0.5
  5. 5. tp = 0.4236 s
  6. 6. tp = 1.006 s

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