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 + 3)(s + 5)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2(s + 3)/((s + 5)(s + 10)). Find the position error constant Kp.

G(s) = 2(s + 3)/((s + 5)(s + 10))
Kp =
2.Easy
R(s)+4(s + 2)s(s + 1)C(s)−

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

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

The input r(t) = 2 + 1t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 20(s + 2)/(s(s + 2)(s + 10)). Find the steady-state error ess.

G(s) = 20(s + 2)/(s(s + 2)(s + 10))r(t) = 2 + 1t
ess =
4.Medium
R(s)+K = 202.50.5s + 1C(s)−

A process G(s) = 2.5/(0.5s + 1) is controlled by a proportional gain K = 20 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 2.5/(0.5s + 1)K = 20
ess = %
5.Hard
R(s)+K = 81s(s + 2)C(s)−

A proportional controller K = 8 drives the plant G(s) = 1/(s(s + 2)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 1/(s(s + 2))K = 8
tp = s
6.Hard
R(s)+K = 401s(s + 4)C(s)−

A proportional controller K = 40 drives the plant G(s) = 1/(s(s + 4)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 1/(s(s + 4))K = 40
tp = s

Answer key

  1. 1. Kp = 0.12
  2. 2. Kv = 8
  3. 3. ess = 0.5
  4. 4. ess = 1.961 %
  5. 5. tp = 1.187 s
  6. 6. tp = 0.5236 s

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