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 + 1)s²(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 1)/(s²(s + 2)). Find the acceleration error constant Ka.

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

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 4)/(s²(s + 4)). Find the acceleration error constant Ka.

G(s) = 20(s + 4)/(s²(s + 4))
Ka =
3.Medium
R(s)+K(s + 2)(s + 4)C(s)−

A unity-feedback loop has G(s) = K/((s + 2)(s + 4)). Find the gain K that gives a steady-state error of 25 % for a step input.

G(s) = K/((s + 2)(s + 4))ess = 25 %
K =
4.Medium
R(s)+K = 5210s + 1C(s)−

A process G(s) = 2/(10s + 1) is controlled by a proportional gain K = 5 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 2/(10s + 1)K = 5
ess = %
5.Hard
R(s)+K = 202s(s + 8)C(s)−

A proportional controller K = 20 drives the plant G(s) = 2/(s(s + 8)) in a unity-feedback loop. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 2/(s(s + 8))K = 20
ts = s
6.Hard
R(s)+K = 85s(s + 8)C(s)−

A proportional controller K = 8 drives the plant G(s) = 5/(s(s + 8)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 5/(s(s + 8))K = 8
tp = s

Answer key

  1. 1. Ka = 2
  2. 2. Ka = 20
  3. 3. K = 24
  4. 4. ess = 9.091 %
  5. 5. ts = 1 s
  6. 6. tp = 0.6413 s

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