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)+10s(s + 1)(s + 10)C(s)−

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

G(s) = 10/(s(s + 1)(s + 10))
Kv =
2.Easy
R(s)+20(s + 1)(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20/((s + 1)(s + 2)). Find the position error constant Kp.

G(s) = 20/((s + 1)(s + 2))
Kp =
3.Medium
r(t) = 4·t²/2+5(s + 4)s²(s + 2)C(s)−

The parabolic input r(t) = 4·t²/2 is applied to a unity-feedback loop with G(s) = 5(s + 4)/(s²(s + 2)). Find the steady-state error ess.

G(s) = 5(s + 4)/(s²(s + 2))r(t) = 4·t²/2
ess =
4.Medium
R(s)+K = 245s + 1C(s)−

A process G(s) = 4/(5s + 1) is controlled by a proportional gain K = 2 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 4/(5s + 1)K = 2
ess = %
5.Hard
R(s)+Kp​ + Ki​/s1s + 4C(s)−

A PI controller C(s) = Kp + Ki/s drives the plant G(s) = 1/(s + 4) in a unity-feedback loop. The closed loop must have ωₙ = 10 rad/s and ζ = 0.6. Find the proportional gain Kp.

G(s) = 1/(s + 4)ωₙ = 10 rad/sζ = 0.6
Kp =
6.Hard
R(s)+K = 52s(s + 4)C(s)−

A proportional controller K = 5 drives the plant G(s) = 2/(s(s + 4)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 2/(s(s + 4))K = 5
%OS = %

Answer key

  1. 1. Kv = 1
  2. 2. Kp = 10
  3. 3. ess = 0.4
  4. 4. ess = 11.11 %
  5. 5. Kp = 8
  6. 6. %OS = 7.691 %

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