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)+5(s + 1)(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 5/((s + 1)(s + 2)). Find the position error constant Kp.

G(s) = 5/((s + 1)(s + 2))
Kp =
2.Easy
R(s)+2(s + 3)s²(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2(s + 3)/(s²(s + 10)). Find the acceleration error constant Ka.

G(s) = 2(s + 3)/(s²(s + 10))
Ka =
3.Medium
r(t) = 10 + 2t+2(s + 1)s(s + 5)C(s)−

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

G(s) = 2(s + 1)/(s(s + 5))r(t) = 10 + 2t
ess =
4.Medium
r(t) = 0.5·t²/2+20(s + 5)s²(s + 10)C(s)−

The parabolic input r(t) = 0.5·t²/2 is applied to a unity-feedback loop with G(s) = 20(s + 5)/(s²(s + 10)). Find the steady-state error ess.

G(s) = 20(s + 5)/(s²(s + 10))r(t) = 0.5·t²/2
ess =
5.Hard
R(s)+K = 85s(s + 10)C(s)−

A proportional controller K = 8 drives the plant G(s) = 5/(s(s + 10)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 5/(s(s + 10))K = 8
%OS = %
6.Hard
R(s)+K2s(s + 10)C(s)−

A proportional controller K drives the plant G(s) = 2/(s(s + 10)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.4.

G(s) = 2/(s(s + 10))ζ = 0.4
K =

Answer key

  1. 1. Kp = 2.5
  2. 2. Ka = 0.6
  3. 3. ess = 5
  4. 4. ess = 0.05
  5. 5. %OS = 1.732 %
  6. 6. K = 78.12

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