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(t) = 5+50(s + 4)(s + 10)C(s)−

A step of size 5 is applied to a unity-feedback loop with G(s) = 50/((s + 4)(s + 10)). Find the steady-state error ess.

G(s) = 50/((s + 4)(s + 10))r(t) = 5·u(t)
ess =
2.Easy
R(s)+2s(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2/(s(s + 10)). Find the velocity error constant Kv.

G(s) = 2/(s(s + 10))
Kv =
3.Medium
r(t) = 5·t²/2+5(s + 5)s²(s + 10)C(s)−

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

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

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

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

A proportional controller K = 8 drives the plant G(s) = 5/(s(s + 2)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 5/(s(s + 2))K = 8
%OS = %
6.Hard
R(s)+K = 252s(s + 2)C(s)−

A proportional controller K = 25 drives the plant G(s) = 2/(s(s + 2)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 2/(s(s + 2))K = 25
%OS = %

Answer key

  1. 1. ess = 2.222
  2. 2. Kv = 0.2
  3. 3. ess = 2
  4. 4. ess = 0.1
  5. 5. %OS = 60.47 %
  6. 6. %OS = 63.84 %

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