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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
R(s)+50(s + 2)(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 50/((s + 2)(s + 5)). Find the position error constant Kp.

G(s) = 50/((s + 2)(s + 5))
Kp =
2.Easy
R(s)+4(s + 3)s²(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 3)/(s²(s + 2)). Find the acceleration error constant Ka.

G(s) = 4(s + 3)/(s²(s + 2))
Ka =
3.Medium
r(t) = 5 + 4t+5s(s + 2)C(s)−

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

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

The parabolic input r(t) = 1·t²/2 is applied to a unity-feedback loop with G(s) = 4(s + 5)/(s²(s + 4)). Find the steady-state error ess.

G(s) = 4(s + 5)/(s²(s + 4))r(t) = 1·t²/2
ess =
5.Hard
R(s)+K = 4010s(s + 8)C(s)−

A proportional controller K = 40 drives the plant G(s) = 10/(s(s + 8)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 10/(s(s + 8))K = 40
%OS = %
6.Hard
R(s)+K = 55s(s + 5)C(s)−

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

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

Answer key

  1. 1. Kp = 5
  2. 2. Ka = 6
  3. 3. ess = 1.6
  4. 4. ess = 0.2
  5. 5. %OS = 52.66 %
  6. 6. %OS = 16.3 %

Full step-by-step solutions: practise this topic on examproblems.com.