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)+2(s + 4)s(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2(s + 4)/(s(s + 2)). Find the velocity error constant Kv.

G(s) = 2(s + 4)/(s(s + 2))
Kv =
2.Easy
R(s)+20(s + 2)(s + 2)(s + 4)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 2)/((s + 2)(s + 4)). Find the position error constant Kp.

G(s) = 20(s + 2)/((s + 2)(s + 4))
Kp =
3.Medium
R(s)+K = 940.5s + 1C(s)−

A process G(s) = 4/(0.5s + 1) is controlled by a proportional gain K = 9 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 4/(0.5s + 1)K = 9
ess = %
4.Medium
R(s)+K = 952s + 1C(s)−

A process G(s) = 5/(2s + 1) is controlled by a proportional gain K = 9 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 5/(2s + 1)K = 9
ess = %
5.Hard
R(s)+8 + Kd​s10s(s + 3)C(s)−

A PD controller C(s) = 8 + Kd·s drives the plant G(s) = 10/(s(s + 3)) in a unity-feedback loop. Find the derivative gain Kd that gives the closed loop a damping ratio ζ = 0.5.

G(s) = 10/(s(s + 3))Kp = 8ζ = 0.5
Kd = s
6.Hard
R(s)+K = 45s(s + 2)C(s)−

A proportional controller K = 4 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 = 4
%OS = %

Answer key

  1. 1. Kv = 4
  2. 2. Kp = 5
  3. 3. ess = 2.703 %
  4. 4. ess = 2.174 %
  5. 5. Kd = 0.5944 s
  6. 6. %OS = 48.64 %

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