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)+5(s + 1)(s + 5)C(s)−

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

G(s) = 5/((s + 1)(s + 5))
Kp =
2.Easy
R(s)+20(s + 2)s(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 2)/(s(s + 2)). What is the system type N?

G(s) = 20(s + 2)/(s(s + 2))
N =
3.Medium
R(s)+K = 221s + 1C(s)−

A process G(s) = 2/(1s + 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) = 2/(1s + 1)K = 2
ess = %
4.Medium
R(s)+K = 20.510s + 1C(s)−

A process G(s) = 0.5/(10s + 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) = 0.5/(10s + 1)K = 2
ess = %
5.Hard
R(s)+K = 251s(s + 6)C(s)−

A proportional controller K = 25 drives the plant G(s) = 1/(s(s + 6)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 1/(s(s + 6))K = 25
tp = s
6.Hard
R(s)+K = 1610s(s + 8)C(s)−

A proportional controller K = 16 drives the plant G(s) = 10/(s(s + 8)) in a unity-feedback loop. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 10/(s(s + 8))K = 16
ts = s

Answer key

  1. 1. Kp = 1
  2. 2. N = 1
  3. 3. ess = 20 %
  4. 4. ess = 50 %
  5. 5. tp = 0.7854 s
  6. 6. ts = 1 s

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