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)+4(s + 5)s(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 5)/(s(s + 2)). What is the system type N?

G(s) = 4(s + 5)/(s(s + 2))
N =
2.Easy
R(s)+20(s + 3)s(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 3)/(s(s + 2)). Find the velocity error constant Kv.

G(s) = 20(s + 3)/(s(s + 2))
Kv =
3.Medium
r(t) = 10t+Ks(s + 1)C(s)−

A unity-feedback loop with G(s) = K/(s(s + 1)) must follow the ramp r(t) = 10t with a steady-state error of 0.01. Find the gain K.

G(s) = K/(s(s + 1))r(t) = 10tess = 0.01
K =
4.Medium
R(s)+K(s + 2)(s + 5)C(s)−

A unity-feedback loop has G(s) = K/((s + 2)(s + 5)). Find the gain K that gives a steady-state error of 2 % for a step input.

G(s) = K/((s + 2)(s + 5))ess = 2 %
K =
5.Hard
R(s)+K2s(s + 6)C(s)−

A proportional controller K drives the plant G(s) = 2/(s(s + 6)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.6.

G(s) = 2/(s(s + 6))ζ = 0.6
K =
6.Hard
R(s)+K = 501s(s + 10)C(s)−

A proportional controller K = 50 drives the plant G(s) = 1/(s(s + 10)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 1/(s(s + 10))K = 50
tp = s

Answer key

  1. 1. N = 1
  2. 2. Kv = 30
  3. 3. K = 1000
  4. 4. K = 490
  5. 5. K = 12.5
  6. 6. tp = 0.6283 s

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