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(t) = 10+5(s + 2)(s + 5)C(s)−

A step of size 10 is applied to a unity-feedback loop with G(s) = 5/((s + 2)(s + 5)). Find the steady-state error ess.

G(s) = 5/((s + 2)(s + 5))r(t) = 10·u(t)
ess =
2.Easy
R(s)+20(s + 3)s(s + 1)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 3)/(s(s + 1)). Find the velocity error constant Kv.

G(s) = 20(s + 3)/(s(s + 1))
Kv =
3.Medium
R(s)+K(s + 4)(s + 5)C(s)−

A unity-feedback loop has G(s) = K/((s + 4)(s + 5)). Find the gain K that gives a steady-state error of 20 % for a step input.

G(s) = K/((s + 4)(s + 5))ess = 20 %
K =
4.Medium
R(s)+K = 202.510s + 1C(s)−

A process G(s) = 2.5/(10s + 1) is controlled by a proportional gain K = 20 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 2.5/(10s + 1)K = 20
ess = %
5.Hard
r(t) = 1t+2 + 0.5/s2(s + 1)(s + 2)C(s)−

A PI controller C(s) = 2 + 0.5/s drives the plant G(s) = 2/((s + 1)(s + 2)) in a unity-feedback loop. Find the steady-state error ess for the ramp input r(t) = 1t.

C(s) = 2 + 0.5/sG(s) = 2/((s + 1)(s + 2))r(t) = 1t
ess =
6.Hard
R(s)+K = 42s(s + 2)C(s)−

A proportional controller K = 4 drives the plant G(s) = 2/(s(s + 2)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 2/(s(s + 2))K = 4
tp = s

Answer key

  1. 1. ess = 6.667
  2. 2. Kv = 60
  3. 3. K = 80
  4. 4. ess = 1.961 %
  5. 5. ess = 2
  6. 6. tp = 1.187 s

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