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)+C(s)G(s)C(s)−

The controller C(s) = 5(s + 1)/s drives the plant G(s) = 5/(s(s + 4)) in a unity-feedback loop. What is the system type N of the loop?

C(s) = 5(s + 1)/sG(s) = 5/(s(s + 4))
N =
2.Easy
R(s)+2(s + 4)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2/((s + 4)(s + 10)). Find the position error constant Kp.

G(s) = 2/((s + 4)(s + 10))
Kp =
3.Medium
r(t) = 2 + 1t+5s(s + 4)C(s)−

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

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

A unity-feedback loop with G(s) = K/(s(s + 2)) must follow the ramp r(t) = 2t with a steady-state error of 0.5. Find the gain K.

G(s) = K/(s(s + 2))r(t) = 2tess = 0.5
K =
5.Hard
R(s)+K = 251s(s + 5)C(s)−

A proportional controller K = 25 drives the plant G(s) = 1/(s(s + 5)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 1/(s(s + 5))K = 25
%OS = %
6.Hard
R(s)+K = 105s(s + 2)C(s)−

A proportional controller K = 10 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 = 10
%OS = %

Answer key

  1. 1. N = 2
  2. 2. Kp = 0.05
  3. 3. ess = 0.8
  4. 4. K = 8
  5. 5. %OS = 16.3 %
  6. 6. %OS = 63.84 %

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