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+2(s + 1)(s + 2)(s + 4)C(s)−

A step of size 10 is applied to a unity-feedback loop with G(s) = 2(s + 1)/((s + 2)(s + 4)). Find the steady-state error ess.

G(s) = 2(s + 1)/((s + 2)(s + 4))r(t) = 10·u(t)
ess =
2.Easy
R(s)+4(s + 2)s(s + 2)(s + 3)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 2)/(s(s + 2)(s + 3)). What is the system type N?

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

A unity-feedback loop with G(s) = K/(s(s + 1)) must follow the ramp r(t) = 5t with a steady-state error of 0.5. Find the gain K.

G(s) = K/(s(s + 1))r(t) = 5tess = 0.5
K =
4.Medium
R(s)+K = 1410s + 1C(s)−

A process G(s) = 4/(10s + 1) is controlled by a proportional gain K = 1 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 4/(10s + 1)K = 1
ess = %
5.Hard
r(t) = 1t+1 + 2/s10(s + 1)(s + 2)C(s)−

A PI controller C(s) = 1 + 2/s drives the plant G(s) = 10/((s + 1)(s + 2)) in a unity-feedback loop. Find the steady-state error ess for the ramp input r(t) = 1t.

C(s) = 1 + 2/sG(s) = 10/((s + 1)(s + 2))r(t) = 1t
ess =
6.Hard
R(s)+K = 14s(s + 2)C(s)−

A proportional controller K = 1 drives the plant G(s) = 4/(s(s + 2)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 4/(s(s + 2))K = 1
%OS = %

Answer key

  1. 1. ess = 8
  2. 2. N = 1
  3. 3. K = 10
  4. 4. ess = 20 %
  5. 5. ess = 0.1
  6. 6. %OS = 16.3 %

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