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)+10s(s + 1)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 10/(s(s + 1)). Find the velocity error constant Kv.

G(s) = 10/(s(s + 1))
Kv =
2.Easy
r(t) = 10+K = 55s + 5y(t)−

A proportional controller K = 5 drives the plant G(s) = 5/(s + 5) in a unity-feedback loop. A step of size 10 is applied. Find the final value of the output y(∞).

G(s) = 5/(s + 5)K = 5r = 10
y(∞) =
3.Medium
R(s)+K = 10.50.5s + 1C(s)−

A process G(s) = 0.5/(0.5s + 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) = 0.5/(0.5s + 1)K = 1
ess = %
4.Medium
r(t) = 2t+Ks(s + 4)C(s)−

A unity-feedback loop with G(s) = K/(s(s + 4)) must follow the ramp r(t) = 2t with a steady-state error of 0.1. Find the gain K.

G(s) = K/(s(s + 4))r(t) = 2tess = 0.1
K =
5.Hard
R(s)+K = 501s(s + 2)C(s)−

A proportional controller K = 50 drives the plant G(s) = 1/(s(s + 2)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 1/(s(s + 2))K = 50
%OS = %
6.Hard
r(t) = 1t+1 + 0.5/s20(s + 2)(s + 4)C(s)−

A PI controller C(s) = 1 + 0.5/s drives the plant G(s) = 20/((s + 2)(s + 4)) in a unity-feedback loop. Find the steady-state error ess for the ramp input r(t) = 1t.

C(s) = 1 + 0.5/sG(s) = 20/((s + 2)(s + 4))r(t) = 1t
ess =

Answer key

  1. 1. Kv = 10
  2. 2. y(∞) = 8.333
  3. 3. ess = 66.67 %
  4. 4. K = 80
  5. 5. %OS = 63.84 %
  6. 6. ess = 0.8

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