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 + 4)s²(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 4)/(s²(s + 5)). Find the acceleration error constant Ka.

G(s) = 4(s + 4)/(s²(s + 5))
Ka =
2.Easy
R(s)+20(s + 5)s²(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 5)/(s²(s + 2)). Find the acceleration error constant Ka.

G(s) = 20(s + 5)/(s²(s + 2))
Ka =
3.Medium
r(t) = 1·t²/2+4(s + 1)s²(s + 10)C(s)−

The parabolic input r(t) = 1·t²/2 is applied to a unity-feedback loop with G(s) = 4(s + 1)/(s²(s + 10)). Find the steady-state error ess.

G(s) = 4(s + 1)/(s²(s + 10))r(t) = 1·t²/2
ess =
4.Medium
r(t) = 3t+20(s + 4)s(s + 4)(s + 5)C(s)−

A ramp r(t) = 3t is applied to a unity-feedback loop with G(s) = 20(s + 4)/(s(s + 4)(s + 5)). Find the steady-state error ess.

G(s) = 20(s + 4)/(s(s + 4)(s + 5))r(t) = 3t
ess =
5.Hard
R(s)+Kp​ + Ki​/s1s + 4C(s)−

A PI controller C(s) = Kp + Ki/s drives the plant G(s) = 1/(s + 4) in a unity-feedback loop. The closed loop must have ωₙ = 5 rad/s and ζ = 0.6. Find the proportional gain Kp.

G(s) = 1/(s + 4)ωₙ = 5 rad/sζ = 0.6
Kp =
6.Hard
R(s)+Kp​ + Ki​/s2s + 4C(s)−

A PI controller C(s) = Kp + Ki/s drives the plant G(s) = 2/(s + 4) in a unity-feedback loop. The closed loop must have ωₙ = 6 rad/s and ζ = 0.5. Find the integral gain Ki.

G(s) = 2/(s + 4)ωₙ = 6 rad/sζ = 0.5
Ki =

Answer key

  1. 1. Ka = 3.2
  2. 2. Ka = 50
  3. 3. ess = 2.5
  4. 4. ess = 0.75
  5. 5. Kp = 2
  6. 6. Ki = 18

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