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)+50s(s + 5)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 50/(s(s + 5)(s + 10)). Find the velocity error constant Kv.

G(s) = 50/(s(s + 5)(s + 10))
Kv =
2.Easy
R(s)+4(s + 2)s²(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 2)/(s²(s + 5)). Find the acceleration error constant Ka.

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

The parabolic input r(t) = 4·t²/2 is applied to a unity-feedback loop with G(s) = 10(s + 3)/(s²(s + 1)). Find the steady-state error ess.

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

The input r(t) = 2 + 5t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 10(s + 3)/(s(s + 1)(s + 2)). Find the steady-state error ess.

G(s) = 10(s + 3)/(s(s + 1)(s + 2))r(t) = 2 + 5t
ess =
5.Hard
R(s)+K10s(s + 6)C(s)−

A proportional controller K drives the plant G(s) = 10/(s(s + 6)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.5.

G(s) = 10/(s(s + 6))ζ = 0.5
K =
6.Hard
R(s)+Kp​ + Ki​/s10s + 2C(s)−

A PI controller C(s) = Kp + Ki/s drives the plant G(s) = 10/(s + 2) in a unity-feedback loop. The closed loop must have ωₙ = 3 rad/s and ζ = 0.7. Find the proportional gain Kp.

G(s) = 10/(s + 2)ωₙ = 3 rad/sζ = 0.7
Kp =

Answer key

  1. 1. Kv = 1
  2. 2. Ka = 1.6
  3. 3. ess = 0.1333
  4. 4. ess = 0.3333
  5. 5. K = 3.6
  6. 6. Kp = 0.22

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