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) = 2+K = 110s + 4y(t)−

A proportional controller K = 1 drives the plant G(s) = 10/(s + 4) in a unity-feedback loop. A step of size 2 is applied. Find the final value of the output y(∞).

G(s) = 10/(s + 4)K = 1r = 2
y(∞) =
2.Easy
r(t) = 1+50(s + 2)(s + 2)(s + 5)C(s)−

A step of size 1 is applied to a unity-feedback loop with G(s) = 50(s + 2)/((s + 2)(s + 5)). Find the steady-state error ess.

G(s) = 50(s + 2)/((s + 2)(s + 5))r(t) = 1·u(t)
ess =
3.Medium
r(t) = 0.5·t²/2+10(s + 5)s²(s + 4)C(s)−

The parabolic input r(t) = 0.5·t²/2 is applied to a unity-feedback loop with G(s) = 10(s + 5)/(s²(s + 4)). Find the steady-state error ess.

G(s) = 10(s + 5)/(s²(s + 4))r(t) = 0.5·t²/2
ess =
4.Medium
r(t) = 1t+10(s + 2)s(s + 4)C(s)−

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

G(s) = 10(s + 2)/(s(s + 4))r(t) = 1t
ess =
5.Hard
R(s)+K = 502s(s + 8)C(s)−

A proportional controller K = 50 drives the plant G(s) = 2/(s(s + 8)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 2/(s(s + 8))K = 50
tp = s
6.Hard
R(s)+Kp​ + Ki​/s10s + 4C(s)−

A PI controller C(s) = Kp + Ki/s drives the plant G(s) = 10/(s + 4) in a unity-feedback loop. The closed loop must have ωₙ = 5 rad/s and ζ = 0.8. Find the integral gain Ki.

G(s) = 10/(s + 4)ωₙ = 5 rad/sζ = 0.8
Ki =

Answer key

  1. 1. y(∞) = 1.429
  2. 2. ess = 0.09091
  3. 3. ess = 0.04
  4. 4. ess = 0.2
  5. 5. tp = 0.3428 s
  6. 6. Ki = 2.5

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