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 + 2)s²(s + 4)C(s)−

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

G(s) = 4(s + 2)/(s²(s + 4))
Ka =
2.Easy
r(t) = 2+K = 201s + 10y(t)−

A proportional controller K = 20 drives the plant G(s) = 1/(s + 10) in a unity-feedback loop. A step of size 2 is applied. Find the final value of the output y(∞).

G(s) = 1/(s + 10)K = 20r = 2
y(∞) =
3.Medium
r(t) = 10 + 5t+2(s + 2)s(s + 5)C(s)−

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

G(s) = 2(s + 2)/(s(s + 5))r(t) = 10 + 5t
ess =
4.Medium
R(s)+K = 520.5s + 1C(s)−

A process G(s) = 2/(0.5s + 1) is controlled by a proportional gain K = 5 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 2/(0.5s + 1)K = 5
ess = %
5.Hard
R(s)+K = 4010s(s + 8)C(s)−

A proportional controller K = 40 drives the plant G(s) = 10/(s(s + 8)) in a unity-feedback loop. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 10/(s(s + 8))K = 40
ts = s
6.Hard
R(s)+K = 501s(s + 8)C(s)−

A proportional controller K = 50 drives the plant G(s) = 1/(s(s + 8)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 1/(s(s + 8))K = 50
%OS = %

Answer key

  1. 1. Ka = 2
  2. 2. y(∞) = 1.333
  3. 3. ess = 6.25
  4. 4. ess = 9.091 %
  5. 5. ts = 1 s
  6. 6. %OS = 11.59 %

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