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 = 35s + 10y(t)−

A proportional controller K = 3 drives the plant G(s) = 5/(s + 10) in a unity-feedback loop. A step of size 2 is applied. Find the final value of the output y(∞).

G(s) = 5/(s + 10)K = 3r = 2
y(∞) =
2.Easy
R(s)+4(s + 1)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4/((s + 1)(s + 10)). Find the position error constant Kp.

G(s) = 4/((s + 1)(s + 10))
Kp =
3.Medium
R(s)+K(s + 2)(s + 5)C(s)−

A unity-feedback loop has G(s) = K/((s + 2)(s + 5)). Find the gain K that gives a steady-state error of 25 % for a step input.

G(s) = K/((s + 2)(s + 5))ess = 25 %
K =
4.Medium
r(t) = 10t+Ks(s + 2)C(s)−

A unity-feedback loop with G(s) = K/(s(s + 2)) must follow the ramp r(t) = 10t with a steady-state error of 0.01. Find the gain K.

G(s) = K/(s(s + 2))r(t) = 10tess = 0.01
K =
5.Hard
R(s)+Kp​ + Ki​/s1s + 2C(s)−

A PI controller C(s) = Kp + Ki/s drives the plant G(s) = 1/(s + 2) in a unity-feedback loop. The closed loop must have ωₙ = 5 rad/s and ζ = 0.7. Find the integral gain Ki.

G(s) = 1/(s + 2)ωₙ = 5 rad/sζ = 0.7
Ki =
6.Hard
R(s)+K5s(s + 8)C(s)−

A proportional controller K drives the plant G(s) = 5/(s(s + 8)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.4.

G(s) = 5/(s(s + 8))ζ = 0.4
K =

Answer key

  1. 1. y(∞) = 1.2
  2. 2. Kp = 0.4
  3. 3. K = 30
  4. 4. K = 2000
  5. 5. Ki = 25
  6. 6. K = 20

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