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)+5(s + 4)s²(s + 2)C(s)−

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

G(s) = 5(s + 4)/(s²(s + 2))
Ka =
2.Easy
R(s)+2(s + 3)(s + 4)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2(s + 3)/((s + 4)(s + 10)). Find the position error constant Kp.

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

A unity-feedback loop has G(s) = K/((s + 4)(s + 5)). Find the gain K that gives a steady-state error of 25 % for a step input.

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

A unity-feedback loop with G(s) = K/(s(s + 4)) must follow the ramp r(t) = 10t with a steady-state error of 0.1. Find the gain K.

G(s) = K/(s(s + 4))r(t) = 10tess = 0.1
K =
5.Hard
R(s)+4 + Kd​s10s(s + 2)C(s)−

A PD controller C(s) = 4 + Kd·s drives the plant G(s) = 10/(s(s + 2)) in a unity-feedback loop. Find the derivative gain Kd that gives the closed loop a damping ratio ζ = 0.6.

G(s) = 10/(s(s + 2))Kp = 4ζ = 0.6
Kd = s
6.Hard
R(s)+20 + Kd​s10s(s + 3)C(s)−

A PD controller C(s) = 20 + Kd·s drives the plant G(s) = 10/(s(s + 3)) in a unity-feedback loop. Find the derivative gain Kd that gives the closed loop a damping ratio ζ = 0.6.

G(s) = 10/(s(s + 3))Kp = 20ζ = 0.6
Kd = s

Answer key

  1. 1. Ka = 10
  2. 2. Kp = 0.15
  3. 3. K = 60
  4. 4. K = 400
  5. 5. Kd = 0.5589 s
  6. 6. Kd = 1.397 s

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