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.

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1.Easy
R(s)+4(s + 1)(s + 1)(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 1)/((s + 1)(s + 5)). Find the position error constant Kp.

G(s) = 4(s + 1)/((s + 1)(s + 5))
Kp =
2.Easy
R(s)+20(s + 1)s²(s + 1)(s + 4)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 1)/(s²(s + 1)(s + 4)). What is the system type N?

G(s) = 20(s + 1)/(s²(s + 1)(s + 4))
N =
3.Medium
R(s)+K(s + 5)(s + 10)C(s)−

A unity-feedback loop has G(s) = K/((s + 5)(s + 10)). Find the gain K that gives a steady-state error of 4 % for a step input.

G(s) = K/((s + 5)(s + 10))ess = 4 %
K =
4.Medium
R(s)+K(s + 1)(s + 5)C(s)−

A unity-feedback loop has G(s) = K/((s + 1)(s + 5)). Find the gain K that gives a steady-state error of 4 % for a step input.

G(s) = K/((s + 1)(s + 5))ess = 4 %
K =
5.Hard
R(s)+K4s(s + 2)C(s)−

A proportional controller K drives the plant G(s) = 4/(s(s + 2)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.6.

G(s) = 4/(s(s + 2))ζ = 0.6
K =
6.Hard
R(s)+K = 54s(s + 6)C(s)−

A proportional controller K = 5 drives the plant G(s) = 4/(s(s + 6)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 4/(s(s + 6))K = 5
%OS = %

Answer key

  1. 1. Kp = 0.8
  2. 2. N = 2
  3. 3. K = 1200
  4. 4. K = 120
  5. 5. K = 0.6944
  6. 6. %OS = 5.833 %

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