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)+5s(s + 1)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 5/(s(s + 1)(s + 10)). Find the velocity error constant Kv.

G(s) = 5/(s(s + 1)(s + 10))
Kv =
2.Easy
R(s)+20(s + 1)s²(s + 4)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 1)/(s²(s + 4)). Find the acceleration error constant Ka.

G(s) = 20(s + 1)/(s²(s + 4))
Ka =
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 5 % for a step input.

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

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

G(s) = 10(s + 2)/(s(s + 2))r(t) = 4t
ess =
5.Hard
R(s)+K1s(s + 6)C(s)−

A proportional controller K drives the plant G(s) = 1/(s(s + 6)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.4.

G(s) = 1/(s(s + 6))ζ = 0.4
K =
6.Hard
R(s)+K = 251s(s + 4)C(s)−

A proportional controller K = 25 drives the plant G(s) = 1/(s(s + 4)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 1/(s(s + 4))K = 25
%OS = %

Answer key

  1. 1. Kv = 0.5
  2. 2. Ka = 5
  3. 3. K = 190
  4. 4. ess = 0.4
  5. 5. K = 56.25
  6. 6. %OS = 25.38 %

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