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)+10(s + 4)s²(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 10(s + 4)/(s²(s + 2)). Find the acceleration error constant Ka.

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

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 2)/(s²(s + 1)). Find the acceleration error constant Ka.

G(s) = 20(s + 2)/(s²(s + 1))
Ka =
3.Medium
R(s)+K = 42.52s + 1C(s)−

A process G(s) = 2.5/(2s + 1) is controlled by a proportional gain K = 4 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 2.5/(2s + 1)K = 4
ess = %
4.Medium
R(s)+K = 200.52s + 1C(s)−

A process G(s) = 0.5/(2s + 1) is controlled by a proportional gain K = 20 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 0.5/(2s + 1)K = 20
ess = %
5.Hard
R(s)+Kp​ + Ki​/s5s + 4C(s)−

A PI controller C(s) = Kp + Ki/s drives the plant G(s) = 5/(s + 4) in a unity-feedback loop. The closed loop must have ωₙ = 8 rad/s and ζ = 1. Find the proportional gain Kp.

G(s) = 5/(s + 4)ωₙ = 8 rad/sζ = 1
Kp =
6.Hard
R(s)+Kp​ + Ki​/s2s + 2C(s)−

A PI controller C(s) = Kp + Ki/s drives the plant G(s) = 2/(s + 2) in a unity-feedback loop. The closed loop must have ωₙ = 2 rad/s and ζ = 0.6. Find the integral gain Ki.

G(s) = 2/(s + 2)ωₙ = 2 rad/sζ = 0.6
Ki =

Answer key

  1. 1. Ka = 20
  2. 2. Ka = 40
  3. 3. ess = 9.091 %
  4. 4. ess = 9.091 %
  5. 5. Kp = 2.4
  6. 6. Ki = 2

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