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)+40(s + 1)(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 40/((s + 1)(s + 5)). Find the position error constant Kp.

G(s) = 40/((s + 1)(s + 5))
Kp =
2.Easy
R(s)+C(s)G(s)C(s)−

The controller C(s) = 2 drives the plant G(s) = 1/(s(s + 10)) in a unity-feedback loop. What is the system type N of the loop?

C(s) = 2G(s) = 1/(s(s + 10))
N =
3.Medium
R(s)+K = 445s + 1C(s)−

A process G(s) = 4/(5s + 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) = 4/(5s + 1)K = 4
ess = %
4.Medium
R(s)+K = 12.50.5s + 1C(s)−

A process G(s) = 2.5/(0.5s + 1) is controlled by a proportional gain K = 1 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/(0.5s + 1)K = 1
ess = %
5.Hard
R(s)+K = 202s(s + 2)C(s)−

A proportional controller K = 20 drives the plant G(s) = 2/(s(s + 2)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 2/(s(s + 2))K = 20
tp = s
6.Hard
R(s)+K = 104s(s + 10)C(s)−

A proportional controller K = 10 drives the plant G(s) = 4/(s(s + 10)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 4/(s(s + 10))K = 10
tp = s

Answer key

  1. 1. Kp = 8
  2. 2. N = 1
  3. 3. ess = 5.882 %
  4. 4. ess = 28.57 %
  5. 5. tp = 0.5031 s
  6. 6. tp = 0.8112 s

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