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)+C(s)G(s)C(s)−

The controller C(s) = 4 drives the plant G(s) = 5/(s(s + 3)) in a unity-feedback loop. What is the system type N of the loop?

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

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

C(s) = 10(s + 2)/sG(s) = 1/(s + 10)
N =
3.Medium
r(t) = 2·t²/2+5(s + 5)s²(s + 5)C(s)−

The parabolic input r(t) = 2·t²/2 is applied to a unity-feedback loop with G(s) = 5(s + 5)/(s²(s + 5)). Find the steady-state error ess.

G(s) = 5(s + 5)/(s²(s + 5))r(t) = 2·t²/2
ess =
4.Medium
r(t) = 10 + 1t+20s(s + 10)C(s)−

The input r(t) = 10 + 1t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 20/(s(s + 10)). Find the steady-state error ess.

G(s) = 20/(s(s + 10))r(t) = 10 + 1t
ess =
5.Hard
R(s)+K = 401s(s + 4)C(s)−

A proportional controller K = 40 drives the plant G(s) = 1/(s(s + 4)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 1/(s(s + 4))K = 40
tp = s
6.Hard
R(s)+K = 1610s(s + 5)C(s)−

A proportional controller K = 16 drives the plant G(s) = 10/(s(s + 5)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 10/(s(s + 5))K = 16
%OS = %

Answer key

  1. 1. N = 1
  2. 2. N = 1
  3. 3. ess = 0.4
  4. 4. ess = 0.5
  5. 5. tp = 0.5236 s
  6. 6. %OS = 53.08 %

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