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(t) = 10+4(s + 1)(s + 10)C(s)−

A step of size 10 is applied to a unity-feedback loop with G(s) = 4/((s + 1)(s + 10)). Find the steady-state error ess.

G(s) = 4/((s + 1)(s + 10))r(t) = 10·u(t)
ess =
2.Easy
R(s)+2(s + 5)s²(s + 1)(s + 3)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2(s + 5)/(s²(s + 1)(s + 3)). What is the system type N?

G(s) = 2(s + 5)/(s²(s + 1)(s + 3))
N =
3.Medium
r(t) = 5·t²/2+20(s + 5)s²(s + 5)C(s)−

The parabolic input r(t) = 5·t²/2 is applied to a unity-feedback loop with G(s) = 20(s + 5)/(s²(s + 5)). Find the steady-state error ess.

G(s) = 20(s + 5)/(s²(s + 5))r(t) = 5·t²/2
ess =
4.Medium
r(t) = 2 + 0.5t+2(s + 4)s(s + 10)C(s)−

The input r(t) = 2 + 0.5t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 2(s + 4)/(s(s + 10)). Find the steady-state error ess.

G(s) = 2(s + 4)/(s(s + 10))r(t) = 2 + 0.5t
ess =
5.Hard
R(s)+K = 402s(s + 8)C(s)−

A proportional controller K = 40 drives the plant G(s) = 2/(s(s + 8)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 2/(s(s + 8))K = 40
%OS = %
6.Hard
R(s)+K = 162s(s + 2)C(s)−

A proportional controller K = 16 drives the plant G(s) = 2/(s(s + 2)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 2/(s(s + 2))K = 16
%OS = %

Answer key

  1. 1. ess = 7.143
  2. 2. N = 2
  3. 3. ess = 0.25
  4. 4. ess = 0.625
  5. 5. %OS = 20.79 %
  6. 6. %OS = 56.88 %

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