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) = 5+K = 45s + 10y(t)−

A proportional controller K = 4 drives the plant G(s) = 5/(s + 10) in a unity-feedback loop. A step of size 5 is applied. Find the final value of the output y(∞).

G(s) = 5/(s + 10)K = 4r = 5
y(∞) =
2.Easy
R(s)+5s(s + 2)(s + 4)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 5/(s(s + 2)(s + 4)). Find the velocity error constant Kv.

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

The parabolic input r(t) = 10·t²/2 is applied to a unity-feedback loop with G(s) = 10(s + 5)/(s²(s + 5)). Find the steady-state error ess.

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

The input r(t) = 2 + 1t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 10/(s(s + 2)(s + 10)). Find the steady-state error ess.

G(s) = 10/(s(s + 2)(s + 10))r(t) = 2 + 1t
ess =
5.Hard
R(s)+K = 101s(s + 5)C(s)−

A proportional controller K = 10 drives the plant G(s) = 1/(s(s + 5)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 1/(s(s + 5))K = 10
%OS = %
6.Hard
R(s)+K = 81s(s + 4)C(s)−

A proportional controller K = 8 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 = 8
%OS = %

Answer key

  1. 1. y(∞) = 3.333
  2. 2. Kv = 0.625
  3. 3. ess = 1
  4. 4. ess = 2
  5. 5. %OS = 1.732 %
  6. 6. %OS = 4.321 %

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