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)+4(s + 2)s²(s + 1)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 2)/(s²(s + 1)). Find the acceleration error constant Ka.

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

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

G(s) = 4(s + 2)/(s²(s + 4))
Ka =
3.Medium
r(t) = 1t+10(s + 2)s(s + 1)(s + 2)C(s)−

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

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

The parabolic input r(t) = 2·t²/2 is applied to a unity-feedback loop with G(s) = 20(s + 5)/(s²(s + 10)). Find the steady-state error ess.

G(s) = 20(s + 5)/(s²(s + 10))r(t) = 2·t²/2
ess =
5.Hard
R(s)+K = 24s(s + 2)C(s)−

A proportional controller K = 2 drives the plant G(s) = 4/(s(s + 2)) in a unity-feedback loop. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 4/(s(s + 2))K = 2
ts = s
6.Hard
r(t) = 2t+5 + 2/s10(s + 4)(s + 5)C(s)−

A PI controller C(s) = 5 + 2/s drives the plant G(s) = 10/((s + 4)(s + 5)) in a unity-feedback loop. Find the steady-state error ess for the ramp input r(t) = 2t.

C(s) = 5 + 2/sG(s) = 10/((s + 4)(s + 5))r(t) = 2t
ess =

Answer key

  1. 1. Ka = 8
  2. 2. Ka = 2
  3. 3. ess = 0.1
  4. 4. ess = 0.2
  5. 5. ts = 4 s
  6. 6. ess = 2

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