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)+50s(s + 1)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 50/(s(s + 1)). Find the velocity error constant Kv.

G(s) = 50/(s(s + 1))
Kv =
2.Easy
r(t) = 1+50(s + 3)(s + 5)(s + 10)C(s)−

A step of size 1 is applied to a unity-feedback loop with G(s) = 50(s + 3)/((s + 5)(s + 10)). Find the steady-state error ess.

G(s) = 50(s + 3)/((s + 5)(s + 10))r(t) = 1·u(t)
ess =
3.Medium
R(s)+K = 115s + 1C(s)−

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

The parabolic input r(t) = 1·t²/2 is applied to a unity-feedback loop with G(s) = 4(s + 4)/(s²(s + 4)). Find the steady-state error ess.

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

A PI controller C(s) = 5 + 4/s drives the plant G(s) = 2/((s + 1)(s + 10)) in a unity-feedback loop. Find the steady-state error ess for the ramp input r(t) = 5t.

C(s) = 5 + 4/sG(s) = 2/((s + 1)(s + 10))r(t) = 5t
ess =
6.Hard
r(t) = 2t+2 + 10/s4(s + 2)(s + 5)C(s)−

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

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

Answer key

  1. 1. Kv = 50
  2. 2. ess = 0.25
  3. 3. ess = 50 %
  4. 4. ess = 0.25
  5. 5. ess = 6.25
  6. 6. ess = 0.5

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