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) = 2+50(s + 1)(s + 4)C(s)−

A step of size 2 is applied to a unity-feedback loop with G(s) = 50/((s + 1)(s + 4)). Find the steady-state error ess.

G(s) = 50/((s + 1)(s + 4))r(t) = 2·u(t)
ess =
2.Easy
R(s)+20(s + 1)s(s + 1)(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 1)/(s(s + 1)(s + 5)). Find the velocity error constant Kv.

G(s) = 20(s + 1)/(s(s + 1)(s + 5))
Kv =
3.Medium
r(t) = 1 + 2t+4(s + 1)s(s + 2)(s + 10)C(s)−

The input r(t) = 1 + 2t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 4(s + 1)/(s(s + 2)(s + 10)). Find the steady-state error ess.

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

A ramp r(t) = 5t is applied to a unity-feedback loop with G(s) = 4(s + 2)/(s(s + 4)). Find the steady-state error ess.

G(s) = 4(s + 2)/(s(s + 4))r(t) = 5t
ess =
5.Hard
R(s)+K5s(s + 2)C(s)−

A proportional controller K drives the plant G(s) = 5/(s(s + 2)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.5.

G(s) = 5/(s(s + 2))ζ = 0.5
K =
6.Hard
r(t) = 1t+5 + 0.5/s20(s + 2)(s + 4)C(s)−

A PI controller C(s) = 5 + 0.5/s drives the plant G(s) = 20/((s + 2)(s + 4)) in a unity-feedback loop. Find the steady-state error ess for the ramp input r(t) = 1t.

C(s) = 5 + 0.5/sG(s) = 20/((s + 2)(s + 4))r(t) = 1t
ess =

Answer key

  1. 1. ess = 0.1481
  2. 2. Kv = 4
  3. 3. ess = 10
  4. 4. ess = 2.5
  5. 5. K = 0.8
  6. 6. ess = 0.8

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