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)+2(s + 4)s(s + 1)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2(s + 4)/(s(s + 1)(s + 10)). Find the velocity error constant Kv.

G(s) = 2(s + 4)/(s(s + 1)(s + 10))
Kv =
2.Easy
R(s)+10(s + 1)(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 10/((s + 1)(s + 2)). Find the position error constant Kp.

G(s) = 10/((s + 1)(s + 2))
Kp =
3.Medium
r(t) = 1t+Ks(s + 1)C(s)−

A unity-feedback loop with G(s) = K/(s(s + 1)) must follow the ramp r(t) = 1t with a steady-state error of 0.05. Find the gain K.

G(s) = K/(s(s + 1))r(t) = 1tess = 0.05
K =
4.Medium
r(t) = 1t+5s(s + 1)(s + 5)C(s)−

A ramp r(t) = 1t is applied to a unity-feedback loop with G(s) = 5/(s(s + 1)(s + 5)). Find the steady-state error ess.

G(s) = 5/(s(s + 1)(s + 5))r(t) = 1t
ess =
5.Hard
r(t) = 5t+5 + 5/s10(s + 1)(s + 4)C(s)−

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

C(s) = 5 + 5/sG(s) = 10/((s + 1)(s + 4))r(t) = 5t
ess =
6.Hard
R(s)+K = 104s(s + 8)C(s)−

A proportional controller K = 10 drives the plant G(s) = 4/(s(s + 8)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 4/(s(s + 8))K = 10
%OS = %

Answer key

  1. 1. Kv = 0.8
  2. 2. Kp = 5
  3. 3. K = 20
  4. 4. ess = 1
  5. 5. ess = 0.4
  6. 6. %OS = 7.691 %

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