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) = 1+20(s + 2)(s + 4)C(s)−

A step of size 1 is applied to a unity-feedback loop with G(s) = 20/((s + 2)(s + 4)). Find the steady-state error ess.

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

A unity-feedback loop has the open-loop transfer function G(s) = 20/(s(s + 2)). Find the velocity error constant Kv.

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

A unity-feedback loop with G(s) = K/(s(s + 2)) must follow the ramp r(t) = 5t with a steady-state error of 0.1. Find the gain K.

G(s) = K/(s(s + 2))r(t) = 5tess = 0.1
K =
4.Medium
r(t) = 4t+20s(s + 10)C(s)−

A ramp r(t) = 4t is applied to a unity-feedback loop with G(s) = 20/(s(s + 10)). Find the steady-state error ess.

G(s) = 20/(s(s + 10))r(t) = 4t
ess =
5.Hard
R(s)+K10s(s + 4)C(s)−

A proportional controller K drives the plant G(s) = 10/(s(s + 4)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.707.

G(s) = 10/(s(s + 4))ζ = 0.707
K =
6.Hard
R(s)+K = 254s(s + 8)C(s)−

A proportional controller K = 25 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 = 25
%OS = %

Answer key

  1. 1. ess = 0.2857
  2. 2. Kv = 10
  3. 3. K = 100
  4. 4. ess = 2
  5. 5. K = 0.8002
  6. 6. %OS = 25.38 %

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