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 + 2)s(s + 2)C(s)−

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

G(s) = 2(s + 2)/(s(s + 2))
Kv =
2.Easy
R(s)+4(s + 3)s²(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 3)/(s²(s + 10)). Find the acceleration error constant Ka.

G(s) = 4(s + 3)/(s²(s + 10))
Ka =
3.Medium
r(t) = 1 + 0.5t+4s(s + 1)(s + 5)C(s)−

The input r(t) = 1 + 0.5t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 4/(s(s + 1)(s + 5)). Find the steady-state error ess.

G(s) = 4/(s(s + 1)(s + 5))r(t) = 1 + 0.5t
ess =
4.Medium
R(s)+K(s + 4)(s + 10)C(s)−

A unity-feedback loop has G(s) = K/((s + 4)(s + 10)). Find the gain K that gives a steady-state error of 5 % for a step input.

G(s) = K/((s + 4)(s + 10))ess = 5 %
K =
5.Hard
R(s)+K = 510s(s + 8)C(s)−

A proportional controller K = 5 drives the plant G(s) = 10/(s(s + 8)) in a unity-feedback loop. Find the peak time tp of the step response.

G(s) = 10/(s(s + 8))K = 5
tp = s
6.Hard
R(s)+K = 102s(s + 4)C(s)−

A proportional controller K = 10 drives the plant G(s) = 2/(s(s + 4)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 2/(s(s + 4))K = 10
%OS = %

Answer key

  1. 1. Kv = 2
  2. 2. Ka = 1.2
  3. 3. ess = 0.625
  4. 4. K = 760
  5. 5. tp = 0.5388 s
  6. 6. %OS = 20.79 %

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