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)+20(s + 5)s²(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 20(s + 5)/(s²(s + 5)). Find the acceleration error constant Ka.

G(s) = 20(s + 5)/(s²(s + 5))
Ka =
2.Easy
R(s)+C(s)G(s)C(s)−

The controller C(s) = 10(s + 1)/s drives the plant G(s) = 5/(s + 10) in a unity-feedback loop. What is the system type N of the loop?

C(s) = 10(s + 1)/sG(s) = 5/(s + 10)
N =
3.Medium
r(t) = 4t+2s(s + 4)(s + 10)C(s)−

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

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

A unity-feedback loop has G(s) = K/((s + 1)(s + 2)). Find the gain K that gives a steady-state error of 10 % for a step input.

G(s) = K/((s + 1)(s + 2))ess = 10 %
K =
5.Hard
R(s)+K = 105s(s + 4)C(s)−

A proportional controller K = 10 drives the plant G(s) = 5/(s(s + 4)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 5/(s(s + 4))K = 10
%OS = %
6.Hard
R(s)+K1s(s + 2)C(s)−

A proportional controller K drives the plant G(s) = 1/(s(s + 2)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.6.

G(s) = 1/(s(s + 2))ζ = 0.6
K =

Answer key

  1. 1. Ka = 20
  2. 2. N = 1
  3. 3. ess = 80
  4. 4. K = 18
  5. 5. %OS = 39.6 %
  6. 6. K = 2.778

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