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)+10s²(s + 4)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 10/(s²(s + 4)). What is the system type N?

G(s) = 10/(s²(s + 4))
N =
2.Easy
R(s)+10(s + 2)(s + 1)(s + 2)C(s)−

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

G(s) = 10(s + 2)/((s + 1)(s + 2))
Kp =
3.Medium
R(s)+K = 1010.5s + 1C(s)−

A process G(s) = 1/(0.5s + 1) is controlled by a proportional gain K = 10 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

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

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

G(s) = 5(s + 1)/(s(s + 4))r(t) = 1 + 0.5t
ess =
5.Hard
R(s)+K = 52s(s + 5)C(s)−

A proportional controller K = 5 drives the plant G(s) = 2/(s(s + 5)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 2/(s(s + 5))K = 5
%OS = %
6.Hard
R(s)+K2s(s + 2)C(s)−

A proportional controller K drives the plant G(s) = 2/(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) = 2/(s(s + 2))ζ = 0.6
K =

Answer key

  1. 1. N = 2
  2. 2. Kp = 10
  3. 3. ess = 9.091 %
  4. 4. ess = 0.4
  5. 5. %OS = 1.732 %
  6. 6. K = 1.389

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