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)+4s²(s + 1)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4/(s²(s + 1)). What is the system type N?

G(s) = 4/(s²(s + 1))
N =
2.Easy
R(s)+4(s + 1)(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4/((s + 1)(s + 5)). Find the position error constant Kp.

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

A ramp r(t) = 2t is applied to a unity-feedback loop with G(s) = 5/(s(s + 1)(s + 10)). Find the steady-state error ess.

G(s) = 5/(s(s + 1)(s + 10))r(t) = 2t
ess =
4.Medium
R(s)+K = 1925s + 1C(s)−

A process G(s) = 2/(5s + 1) is controlled by a proportional gain K = 19 in a unity-feedback loop. Find the steady-state error ess for a step, as a percentage of the step size.

G(s) = 2/(5s + 1)K = 19
ess = %
5.Hard
R(s)+K = 52s(s + 4)C(s)−

A proportional controller K = 5 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 = 5
%OS = %
6.Hard
r(t) = 1t+1 + 2/s5(s + 1)(s + 10)C(s)−

A PI controller C(s) = 1 + 2/s drives the plant G(s) = 5/((s + 1)(s + 10)) in a unity-feedback loop. Find the steady-state error ess for the ramp input r(t) = 1t.

C(s) = 1 + 2/sG(s) = 5/((s + 1)(s + 10))r(t) = 1t
ess =

Answer key

  1. 1. N = 2
  2. 2. Kp = 0.8
  3. 3. ess = 4
  4. 4. ess = 2.564 %
  5. 5. %OS = 7.691 %
  6. 6. ess = 1

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