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 + 2)(s + 6)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4/(s²(s + 2)(s + 6)). What is the system type N?

G(s) = 4/(s²(s + 2)(s + 6))
N =
2.Easy
R(s)+5s(s + 1)(s + 2)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 5/(s(s + 1)(s + 2)). Find the velocity error constant Kv.

G(s) = 5/(s(s + 1)(s + 2))
Kv =
3.Medium
r(t) = 10·t²/2+5(s + 2)s²(s + 4)C(s)−

The parabolic input r(t) = 10·t²/2 is applied to a unity-feedback loop with G(s) = 5(s + 2)/(s²(s + 4)). Find the steady-state error ess.

G(s) = 5(s + 2)/(s²(s + 4))r(t) = 10·t²/2
ess =
4.Medium
R(s)+K = 522s + 1C(s)−

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

G(s) = 2/(2s + 1)K = 5
ess = %
5.Hard
R(s)+K = 45s(s + 6)C(s)−

A proportional controller K = 4 drives the plant G(s) = 5/(s(s + 6)) in a unity-feedback loop. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 5/(s(s + 6))K = 4
ts = s
6.Hard
R(s)+K = 84s(s + 8)C(s)−

A proportional controller K = 8 drives the plant G(s) = 4/(s(s + 8)) in a unity-feedback loop. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 4/(s(s + 8))K = 8
ts = s

Answer key

  1. 1. N = 2
  2. 2. Kv = 2.5
  3. 3. ess = 4
  4. 4. ess = 9.091 %
  5. 5. ts = 1.333 s
  6. 6. ts = 1 s

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