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 + 4)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2(s + 2)/(s(s + 4)(s + 10)). Find the velocity error constant Kv.

G(s) = 2(s + 2)/(s(s + 4)(s + 10))
Kv =
2.Easy
R(s)+50s(s + 1)(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 50/(s(s + 1)(s + 5)). Find the velocity error constant Kv.

G(s) = 50/(s(s + 1)(s + 5))
Kv =
3.Medium
R(s)+K = 210.5s + 1C(s)−

A process G(s) = 1/(0.5s + 1) is controlled by a proportional gain K = 2 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 = 2
ess = %
4.Medium
r(t) = 0.5t+10s(s + 4)(s + 10)C(s)−

A ramp r(t) = 0.5t is applied to a unity-feedback loop with G(s) = 10/(s(s + 4)(s + 10)). Find the steady-state error ess.

G(s) = 10/(s(s + 4)(s + 10))r(t) = 0.5t
ess =
5.Hard
R(s)+K = 502s(s + 10)C(s)−

A proportional controller K = 50 drives the plant G(s) = 2/(s(s + 10)) in a unity-feedback loop. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 2/(s(s + 10))K = 50
ts = s
6.Hard
R(s)+K5s(s + 6)C(s)−

A proportional controller K drives the plant G(s) = 5/(s(s + 6)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.4.

G(s) = 5/(s(s + 6))ζ = 0.4
K =

Answer key

  1. 1. Kv = 0.1
  2. 2. Kv = 10
  3. 3. ess = 33.33 %
  4. 4. ess = 2
  5. 5. ts = 0.8 s
  6. 6. K = 11.25

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