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)+4(s + 5)(s + 10)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4/((s + 5)(s + 10)). Find the position error constant Kp.

G(s) = 4/((s + 5)(s + 10))
Kp =
2.Easy
R(s)+4(s + 1)s(s + 3)(s + 4)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 4(s + 1)/(s(s + 3)(s + 4)). What is the system type N?

G(s) = 4(s + 1)/(s(s + 3)(s + 4))
N =
3.Medium
r(t) = 10t+Ks(s + 10)C(s)−

A unity-feedback loop with G(s) = K/(s(s + 10)) must follow the ramp r(t) = 10t with a steady-state error of 0.05. Find the gain K.

G(s) = K/(s(s + 10))r(t) = 10tess = 0.05
K =
4.Medium
r(t) = 2t+10s(s + 5)C(s)−

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

G(s) = 10/(s(s + 5))r(t) = 2t
ess =
5.Hard
R(s)+K = 401s(s + 5)C(s)−

A proportional controller K = 40 drives the plant G(s) = 1/(s(s + 5)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 1/(s(s + 5))K = 40
%OS = %
6.Hard
R(s)+K10s(s + 10)C(s)−

A proportional controller K drives the plant G(s) = 10/(s(s + 10)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.6.

G(s) = 10/(s(s + 10))ζ = 0.6
K =

Answer key

  1. 1. Kp = 0.08
  2. 2. N = 1
  3. 3. K = 2000
  4. 4. ess = 1
  5. 5. %OS = 25.87 %
  6. 6. K = 6.944

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