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 + 3)s(s + 4)(s + 5)C(s)−

A unity-feedback loop has the open-loop transfer function G(s) = 2(s + 3)/(s(s + 4)(s + 5)). Find the velocity error constant Kv.

G(s) = 2(s + 3)/(s(s + 4)(s + 5))
Kv =
2.Easy
r(t) = 2+K = 101s + 5y(t)−

A proportional controller K = 10 drives the plant G(s) = 1/(s + 5) in a unity-feedback loop. A step of size 2 is applied. Find the final value of the output y(∞).

G(s) = 1/(s + 5)K = 10r = 2
y(∞) =
3.Medium
r(t) = 1 + 2t+10s(s + 5)C(s)−

The input r(t) = 1 + 2t (a step plus a ramp) 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) = 1 + 2t
ess =
4.Medium
r(t) = 2 + 0.5t+10s(s + 2)(s + 5)C(s)−

The input r(t) = 2 + 0.5t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 10/(s(s + 2)(s + 5)). Find the steady-state error ess.

G(s) = 10/(s(s + 2)(s + 5))r(t) = 2 + 0.5t
ess =
5.Hard
R(s)+K = 1010s(s + 8)C(s)−

A proportional controller K = 10 drives the plant G(s) = 10/(s(s + 8)) in a unity-feedback loop. Find the percent overshoot %OS of the step response.

G(s) = 10/(s(s + 8))K = 10
%OS = %
6.Hard
R(s)+K1s(s + 2)C(s)−

A proportional controller K drives the plant G(s) = 1/(s(s + 2)) in a unity-feedback loop. Find the gain K that gives the closed loop a damping ratio ζ = 0.707.

G(s) = 1/(s(s + 2))ζ = 0.707
K =

Answer key

  1. 1. Kv = 0.3
  2. 2. y(∞) = 1.333
  3. 3. ess = 1
  4. 4. ess = 0.5
  5. 5. %OS = 25.38 %
  6. 6. K = 2.001

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