Block diagrams worksheet with answers

Free printable Block diagrams worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
R(s)+10GC(s)0.025H+

An amplifier with gain G = 10 has positive feedback through a path with gain H = 0.025 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 10H = 0.025positive feedback
T =
2.Easy
R(s)+12s + 1G(s)C(s)−

A plant G(s) = 12/(s + 1) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 12/(s + 1)unity negative feedback
τ = s
3.Medium
R(s)+K(s + 8)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 8)(s + 12)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).

G(s) = K/((s + 8)(s + 12))unity negative feedback
K =
4.Medium
R(s)+3K+5s + 6G(s)C(s)4H₁−−

The plant G(s) = 5/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 3 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 5/(s + 6)H₁ = 4K = 3
p =
5.Hard
R(s)+Kcontroller+D(s)+7s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 7/(s + 4) in a unity negative feedback loop. A disturbance step of size 1 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.0875.

G(s) = 7/(s + 4)D = 1css ≤ 0.0875
K =
6.Hard
R(s)+K(s + 1)(s + 2)(s + 4)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 2)(s + 4)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/((s + 1)(s + 2)(s + 4))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = 13.33
  2. 2. τ = 0.07692 s
  3. 3. K = 4
  4. 4. p = −41
  5. 5. K = 10.86
  6. 6. ω = 3.742 rad/s

Full step-by-step solutions: practise this topic on examproblems.com.