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)+16s + 8G(s)C(s)−

A plant G(s) = 16/(s + 8) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 16/(s + 8)unity negative feedback
τ = s
2.Easy
R(s)+16GC(s)0.04H+

An amplifier with gain G = 16 has positive feedback through a path with gain H = 0.04 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 16H = 0.04positive feedback
T =
3.Medium
R(s)+Ks(s + 10)G(s)C(s)−

The plant G(s) = K/(s(s + 10)) 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(s + 10))unity negative feedback
K =
4.Medium
R(s)+K(s + 3)(s + 9)G(s)C(s)−

The plant G(s) = K/((s + 3)(s + 9)) 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 + 3)(s + 9))unity negative feedback
K =
5.Hard
R(s)+Ks(s + 3)(s + 9)G(s)C(s)−

The plant G(s) = K/(s(s + 3)(s + 9)) 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(s + 3)(s + 9))unity negative feedback
ω = rad/s
6.Hard
R(s)+62s(s + 9)G(s)C(s)1H−

The plant G(s) = 62/(s(s + 9)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 62/(s(s + 9))H = 1
ωd = rad/s

Answer key

  1. 1. τ = 0.04167 s
  2. 2. T = 44.44
  3. 3. K = 25
  4. 4. K = 9
  5. 5. ω = 5.196 rad/s
  6. 6. ωd = 6.461 rad/s

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