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)+3s + 2G(s)C(s)−

A plant G(s) = 3/(s + 2) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 3/(s + 2)unity negative feedback
T(0) =
2.Easy
R(s)+16GC(s)0.02H+

An amplifier with gain G = 16 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 16H = 0.02positive feedback
T =
3.Medium
R(s)+Ks(s + 19)G(s)C(s)−

The plant G(s) = K/(s(s + 19)) 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 + 19))unity negative feedback
K =
4.Medium
R(s)+33s + 10G(s)C(s)0.25H−

A plant G(s) = 33/(s + 10) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. Find the time constant τ of the closed loop.

G(s) = 33/(s + 10)H = 0.25
τ = s
5.Hard
R(s)+32s(s + 5)G(s)C(s)1H−

The plant G(s) = 32/(s(s + 5)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 32/(s(s + 5))H = 1
σ =
6.Hard
R(s)+K(s + 3)(s + 7)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 3)(s + 7)(s + 8)) 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 + 3)(s + 7)(s + 8))unity negative feedback
ω = rad/s

Answer key

  1. 1. T(0) = 0.6
  2. 2. T = 23.53
  3. 3. K = 90.25
  4. 4. τ = 0.05479 s
  5. 5. σ = −2.5
  6. 6. ω = 10.05 rad/s

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