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)+2G₁9G₂C(s)0.2H−

In the block diagram the forward path has the gains G₁ = 2 and G₂ = 9 in series, and the negative feedback path has the gain H = 0.2. Find the overall gain T = C/R.

G₁ = 2G₂ = 9H = 0.2
T =
2.Easy
R(s)+8G₁9G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 8 and G₂ = 9 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 8G₂ = 9H = 0.25
T =
3.Medium
R(s)+33s + 10G(s)C(s)2H−

A plant G(s) = 33/(s + 10) is controlled in a negative feedback loop whose sensor has the gain H = 2. A step of size 10 is applied at R. Find the steady-state output css.

G(s) = 33/(s + 10)H = 2R = 10
css =
4.Medium
R(s)+K(s + 1)(s + 5)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 5)) 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 + 1)(s + 5))unity negative feedback
K =
5.Hard
R(s)+Ks(s + 2)(s + 9)G(s)C(s)−

The plant G(s) = K/(s(s + 2)(s + 9)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/(s(s + 2)(s + 9))unity negative feedback
Kmax =
6.Hard
R(s)+K(s + 2)(s + 4)(s + 5)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 4)(s + 5)) 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 + 2)(s + 4)(s + 5))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = 3.913
  2. 2. T = 3.789
  3. 3. css = 4.342
  4. 4. K = 4
  5. 5. Kmax = 198
  6. 6. ω = 6.164 rad/s

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