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)+8GC(s)0.1H+

An amplifier with gain G = 8 has positive feedback through a path with gain H = 0.1 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 8H = 0.1positive feedback
T =
2.Easy
R(s)+5G₁5G₂C(s)0.2H−

In the block diagram the forward path has the gains G₁ = 5 and G₂ = 5 in series, and the negative feedback path has the gain H = 0.2. Find the overall gain T = C/R.

G₁ = 5G₂ = 5H = 0.2
T =
3.Medium
R(s)+38s + 6G(s)C(s)0.2H−

A plant G(s) = 38/(s + 6) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.

G(s) = 38/(s + 6)H = 0.2
τ = s
4.Medium
R(s)+Ks(s + 4)G(s)C(s)−

The plant G(s) = K/(s(s + 4)) 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 + 4))unity negative feedback
K =
5.Hard
R(s)+62s(s + 10)G(s)C(s)2H−

The plant G(s) = 62/(s(s + 10)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 62/(s(s + 10))H = 2
ωd = rad/s
6.Hard
R(s)+Kcontroller+D(s)+7s + 9plantC(s)−

A proportional controller K drives the plant G(s) = 7/(s + 9) 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 0.03889.

G(s) = 7/(s + 9)D = 1css ≤ 0.03889
K =

Answer key

  1. 1. T = 40
  2. 2. T = 4.167
  3. 3. τ = 0.07353 s
  4. 4. K = 4
  5. 5. ωd = 9.95 rad/s
  6. 6. K = 24.43

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