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)+7GC(s)0.1H+

An amplifier with gain G = 7 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 = 7H = 0.1positive feedback
T =
2.Easy
R(s)3G₂10G₃+−3G₁C(s)

The signal R splits into two parallel blocks G₂ = 3 and G₃ = 10. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 3. Find the overall gain T = C/R.

G₁ = 3G₂ = 3G₃ = 10signs: + G₂, − G₃
T =
3.Medium
R(s)+58s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 58/(s(s + 10)). The reference is a ramp r(t) = 10·t. Find the steady-state error ess.

G(s) = 58/(s(s + 10))r(t) = 10·t
ess =
4.Medium
R(s)+52s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 52/(s(s + 8)). The reference is a ramp r(t) = 2·t. Find the steady-state error ess.

G(s) = 52/(s(s + 8))r(t) = 2·t
ess =
5.Hard
R(s)+Kcontroller+D(s)+1s + 5plantC(s)−

A proportional controller K drives the plant G(s) = 1/(s + 5) in a unity negative feedback loop. A disturbance step of size 2 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.004.

G(s) = 1/(s + 5)D = 2css ≤ 0.004
K =
6.Hard
R(s)+9s + 2G₁+1s + 2G₂C(s)0.5H₁−0.1H₂−

Reduce the block diagram with G₁ = 9/(s + 2), G₂ = 1/(s + 2), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 9/(s + 2)G₂ = 1/(s + 2)H₁ = 0.5H₂ = 0.1
T(0) =

Answer key

  1. 1. T = 23.33
  2. 2. T = −21
  3. 3. ess = 1.724
  4. 4. ess = 0.3077
  5. 5. K = 495
  6. 6. T(0) = 1.525

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