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)+2GC(s)0.1H+

An amplifier with gain G = 2 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 = 2H = 0.1positive feedback
T =
2.Easy
R(s)3G₂7G₃+−5G₁C(s)

The signal R splits into two parallel blocks G₂ = 3 and G₃ = 7. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 5. Find the overall gain T = C/R.

G₁ = 5G₂ = 3G₃ = 7signs: + G₂, − G₃
T =
3.Medium
R(s)+K(s + 4)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 4)(s + 7)) 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 + 4)(s + 7))unity negative feedback
K =
4.Medium
R(s)+20K+5s + 6G(s)C(s)5H₁−−

The plant G(s) = 5/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 20 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 5/(s + 6)H₁ = 5K = 20
T(0) =
5.Hard
R(s)+5s + 5G₁+3s + 7G₂C(s)1H₁−0.5H₂−

Reduce the block diagram with G₁ = 5/(s + 5), G₂ = 3/(s + 7), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 5/(s + 5)G₂ = 3/(s + 7)H₁ = 1H₂ = 0.5
T(0) =
6.Hard
R(s)+Kcontroller+D(s)+8s + 9plantC(s)−

A proportional controller K drives the plant G(s) = 8/(s + 9) in a unity negative feedback loop. A disturbance step of size 5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.08889.

G(s) = 8/(s + 9)D = 5css ≤ 0.08889
K =

Answer key

  1. 1. T = 2.5
  2. 2. T = −20
  3. 3. K = 2.25
  4. 4. T(0) = 0.7634
  5. 5. T(0) = 0.2609
  6. 6. K = 55.13

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