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)+9s + 8G(s)C(s)−

A plant G(s) = 9/(s + 8) is placed in a unity negative feedback loop. A step of size 2 is applied at R. Find the steady-state output css.

G(s) = 9/(s + 8)unity negative feedbackR = 2
css =
2.Easy
R(s)+7G₁9G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 7 and G₂ = 9 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 7G₂ = 9H = 0.05
T =
3.Medium
R(s)+Ks(s + 12)G(s)C(s)−

The plant G(s) = K/(s(s + 12)) 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 + 12))unity negative feedback
K =
4.Medium
R(s)+12K+10s + 3G(s)C(s)2H₁−−

The plant G(s) = 10/(s + 3) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 12 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 10/(s + 3)H₁ = 2K = 12
p =
5.Hard
R(s)+7s + 5G₁+7s + 2G₂C(s)1H₁−0.1H₂−

Reduce the block diagram with G₁ = 7/(s + 5), G₂ = 7/(s + 2), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 7/(s + 5)G₂ = 7/(s + 2)H₁ = 1H₂ = 0.1
T(0) =
6.Hard
R(s)+20s + 4G₁+8s + 3G₂C(s)1H₁−1H₂−

Reduce the block diagram with G₁ = 20/(s + 4), G₂ = 8/(s + 3), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 20/(s + 4)G₂ = 8/(s + 3)H₁ = 1H₂ = 1
T(0) =

Answer key

  1. 1. css = 1.059
  2. 2. T = 15.18
  3. 3. K = 36
  4. 4. p = −143
  5. 5. T(0) = 0.982
  6. 6. T(0) = 0.7843

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