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)+15s + 4G(s)C(s)−

A plant G(s) = 15/(s + 4) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 15/(s + 4)unity negative feedback
τ = s
2.Easy
R(s)+16G₁9G₂C(s)0.2H−

In the block diagram the forward path has the gains G₁ = 16 and G₂ = 9 in series, and the negative feedback path has the gain H = 0.2. Find the overall gain T = C/R.

G₁ = 16G₂ = 9H = 0.2
T =
3.Medium
R(s)+14s + 1G(s)C(s)0.1H−

A plant G(s) = 14/(s + 1) is controlled in a negative feedback loop whose sensor has the gain H = 0.1. A step of size 24 is applied at R. Find the steady-state output css.

G(s) = 14/(s + 1)H = 0.1R = 24
css =
4.Medium
R(s)+5(s + 2)(s + 5)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 5(s + 2)/((s + 5)(s + 9)). A step of size 10 is applied at the reference. Find the steady-state error ess.

G(s) = 5(s + 2)/((s + 5)(s + 9))R = 10
ess =
5.Hard
R(s)+Kcontroller+D(s)+7s + 5plantC(s)−

A proportional controller K drives the plant G(s) = 7/(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 0.056.

G(s) = 7/(s + 5)D = 2css ≤ 0.056
K =
6.Hard
R(s)+Kcontroller+D(s)+10s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 10/(s + 4) in a unity negative feedback loop. A disturbance step of size 0.5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.125.

G(s) = 10/(s + 4)D = 0.5css ≤ 0.125
K =

Answer key

  1. 1. τ = 0.05263 s
  2. 2. T = 4.832
  3. 3. css = 140
  4. 4. ess = 8.182
  5. 5. K = 35
  6. 6. K = 3.6

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