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.

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1.Easy

The signal R splits into two parallel blocks G₂ = 13 and G₃ = 9. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 8. Find the overall gain T = C/R.

G₁ = 8G₂ = 13G₃ = 9signs: + G₂, + G₃

T =

2.Easy

A plant G(s) = 6/(s + 8) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 6/(s + 8)unity negative feedback

p =

3.Medium

A unity negative feedback loop has G(s) = 4(s + 3)/((s + 6)(s + 9)). A step of size 2 is applied at the reference. Find the steady-state error e_ss.

G(s) = 4(s + 3)/((s + 6)(s + 9))R = 2

e_ss =

4.Medium

The plant G(s) = K/((s + 3)(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 + 3)(s + 7))unity negative feedback

K =

5.Hard

The plant G(s) = K/((s + 1)(s + 3)(s + 6)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/((s + 1)(s + 3)(s + 6))unity negative feedback

ω = rad/s

6.Hard

The plant G(s) = K/((s + 1)(s + 3)(s + 7)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/((s + 1)(s + 3)(s + 7))unity negative feedback

ω = rad/s

Answer key

1. T = 176
2. p = −14
3. e_ss = 1.636
4. K = 4
5. ω = 5.196 rad/s
6. ω = 5.568 rad/s

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