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
R(s)8G₂2G₃+−7G₁C(s)

The signal R splits into two parallel blocks G₂ = 8 and G₃ = 2. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 7. Find the overall gain T = C/R.

G₁ = 7G₂ = 8G₃ = 2signs: + G₂, − G₃
T =
2.Easy
R(s)+6s + 1G(s)C(s)−

A plant G(s) = 6/(s + 1) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 6/(s + 1)unity negative feedback
T(0) =
3.Medium
R(s)+Ks(s + 16)G(s)C(s)−

The plant G(s) = K/(s(s + 16)) 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 + 16))unity negative feedback
K =
4.Medium
R(s)+1(s + 6)(s + 5)(s + 7)G(s)C(s)−

A unity negative feedback loop has G(s) = 1(s + 6)/((s + 5)(s + 7)). A step of size 10 is applied at the reference. Find the steady-state error ess.

G(s) = 1(s + 6)/((s + 5)(s + 7))R = 10
ess =
5.Hard
R(s)+12s + 5G₁+10s + 7G₂C(s)1H₁−1H₂−

Reduce the block diagram with G₁ = 12/(s + 5), G₂ = 10/(s + 7), 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 = 12/(s + 5)G₂ = 10/(s + 7)H₁ = 1H₂ = 1
T(0) =
6.Hard
R(s)+K(s + 1)(s + 4)(s + 5)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 4)(s + 5)) 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 + 4)(s + 5))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = 42
  2. 2. T(0) = 0.8571
  3. 3. K = 64
  4. 4. ess = 8.537
  5. 5. T(0) = 0.5854
  6. 6. ω = 5.385 rad/s

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