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)+17G₁9G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 17 and G₂ = 9 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 17G₂ = 9H = 0.1
T =
2.Easy
R(s)+18GC(s)0.01H+

An amplifier with gain G = 18 has positive feedback through a path with gain H = 0.01 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 18H = 0.01positive feedback
T =
3.Medium
R(s)+4(s + 8)(s + 2)(s + 7)G(s)C(s)−

A unity negative feedback loop has G(s) = 4(s + 8)/((s + 2)(s + 7)). A step of size 1 is applied at the reference. Find the steady-state error ess.

G(s) = 4(s + 8)/((s + 2)(s + 7))R = 1
ess =
4.Medium
R(s)+8s + 9G(s)C(s)0.2H−

A plant G(s) = 8/(s + 9) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.

G(s) = 8/(s + 9)H = 0.2
τ = s
5.Hard
R(s)+K(s + 3)(s + 5)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 3)(s + 5)(s + 7)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/((s + 3)(s + 5)(s + 7))unity negative feedback
Kmax =
6.Hard
R(s)+4s + 5G₁+7s + 4G₂C(s)0.5H₁−1H₂−

Reduce the block diagram with G₁ = 4/(s + 5), G₂ = 7/(s + 4), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 4/(s + 5)G₂ = 7/(s + 4)H₁ = 0.5H₂ = 1
T(0) =

Answer key

  1. 1. T = 9.387
  2. 2. T = 21.95
  3. 3. ess = 0.3043
  4. 4. τ = 0.09434 s
  5. 5. Kmax = 960
  6. 6. T(0) = 0.4275

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