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

A plant G(s) = 10/(s + 10) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 10/(s + 10)unity negative feedback

T(0) =

2.Easy

In the block diagram the forward path has the gains G₁ = 6 and G₂ = 9 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 6G₂ = 9H = 1

T =

3.Medium

A plant G(s) = 5/(s + 4) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. A step of size 5 is applied at R. Find the steady-state output c_ss.

G(s) = 5/(s + 4)H = 0.25R = 5

c_ss =

4.Medium

A unity negative feedback loop has G(s) = 1(s + 2)/((s + 4)(s + 9)). A step of size 1 is applied at the reference. Find the steady-state error e_ss.

G(s) = 1(s + 2)/((s + 4)(s + 9))R = 1

e_ss =

5.Hard

The plant G(s) = K/((s + 4)(s + 5)(s + 8)) 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 + 4)(s + 5)(s + 8))unity negative feedback

ω = rad/s

6.Hard

The plant G(s) = 80/(s(s + 2)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their imaginary part ω_d (the positive value), in rad/s.

G(s) = 80/(s(s + 2))H = 0.5

ω_d = rad/s

Answer key

1. T(0) = 0.5
2. T = 0.9818
3. c_ss = 4.762
4. e_ss = 0.9474
5. ω = 9.592 rad/s
6. ω_d = 6.245 rad/s

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