Question 21.33: A system is modelled by the differential equations x' + 2x ......

Engineering Mathematics A Foundation for Electronic, Electrical, Communications and Systems Engineers [1040294]

A system is modelled by the differential equations

x’ + 2x = f(t) (21.10)

2y’-y=x(t) (21.11)

In Equation (21.10) the input is f(t) and the output is x(t). In Equation (21.11), x(t) is the input and y(t) is the final output of the system. Find the overall system transfer function assuming zero initial conditions.

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The output from Equation (21.10) is x(t); this forms the input to Equation (21.11). The block diagrams for Equations (21.10) and (21.11) are combined into a single block diagram as shown in Figure 21.9. Using Rule 1, the overall system transfer function can then be found:

G(s)=\frac{Y(s)}{F(s)}=\frac{1}{(s+2)(2 s-1)}

This transfer function relates Y(s) and F(s) (see Figure 21.10).

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