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Question 21.34: A system is represented by the differential equations 2x' -......

A system is represented by the differential equations

\begin{aligned} 2 x^{\prime}-x & =f(t) \\ y^{\prime}+3 y & =x(t) \\ z^{\prime}+z & =y(t) \end{aligned}

The initial input is f(t) and the final output is z(t). Find the overall system transfer function, assuming zero initial conditions.

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The transfer function for each equation is found and combined into one block diagram (see Figure 21.11). The three blocks are simplified to a single block as shown in Figure 21.12. The overall system transfer function is

G(s)=\frac{Z(s)}{F(s)}=\frac{1}{(2 s-1)(s+3)(s+1)} .
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