Suppose that the following continuous-time lead compensator [D(s)=frac{10(s+1)}{s+10}] is to be used in controlling the plant [G(s)=frac{20}{s(s+1)(s+10)}

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Suppose that the following continuous-time lead compensator

\[D(s)=\frac{10(s+1)}{s+10}\]


is to be used in controlling the plant \[G(s)=\frac{20}{s(s+1)(s+10)}
\]
If this system is to be implemented using a digital computer at a sampling interval 0.1 sec, determine the transfer function \(D(z)\) of the controller using:

(a) Pole-zero matching method

(b) Tustin's conversion method

(c) Bilinear transformation method

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