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Marcus Müller
Marcus Müller
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I've been tasked with finding the pulse transfer function G(z) of the combination of the following equation \begin{equation}G_p(s) = {10\over (s+1)(s+2)(s+3)} \end{equation} and a zero order hold.

I started by combining the hold with the equation to obtain   

\begin{equation} {10(1-e^{-sT})\over s(s+1)(s+2)(s+3)} \end{equation} and

and then splitting this up to the equations \begin{equation} {1\over s(s+1)} \\ {1\over (s+2)(s+3)} \\ {10(1-e^{-sT})}\end{equation} finding

\begin{align} {1\over s(s+1)} \tag1\\ {1\over (s+2)(s+3)}\tag2 \\ {10(1-e^{-sT})}\tag3 \end{align}

finding the z transform of each one, and finally combining them together. I'm not sure if I've went about this in the right way, the answer I obtained seems very complicated and I can't find any similar examples. Can anyone who knows how to do this tell me if I'm going about this correctly and point me in the right direction?

I've been tasked with finding the pulse transfer function G(z) of the combination of the following equation \begin{equation}G_p(s) = {10\over (s+1)(s+2)(s+3)} \end{equation} and a zero order hold.

I started by combining the hold with the equation to obtain  \begin{equation} {10(1-e^{-sT})\over s(s+1)(s+2)(s+3)} \end{equation} and then splitting this up to the equations \begin{equation} {1\over s(s+1)} \\ {1\over (s+2)(s+3)} \\ {10(1-e^{-sT})}\end{equation} finding the z transform of each one, and finally combining them together. I'm not sure if I've went about this in the right way, the answer I obtained seems very complicated and I can't find any similar examples. Can anyone who knows how to do this tell me if I'm going about this correctly and point me in the right direction?

I've been tasked with finding the pulse transfer function G(z) of the combination of the following equation \begin{equation}G_p(s) = {10\over (s+1)(s+2)(s+3)} \end{equation} and a zero order hold.

I started by combining the hold with the equation to obtain 

\begin{equation} {10(1-e^{-sT})\over s(s+1)(s+2)(s+3)} \end{equation}

and then splitting this up to the equations

\begin{align} {1\over s(s+1)} \tag1\\ {1\over (s+2)(s+3)}\tag2 \\ {10(1-e^{-sT})}\tag3 \end{align}

finding the z transform of each one, and finally combining them together. I'm not sure if I've went about this in the right way, the answer I obtained seems very complicated and I can't find any similar examples. Can anyone who knows how to do this tell me if I'm going about this correctly and point me in the right direction?

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Ca01an
Ca01an
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Calculating pulse transfer function

I've been tasked with finding the pulse transfer function G(z) of the combination of the following equation \begin{equation}G_p(s) = {10\over (s+1)(s+2)(s+3)} \end{equation} and a zero order hold.

I started by combining the hold with the equation to obtain \begin{equation} {10(1-e^{-sT})\over s(s+1)(s+2)(s+3)} \end{equation} and then splitting this up to the equations \begin{equation} {1\over s(s+1)} \\ {1\over (s+2)(s+3)} \\ {10(1-e^{-sT})}\end{equation} finding the z transform of each one, and finally combining them together. I'm not sure if I've went about this in the right way, the answer I obtained seems very complicated and I can't find any similar examples. Can anyone who knows how to do this tell me if I'm going about this correctly and point me in the right direction?