The Controller transfer function is given by \( G_c(s) = k(1+\frac{1}{T_rs})\)
The Analoge PI Controller is given by \(M_n=k(e_n + \frac {T}{T_r} \sum^{n}_{j=1} e_j_-_1)\)
where k=0.2, Tr=1 and Sampling Time T=0.1
\( G_c(s) = k(1+\frac{1}{T_rs})\)
\( G_c(s) = 0.2(1+\frac{1}{s})\)
\(= 0.2+\frac{0.2}{s} \Rightarrow = \frac{0.2s+0.2}{s}\)
To change from the s to z domain use \( \frac{1}{s} \Rightarrow \frac{z}{z-1}\)
I am having trouble with the transformation as the answer I am getting is
\(\frac{0.2z^2+0.2z}{z-1}\)
The transfer function of the control object with a ZOH is
\(G_H_P(z) = \frac {0.1}{z-0.9}\) and I have been trying to work out the closed loop system transfer function but it becomes complicated which makes me think that I am incorrect with \(\frac{0.2z^2+0.2z}{z-1}\)
Any suggestion??
Thanks
The Analoge PI Controller is given by \(M_n=k(e_n + \frac {T}{T_r} \sum^{n}_{j=1} e_j_-_1)\)
where k=0.2, Tr=1 and Sampling Time T=0.1
\( G_c(s) = k(1+\frac{1}{T_rs})\)
\( G_c(s) = 0.2(1+\frac{1}{s})\)
\(= 0.2+\frac{0.2}{s} \Rightarrow = \frac{0.2s+0.2}{s}\)
To change from the s to z domain use \( \frac{1}{s} \Rightarrow \frac{z}{z-1}\)
I am having trouble with the transformation as the answer I am getting is
\(\frac{0.2z^2+0.2z}{z-1}\)
The transfer function of the control object with a ZOH is
\(G_H_P(z) = \frac {0.1}{z-0.9}\) and I have been trying to work out the closed loop system transfer function but it becomes complicated which makes me think that I am incorrect with \(\frac{0.2z^2+0.2z}{z-1}\)
Any suggestion??
Thanks