- #1
rakso
- 18
- 0
Summary:: Control Theory root equation pole
Hi, I ran into a simple question but somehow I can't get it right.
My work this far:
## G_0(s) = G(s) \cdot K \cdot \frac{1}{T_I s} = \frac{k}{\tau s +1} \cdot \frac{2\beta \tau -1}{k} \cdot \frac{2\beta^2 \tau}{Kks} = \frac{2\beta^2\tau}{s(\tau s +1)},##
## G_{cl}(s) = \frac{G_0}{1+G_0} = \frac{2\beta^2 \tau}{s(\tau s +1)+2\beta^2 \tau}.##
Hence the characteristic equation for the poles is ## \phi(s) = s(\tau s +1)+2\beta^2 \tau##, but ## s = -\beta \pm i \beta ## is not a root.
Does anyone see my error?
Muchos gracias
Hi, I ran into a simple question but somehow I can't get it right.
My work this far:
## G_0(s) = G(s) \cdot K \cdot \frac{1}{T_I s} = \frac{k}{\tau s +1} \cdot \frac{2\beta \tau -1}{k} \cdot \frac{2\beta^2 \tau}{Kks} = \frac{2\beta^2\tau}{s(\tau s +1)},##
## G_{cl}(s) = \frac{G_0}{1+G_0} = \frac{2\beta^2 \tau}{s(\tau s +1)+2\beta^2 \tau}.##
Hence the characteristic equation for the poles is ## \phi(s) = s(\tau s +1)+2\beta^2 \tau##, but ## s = -\beta \pm i \beta ## is not a root.
Does anyone see my error?
Muchos gracias
