User:Damian/Current Controller

ShoutWiki — express yourself and be heard!
Jump to navigation Jump to search
  • Plant
<math>G_{el} = \frac{1}{Ls+R}</math>
  • PI-Controller
<math>G_{PI} = K_r \left(1+\frac{1}{T_ns}\right)</math>
  • Closed loop transfer function
<math> G_c =\frac{K_r}{T_nL} \cdot \frac{T_ns+1}{s^2+\frac{R+K_r}{L}s+\frac{K_r}{T_nL}}</math>
  • Pole placement
<math>

\begin{array}{lcccc} s^2 & : & 1 & = & 1 \\ s & : & \frac{R+K_r}{L} & = & 2D\omega_0 \\ 1 & : & \frac{K_r}{T_nL} & = & \omega_0^2 \end{array} </math>

<math>

K_r = 2D\omega_0L-R </math>

<math>

T_n = \frac{2D}{\omega_0}-\frac{R}{L\omega_0^2} </math>

  • To avoid overshoot of integrator
<math> \omega_0 \leq \frac{1}{T_n}</math>
<math> \omega_0 \leq \frac{R}{L(2D-1)}</math>
  • With <math> D = 0.5 </math> the integrator causes no additional overshoot and <math> \omega_0 </math> can be choosen arbitrary.