Quadratic optimal control for PID control can be examined by the following applet:-

Some examples are:-

Parameters (0.9, 1.0, 0.5, 0.5, 0.9, 0.28, 2.0), J = 1.984808 with closed loop poles at -2.809, -1.099 ± j0.4643. This is a minimum for variation of K, Ti or Td.

Parameters (1.4, 1.0, 1.0, 0.5, 1.4, 0.41, 2.0), J = 1.988195 with closed loop poles at -2.595, -0.776 ± j0.4099. This is a minimum for variation of K, Ti or Td.

Gif image below shows how applet should appear.

COPYRIGHT © 2006 Cuthbert Nyack.