Sometimes it is desirable to choose control parameters or inputs which optimises some parameter associated with the system. Here P, PD and PI control and modified inputs are examined subject to minimisation of the quadratic performance index J given by the following equation where e is the error and m is a weighting parameter:-

The error determines the output from a proportional controller while the derivative of the error determines the output from a derivative controller.

Because of the numerical approximations used here for J, the numerical values obtained for J are approximate, accuracy increases with decreasing hgain.

When enabled some of the applets are illustrated below:-

COPYRIGHT © 2006 Cuthbert Nyack.