  The PID controller parameters can be adjusted in such a manner that it gives
the desired frequency response and the results are found using the Bodes
integral formula in order to adjust the slope of the nyquist curve in a desired
manner. The same idea is applied for plants with time delay . The same has also
been done in a new approach . The delay term is approximated as a transfer
function using Pade approximation and then the Bode integral is used to
determine the controller parameters. Both the methodologies are demonstrated
with MATLAB simulation of representative plants and accompanying PID
controllers. A proper comparison of the two methodologies is also done. The PID
controller parameters are also tuned using a real coded Genetic Algorithm (GA)
and a proper comparison is done between the three methods.
