Stability Analysis Of Delayed System Using Bodes Integral
  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. 
Anish Acharya, Debatri Mitra, Kaushik Halder
cs.SY