In my opinion, for a certain plant, we can find the PID parameters by minimizing different indices using say, genetic algorithm, then we select the set of parameters that gives the best closed-loop response.
All methods are valuable, but if you have process model, pole placement procedure, can ensure good performance. For pole placement you can use e.g. Ioan Doree Landau books and papers (RST controller in PID representation).
It is very interesting question. There are several techniques to design PID controller. For changing of Kp, Ki, Kd permutation-ally creating the effect of system transient responses. Firstly, Determination of proper Controller is very impotent. You may go through with my paper http://www.ijsrp.org/research-paper-0812/ijsrp-p0823.pdf Table 1 (Tuning effect ). To chose perfect controller . After that, the actual value setting consideration of theses Gains, you first try traditional ZN, CC etc. different method then you try for advanced computational technological method (PSO,GA, BF etc). every case you determine the output responses and calculate the several errors. In which case the error is minimum, set that Controller as a perfect controller. You get total MATLAB code in this paper http://www.ijsrp.org/research-paper-0812/ijsrp-p0823.pdf ....I hope it may helpful to you...... Thank you...