For a long time determining the stability issue of characteristic polynomials has played avery important role in Control System Engineering. This thesis addresses the traditionalcontrol issues such as stabilizing a system with any certain controller analyzingcharacteristic polynomial, yet a new perspective to solve them. Particularly, in this thesis,Proportional-Integral-Derivative (PID) controller is considered for a fixed structuredcontroller. This research aims to attain controller gain set satisfying given performancespecifications, not from the exact mathematical model, but from the empirical data of thesystem. Therefore, instead of a characteristic polynomial equation, a speciallyformulated characteristic rational function is investigated for the stability of the systemin order to use only the frequency data of the plant. Because the performance satisfactionis highly focused on, the characteristic rational function for the investigation of thestability is mainly dealt with the complex coefficient polynomial case rather than realone through whole chapters, and the mathematical basis for the complex case is prepared.For the performance specifications, phase margin is considered first since it is avery significant factor to examine the system's nominal stability extent (nominal performance). Second, satisfying H norm constraints is handled to make a more robustclosed loop feedback control system. Third, we assume undefined, but bounded outsidenoise, exists when estimating the system's frequency data. While considering theseuncertainties, a robust control system which meets a given phase margin performance, isattained finally (robust performance).In this thesis, the way is explained how the entire PID controller gain setssatisfying the given performances mentioned in the above are obtained. The approachfully makes use of the calculating software e.g. MATLAB(R) in this research and isdeveloped in a systematically and automatically computational aspect. The result ofsynthesizing PID controller is visualized through the graphic user interface of acomputer.
