Synthesis of robust PID controllers design with complete information on pre-specifications for the FOPTD systems

This paper provides a new design synthesis for the stable PID controllers to achieve the robustness to the system gain variations based on the first order plus time delay (FOPTD) systems. This designed PID controller is robust not only to the uncertainty of the plant steady-state gain, but also to the entire variations of the controller coefficients. The stability regions of the PID controller parameters are first determined according to a graphical stability criterion. According to two pre-specifications and the flat phase tuning constraint, a specific point in the three-dimension PID parameter-space can be determined. This designed PID controller can be, stable for sure as its parameter point is located in the stability region, and also robust to system gain variations according to the flat phase constraint. The important contribution of this proposed design synthesis is that, it provides the reliable procedures of designing the stable PID controller with robustness to the system gain variations, moreover, it can collect the complete information of the achievable design pre-specifications, which is the significant principle problem for the PID controllers synthesis in this paper.