A numerical design of the optimal PI and PID controller for linear plants with dead time based on the stability region discretization

Abstract The paper describes a practical numerical procedure of the design of the PI and PID controller for arbitrary SISO linear plant with dead time. The controller settings are obtained by optimization of an error response functional with a possible constraint reflecting the stability margin requirements, in the closed‐loop stability region. In this way, it is possible to find the controller settings giving fast and damped responses even in the situations when classical methods fail. The stability region is constructed automatically in the plain of the controller parameters and , using as a tuning parameter, optimized in an outer loop. This approach enables to include a low‐pass filter at the derivative component, which has to be used in real conditions. For automatic partitioning into stable and unstable regions, a high‐resolution discretization of the space of the controller parameters is used, which requires a suitable compact representation of the regions in the computer memory. The optimization of the controller parameters then can be carried out with advantage directly in the discrete domain by a restricted‐step algorithm. The computation is not a time‐demanding job for current personal computers, although it relies on their computational power and memory capacity. For implementation, any compiled programming language can be used without need of any additional software tools or libraries.