An LMI based PID controller for load frequency control in power system

In this article a methodology for designing a minimum gain PID controller for load frequency control in power system is proposed. The resulting PID controller reduces the required control effort while guaranteeing that pre-defined design specifications like settling time and damping ratio are achieved in the response. For this purpose a subset of the complex plane corresponding to the design specifications is mapped onto a stability region in the coefficient space of the characteristic polynomial. This stability region in the polynomial coefficient space defines an LMI which is used as a constraint in minimizing the PID gains of the controller. The effectiveness of the proposed design methodology is demonstrated through case studies with steam and hydraulic units.