LMI Based Robust PID Controller Design for PWR with Bounded Uncertainty using Interval Approach

Pressurized Water Reactors are popular in the nuclear power generation industry due to their self-regulating and self-stabilizing features which in turn help them to perform load-following operation. However, fast power maneuvering is a challenging task due to inherent nonlinearity in a reactor. It leads to changes in the behavior with variation in reactor power. Further, the heat transfers from fuel to coolant and the reactivity changes due to variation in fuel and coolant temperatures introduces uncertainty in the system. Thus, it is essential to design a robust controller for load-following operation. In this paper, the point kinetics model of PWR coupled with the Mann's thermal-hydraulic model has been considered in addition to power sensor model and actuator model. This model has been identified as an interval system with bounded parametric uncertainties in measurements (fuel and coolant). The work then formulates a methodology to design a single robust PID controller using linear matrix inequalities by varying the weighting matrices. The outcomes have been validated using MATLAB simulations and discreetly exemplified in the result section.