Spatial Control of a Large PHWR by Decentralized Periodic Output Feedback and Model Reduction Techniques

Abstract

Nuclear reactors of small and medium size are generally described by point kinetics model, however, this model is not valid in case of a large reactor, because in that flux shape undergoes appreciable variation with time. The behaviour of large reactor core can be explained with reasonable accuracy by spatial model like nodal model, which considers the reactor to be divided into number of regions or nodes. The thermal feedbacks which introduce nonlinearity into the problem, should be considered for realistic modeling. The spatial model of 540-MWe PHWR developed in is augmented with the dynamics of coolant and fuel temperatures and a 72nd-order model is obtained. As working with such a large model is difficult from the point of view of numerical computations, the new model having 14 inputs and 14 outputs, is suitably reduced by aggregation technique to obtain a 26th-order reduced model, which is more suitable to handle. The design of spatial controller by a state feedback based on reduced model needs the availability of all the states of the system for feedback purpose. As all the states of the reactor are not accessible for measurement, one has to resort to output feedback. Also, as the stability is not guaranteed by static output feedback, here the spatial controller is designed by periodic output feedback which is static in nature and at the same time guarantees complete closed-loop pole assignability. The various zones in a large reactor are coupled and a change in the control input to any zone causes respective change in the neutron flux of the other neighbouring zones, which may not be desirable. Therefore, a decentralized controller would serve as a better option, as it ensures that the input to any zone affects corresponding zone only and other zones are not affected by it. The above idea of periodic output feedback controller design yields a gain matrix with large magnitude, which amplifies measurement noise and is difficult to implement practically. Hence, it is desirable to keep the gain low. This objective is suitably expressed as LMI problem and putting appropriate design constraints, a better gain is obtained. The nonlinear model of the 540-MWe PHWR with the controller as above is tested for the reactivity transient simulation and the results of such a simulation are presented