Spatial control of a large pressurized heavy water reactor by fast output sampling technique

In this paper a method is presented to design a controller for discrete two time scale system based on fast output sampling technique. Using similarity transformation the two time scale system is converted into a block diagonal form which is then partitioned into two subsystems, namely, a fast subsystem and a slow subsystem. Now state feedback controls are designed separately for the slow subsystem and the fast subsystem. Then a composite state feedback control is obtained from the state feedback controls designed for subsystems to assign the eigenvalues of the entire system at arbitrary locations. This composite state feedback gain is realized by using fast output sampling feedback gain. Thus the states of the system are not needed for feedback. But in practice there are two problems in realizing the state feedback gain exactly viz. poor error dynamics and noise sensitivity. So a linear matrix inequality formulation is used to overcome these undesired effects. The method has been applied to a large pressurized heavy water reactor (PHWR) for control of xenon induced spatial oscillations. A particular grouping of the state variables has been considered to decompose the system into the slow subsystem and the fast subsystem. Then fast output sampling fedback gains have been calculated. The efficacy of the control has been demonstrated by simulation of transient behavior of the nonlinear model of the PHWR.