Spatial control of a large PHWR by piecewise constant periodic output feedback

The paper presents the design of piecewise constant periodic output feedback control for a discrete-time singularly perturbed system resulting from the discretization of a continuous-time standard singularly perturbed system. By a suitable linear transformation of state variables, the given continuous-time singularly perturbed model is converted into a block triangular form in which the fast subsystem is decoupled. The discrete-time model corresponding to the transformed model also exhibits a two time scale property if sampling period is larger than the parameter E. Now an output injection matrix is found that stabilizes the slow subsystem. The periodic output feedback gain is then calculated only for the slow subsystem and the same for the fast subsystem is set equal to zero. Finally the periodic output feedback gain for the composite system is obtained using the periodic output feedback gains computed separately for the slow and fast subsystems. An approach has been suggested whereby the determination of periodic output feedback gain for the slow subsystem can be converted into an optimization problem. By minimization of the suggested performance index the closed loop system behavior is improved. The method has been applied to a large pressurized heavy water reactor (PHWR) for control of xenon-induced spatial oscillations. A particular grouping of state variables has been suggested for obtaining the model in standard singularly perturbed form. The periodic output feedback gain is then calculated. The efficacy of control has been demonstrated by simulation of transient behavior of the nonlinear model of the PHWR.