The Influence of Resonance Scattering to the Doppler Reactivity Coefficient

The paper presents the results of an evaluation of the effect of scattering on resonances in calculating the Doppler reactivity coefficient using the data preparation algorithms implemented in the GRUCON processing program. A comparison of the free-gas model with the resonance scattering model and published results of calculations performed using other methods of data preparation is presented. On the benchmark of Mosteller for light water grids with various fuel compositions it was shown that taking into account resonances in the differential cross sections of elastic scattering of uranium-238 leads to a shift of the Doppler reactivity coefficient by ~ 10% towards negative values, thereby increasing the negative feedback with the temperature of the fuel

Feedback Control Design Maximizing the Region of Attraction of Stochastic Systems Using Polynomial Chaos Expansion

A feedback control design is proposed for stochastic systems with finite second moment which aims at maximising the region of attraction of the equilibrium point. Polynomial Chaos (PC) expansions are employed to represent the stochastic closed loop system by a higher dimensional set of deterministic equations. By using the PC expanded system representation, the available information on the uncertainty affecting the system explicitly enters the control design problem. Further, this allows Lyapunov methods for deterministic systems to be used to formulate the stability criteria certifying the region of attraction. These criteria are parametrized by the feedback gain and formulated in a polynomial optimization program which is solved using sum-of-squares methods. This approach offers flexibility in the choice of the stochastic feedback law and accounts for input constraints. The application is demonstrated by two numerical examples