![]() Lipinski and Vacroux, 1970 Lipinski W.C., Vacroux A.G., Optimal digital computer control of nuclear reactors, IEEE Trans.Lasarevic, 1972 Lasarevic B., Modal approach to the optimal control system synthesis of a nuclear reactor, Int.Kim, 1981 Kim S.H., Exact solution for suboptimal control of nuclear reactors with distributed parameters, Nuclear Sci.Karppinen, 1977 Karppinen J., Spatial reactor control methods, Nuclear Sci.Godet and Gorez, 1982 Godet J., Gorez R, Optimal control of primary coolant temperature in a nuclear plant, Automatica 18 ( 1982) 373– 383.El-Bossioni and Poncelet, 1974 El-Bossioni A.A., Poncelet C.B., Minimal time control of spatial xenon oscillations in nuclear power reactors, Nuclear Sci.Ebert, 1982 Ebert D.D., Practicality of and benefits from the applications of optimal control to pressurized water reactor maneuvers, Nuclear Technol.Cho and Grossmann, 1983 Cho N.Z., Grossmann L.M., Optimal control for xenon spatial oscillations in load following of a nuclear reactor, Nuclear Sci.Cherchas and Lake, 1977 Cherchas D.B., Lake R.T., An optimal algorithm for nuclear reactor load cycling, Automatica 13 ( 1977) 279– 285.Chaudhuri, 1972 Chaudhuri S.P., Distributed optimal control in nuclear reactors, Int.Bruni et al., 1974 Bruni C., Di Pillo G., Koch G., Bilinear systems: an appealing class of “nearly linear” systems in theory and applications, IEEE Trans.Berka, 1981 Berka M., A discrete-time control algorithm for nuclear reactor spatial control, in: M.A.Sc.Bereznai and Sinha, 1971 Bereznai G.T., Sinha N.K., Adaptive control of nuclear reactors using a digital computer, IEEE Trans.II, Kernforschungszentrum, Karlsruhe, 1981, p. Advances in Mathematical Methods for the Solution of Nuclear Engineering Problems, Munich, Federal Republic of Germany, 2, Vol. Beraha and Karppinen, 1981 Beraha D., Karppinen J., Power distribution control by hierarchical optimization techniques, Proc.Ash, 1979 Ash M., Nuclear Reactor Kinetics, McGraw-Hill, New York, 1979.Ten simulation tests are run for the latter two and it is found that the optimal control algorithm works better than the PI control algorithm at the cost of computational effort. Performance indices for complete state feedback, PI controlled and optimally controlled response are computed and compared. An alternate optimal control approach for improving the stable response is developed with the performance index being a function of the power deviation from a prescribed value. ![]() An incomplete state feedback algorithm for improving the stable response is proposed, that is, a proportional and integral (PI) control algorithm which uses only some of the measurable state variables. A complete state feedback control algorithm is then determined for a “base-load” cycle such that the resulting system is stable. The open-loop response is demonstrated to be unstable. This model, considering eight variables, is discretized with respect to time. A bilinear continuous-time model is used for the development. A discrete-time modal model and discrete-time control algorithmṡ for nuclear reactor space-time dynamics and control are developed.
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