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36] Vaughan, N. D. and J. B. Gamble, “The modeling and simulation of a proportional solenoid valve,” the ASME Winter Annual Meeting, Dallas, TX, November 1990. [37] Urs Cristen, Martin F. Weilenmann, and Hans P. Geering, “Design of H2 and H_infinity Controllers with Two Degrees of Freedom,” Proceedings of American Control Conference, pp. 2391-2395, Baltimore, MD, June 29- July 1, 1994. List Of Symbols and Abbreviations ARE Algebraic Ricatti Equation CLTI Continuous Linear Time Invariant DLTI Discrete Linear Time Invariant G (s) Plant transfer function H8 Hardy Space LQ Linear Quadratic LQG Linear Quadratic Gaussian LQR Linear Quadratic Regulator LTI Linear Time Invariant LTR Loop Transfer Recovery MIMO Multiple Input Multiple Output MISO Multiple Input Single Output N (·) Actuator or sensor nonlinearity NI (·) Actuator or sensor inverse nonlinearity ORNL Oak Ridge National Laboratory PID Proportional Integral Derivative SISO Single Input Single Output ¦ A¦ Norm of matrix A ¦ y¦ Norm of vector y 27 Attachment I.

Bailey, “Robust Control Technique for Nuclear Power Plants,” Instrumentation and Controls Division, Oak Ridge National Laboratory, ORNL/TM-10916, March 1989. [15] H. Kwakernaak and R. Sivan, “Linear Optimal Control Systems,” Wiley-Interscience, New York, 1972. ,”Springer-Verlag, Berlin, 1995. , “Passive adaptive control of nonlinear systems,” International Journal of Adaptive Control and Signal Processing, vol. 7, no. 5, pp. 339-352, 1993 [19] Kransnoselskii, M. A. and A. V. Pokrovskii, “Control systems with Hysteresis,” Springer-Verlag, Berlin, 1983.

The variable G3 is positive. We divide the steam generator dynamics into four linearized regions with respect to operating power level and assume that the dynamics vary linearly over these regions. These variations of the plant parameters with respect to power level are presented in th graphical form. The actual plant parameters may vary differently, so we study the performance of the controller under the situations when the parameter drifts from what is projected by linear interpolation. Systematic approaches such as LQR method is used to derive the control law where some objectives functions are minimized to derive an optimal controller.

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