2286 zyxwvutsrqponmlk IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 39, NO. 6, DECEMBER 1992 LQG/LTR Robust Control of Nuclear Reactors with Improved Temperature Performance Adel Ben-Abdennour, Robert M. Edwards, and Kwang Y. Lee Abstract-Controller robustness is always a major concern. A controller that meets certain performance design objectives can- not be satisfactory unless it can preserve such quality in the presence of expected uncertainties. For nuclear reactors, a con- troller that preserves stability and performancefor a wide range of operating conditions and disturbances is especially desirable. This paper presents the design of a robust controller using the linear quadratic gaussian with loop transfer recovery (LQG/ LTR) for nuclear reactors with the objective of keeping a desir- able performance for reactor fuel temperature and temperature of the coolant leaving the reactor for a wide range of reactor power. The obtained results are compared to an observer-based state feedback optimal reactor temperature controller. Sensitiv- ity analysis of the dominant closed-loop eigenvalues and nonlin- ear simulation are used to demonstrate and compare the perfor- mance and robustness of the two controllers. The LQG/LTR approach is systematic, methodical, easy to design, and can give improved temperature performance over a wide range of reactor operation. I. INTRODUCTION E design of a control system is usually based on a times, the design procedure goes through the usual simpli- fication, such as linearization about an operating point or lumped parameter approximation, etc. The result is an approximate plant or, as often referred to, uncertain plant. The usual sources of uncertainties are due to lin- earization of a nonlinear system, unmodeled dynamics, sensor/actuator noise, and undesired external distur- bances on different parts of the system. The designer must, therefore, be concerned about how well the con- troller will work with the actual plant to achieve the design objectives, and whether it is possible to design a zyxwvu T” nominal model of the plant to be controlled. Often- Manuscript received June 10, 1992; revised August 14, 1992. This work was supported in part by a grant from the United States Department of Energy, University Grant no. DE-FG-07-89ER 12889, Intelligent Dis- tributed Control for Nuclear Power Plants. However, any findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of U.S. D.O.E. A. Ben-Abdennour and K. Y. Lee are with the Department of Electri- cal and Computer Engineering, The Pennsylvania State University, Uni- versity Park, PA 16802. R. M. Edwards is with the Department of Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802. IEEE Log Number 9203990. controller that takes care not only of these given uncer- tainties but also of others, such as those due to compo- nent failures, changes in environmental conditions, manu- facturing tolerances, and wear due to aging, etc. Over the last decade, the above challenging questions motivated theoreticians and practitioners to develop a control methodology which is, today, known as zyxw Robust zyx Control. The robust control problem is the problem of analyzing and designing an accurate control system given models with significant uncertainties [l]; synthesizing a control law which maintains system response and error signals to within prespecified tolerances despite the ef- fects of uncertainty on the system [2]; or maintaining stability for all plant models in an expected “band of uncertainty” [3]. Many approaches have been developed for the robust control problem and yet more are under investigation. However, the linear quadratic gaussian with loop transfer recovery (LQG/LTR) got a special attention due to its effectiveness in accommodating plant uncertainty in a more systematic yet more straight forward way. The LQG/LTR robust controller has been considered for a nuclear power plant deaerator and has been shown to provide not only desirable performance in normal opera- tion of the controlled plant, but also in fault accommoda- tion and for good robustness to plant uncertainties [4]-[7]. This paper demonstrates the robustness of the LQG/LTR controller for improving nuclear reactor tem- perature response, and compares it to a robust observer- based optimal state feedback controller designed in recent years [SI-[ 103. The systematic LQG/LTR controller gives improved temperature performance over a wide range of reactor operation. This paper is organized as follows. Section I1 presents the reactor modeling. Section I11 pre- sents the LQG/LTR controller design. Simulation results and discussion are given in Section IV, and conclusions are drawn in Section V. 11. REACTOR MODEL The nominal pressurized water reactor (PWR) model for controller design used in this paper is point kinetics with one delayed neutron group and temperature feed- back from lumped fuel and coolant temperature calcula- 0018-9499/92$03.00 zyxwvutsr 0 1992 IEEE