International Journal of Computer Applications (0975 – 8887) Volume 176 – No.2, October 2017 33 Robust H2 Control of the Nuclear Reactor Systems Rehab M. Saeed Nuclear research center Egyptian Atomic Energy Authority Gamal M. El Bayoumi Aeronautics and Aerospace engineering dep. Cairo university ABSTRACT Robust control theory aims to analyze and design an accurate control system when the system has significant uncertainties. The goal is to synthesize a control law to maintain the system response and error signals to be within given tolerances despite the effect of the uncertainties on the system and to maintain the stability for all plant models in an expected band of uncertainty [1]. In this paper the design of a robust controller using the linear quadratic Gaussian, H2 optimal control and the robust tracking with disturbance rejection algorithms are represented where the fuel and coolant temperatures feedback are included. Keywords Robust control, kinetic equation, Linear Quadratic Gaussian, H2 optimal control, nuclear reactor. 1. INTRODUCTION The problem is to find a well-defined optimal controller to be applied to the nuclear reactor system. As the actual nuclear reactor system equations shows that the system is nonlinear in its nature, so it is difficult to design a suitable controller for this system directly, instead of that the design is based on a linearized model of the plant to be controlled [2], then the obtained controller is applied to the actual system. The design procedure goes through some simplifications such as linearization about an equilibrium point, lumped parameters approximations or time delay, etc. The result is an approximate plant or as referred often uncertain plant. These uncertainties are due to linearization of the nonlinear system, unmolded dynamics, sensor and actuator noise ,and undesired external disturbances, to overcome all of these uncertainties it is important to concern about how the controller will work with the actual plant and to make sure that the design objectives will be achieved, another important point to know is whether the controller takes care not only of the given uncertainties but also of uncertainties that will appear due to the component failures, changes in environmental conditions and, manufacturing tolerance [1]. Many approaches have been suggested and developed for the robust control problems such as conventional feedback, optimal H ∞ controller and robust gain scheduling controller [2] however there is no attention paid to the H2 optimal control, the solution of H 2 control problem is robust and optimal as it considers and deals with input and output disturbances. A special case of the H2 robust control is LQG/LTR method which can be solved in two stages where the disturbance is considered as a white noise and affects the output Cx as in the following equations        , (1)        (2)        (3) where z and y are the output vectors while w is the disturbance and u is the control signal. H2 optimal control aims to find a controller K which stabilizes the plant and minimizes the following cost function:         (4) Where    is the H2 norm,                      is the augmented system and K is the desired controller [2]. The cost function                 is minimized by the statistical space feedback controller      (5) Where               (6) And P is the solution of the following Riccati equation:                         (7) Hence H2 optimal estimation problem is equal to dual control problem where it is equivalent to state feedback control problem. The optimal controller consists of H2 optimal state estimator and H2 optimal state feedback of the estimated state which can be the same as Linear Quadratic Gaussian problem with loop transfer recovery (LQG/LTR) due to its effectiveness in accommodating plant uncertainty [3]. The procedure is a straight forward way beside it provides not only a desirable performance in normal of the controlled plant but also in fault accommodation. The paper discusses the robustness of the H2 optimal control and LQG controller to improve the nuclear reactor power response and the temperature response then the results is compared to those obtained using robust tracking problem with disturbance rejection. The paper is organized as follows: section 2 represents the nuclear reactor model (actual and nominal plants).Section3 introduce the H2 optimal control and LQG, robust tracking with disturbance rejection is represented in section 4. The results are found in section 5, and the main conclusions are summarized in section 6.