International Journal of Computer Applications (0975 – 8887) Volume 178 – No.4, November 2017 15 Robust H ∞ Controller Design for the Nuclear Reactor Systems Rehab M. Saeed Nuclear Research Center Egyptian Atomic Energy Authority Gamal M. El Bayoumi Aerospace Engineering Dept. Cairo University Ibrahim E. Zeidan Computers and Systems Engineering Dept. Zagazig University ABSTRACT As it is important to improve the response of the nuclear reactor power system, many approaches tried to find the best way to design the suitable robust controller .This paper introduces the solution of H ∞ control problem of the nuclear reactor systems as a robust controller that achieves both the robustness and performance improvement. Keywords H∞, Robust control, nuclear reactor systems, robustness 1. INTRODUCTION The first mission of the design of the H∞ controller is to make the system insensitive towards the externals disturbances .this means that it is important to make the output independent of the external disturbance as possible [1]. The solution of the H ∞ problem can be formulated in many ways [2], one is the Glover-Doyle algorithm which is the classic formulation as it achieves the basic mixed performance and robustness objectives through solving a family of stabilizing controllers such that   (, ) ≤ Where P(s) represents the plant nominal transfer function, K(s) represents feedback controller and  is the H ∞ norm. Another techniques are used for the design of the H ∞ controllers such as two transfer function method and three transfer function method [2]. The properties of designing a controller using H ∞ method can be summarized as that the stabilizing feedback low u(s) =K(s) y(s) minimizes the norm of the closed loop transfer function, and it is suitable for the weighted mixed sensitivity problem where H ∞ controller always cancels the stable poles of the plant with its transmission zeroes so the unstable poles of the plant inside the specified bandwidth will be shifted to its mirror image once a H ∞ feedback loop is closed, another property is that using suitable weighting functions will allow very precise frequency domain loop shaping [3]. Mixed weight H-infinity controllers [4] will provide a closed loop response of the system according to the design specifications such as model uncertainty, disturbance attenuation at high frequencies,….etc. The H ∞ controllers are of high order this may lead to large control requirements, also additional frequency dependent weights are augmented to the system. The selection of the additional frequency dependent weights depends on what stability and performance design specifications are required to be shown [5]. Conventionally, H ∞ controller employs two transfer functions which divide a complex control problem into two separate sections, one deals with stability and the other deals with the performance. So the objective of designing H ∞ controller is to find a controller K, which based on the information v, generates a control signal u, which compensates the influence of w on z and minimizes the closed loop norm w to z. The paper is organized as follow, section 2 represents the nuclear reactor model (actual and nominal plants).Section3 introduce the H ∞ optimal control while the simulation results are represented in section 4 and the conclusion is introduced in section 5. 2. NUCLEAR REACTOR MODELING The model used in this paper is the nominal Pressurized Water Reactor model (PWR-type) TMI nuclear power plant reactor and its kinetic equation with one delayed neutron group and temperature feedback. The actual system equations can be summarized in the following equations [6]: dn dt = δρ−β ∧ n − λc (1) dc dt = β ∧ n − λc (2) Where, n ≡ neutron density ( n cm 3 ) c ≡ neutron precursor density  atom cm 3  λ ≡ effective precursor radioactive decay constants −1  ∧≡ effective prompt neutron lifetime(s) β ≡ fraction of delayed fission neutrons k ≡ k eff ≡ effective neutron multiplication factor δρ ≡ k−1 k ≡ reactivity (Since k≈1.000, δρ ≈k-1 ; at steady state k=1 , δρ =0) For computational purposes the normalized versions of equations (1) and (2) will be used so the normalized equations will be as follow: dn r dt = δρ−β ∧ n r + β ∧ c r (3) dc r dt = λn r − λc r (4) n 0 ≡ initial equilibrium steady − stateneutron density, c 0 ≡ initial equilibrium steady stateprecursor density