A nonlinear optimal control approach for pressurized-water nuclear reactors

A new nonlinear optimal control method is proposed for solving the problem of control and stabilization of pressurized-water nuclear reactors (PWR). The dynamic model of this nuclear reactor is not directly feedback linearizable. Besides, the solution of the associated control problem is nontrivial due to complex nonlinear dynamics and the use of one single control input. To apply the proposed nonlinear optimal control method, the dynamic model of the pressurized-water reactor undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization takes place through first-order Taylor series expansion and through the computation of the Jacobian matrices of the nuclear reactor’s state-space description. For the approximately linearized model of the nuclear reactor an H-infinity feedback controller is designed. Actually, the H-infinity controller stands for the solution of the optimal control problem for the nuclear reactor under uncertainty and external perturbations. For the computation of the feedback gains of the H-infinity controller an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control algorithm are proven through Lyapunov analysis. First, it shown that the control scheme achieves H-infinity tracking performance which signifies robustness for the control loop of the nuclear reactor under uncertainties and exogenous disturbances. Next, it is also shown that the control loop of the pressurized-water nuclear reactor is globally asymptotically stable. The proposed control method achieves fast and accurate tracking of setpoints under moderate variations of the control inputs.