In the dissertation we study gain-scheduled control, fault-tolerant control and fault-tolerant and gain-scheduled control of a nuclear steam generator in the $L_2$-norm sense.
First, in order to implement these control systems we obtain the steam generator mathematical model of Kori unit 1 nuclear power plant. In general a steam generator model may be developed by using physical laws or by processing the plant input/output data obtained by performing various experiments. An exact steam generator model should produce the same behavior as the plant, provided the input to the model and initial conditions are exactly the same as those of the plant. But even if the exact model becomes available, its dimension is likely to be very high and its description is nonlinear or time varying to the point that its usefulness from the control design viewpoint is none. In the dissertation, a mathematical model of the steam generator of Kori unit 1 nuclear power plant is developed as the 4th order piecewise affine linear parameter varing (LPV) system. Through genetic algorithm that model is obtained with input/output data sets generated from Kori unit 1 nuclear power plant simulator, FISA.
Secondly, for a piecewise affine LPV steam generator model, we study to design gain-scheduled controllers in the sense of $L_2$-norm using linear matrix inequalities (LMIs) technique. A sufficient condition for gain-scheduled $L_2$ control is investigated in terms of an LMI using Lyapunov function. In addition, we extend it for uncertain piecewise affine LPV systems. We also test the performance of gain-scheduled $L_2$ control for Kori unit 1 steam generator model and Irving's model. The simulations show that the proposed controller is superior to that of PID controllers.
Third, we study a design method of fault-tolerant controller guaranteeing an acceptable level of performance and stability in the sense of $H_\infty$ norm, in the face of sensor and/or controller failures in the dual-controller configuration. A sufficient condition satisfying the fault-tolerant control expressed in terms of LMIs is obtained. The controller performance is test by simulator FISA and Irving's model under several fault situations.
Finally, based on the gain-scheduled $L_2$ control law and fault-tolerant control law, we investigate a fault-tolerant gain-scheduled $L_2$ control law for piecewise affine LPV systems. We induce sufficient condition for existence of fault-tolerant gain-scheduled $L_2$ control and show the controller design method in terms of LMIs. We obtain fault-tolerant gain-scheduled $L_2$ controller for Kori unit 1 and Irving's steam generator model and test the controller performance with simulator FISA and Irving model.
Consequently, in the dissertation, we has proposed the steam generator mathematical model of Kori unit 1 nuclear power plant, which is expressed as 4th order piecewise affine LPV system, and develop gain-scheduled control law, fault-tolerant control law, and fault-tolerant gain-scheduled $L_2$ control law. Also through the simulations it is shown that the proposed fault-tolerant gain-scheduled controller is effective for a nuclear steam generator system which requires a high reliable and good performance control system.
