Coordinated discrete-time super-twisting sliding mode controller coupled with time-delay estimator for PWR-based nuclear steam supply system

The coordination control problem for the core thermal power of the nuclear reactor (NR) and the water level of the nuclear steam generator (SG) is a crucial challenge for real-time model-based control of a pressurized- water reactor (PWR)-based nuclear steam supply system (NSSS). In this paper, a new coordinated discrete-time super-twisting sliding mode controller (CDTSTSMC) coupled with time-delay estimators (TDEs) is proposed, tackling the coordination control problem for the core thermal power of the NR and the water level of the nuclear SG in the presence of unknown dynamics, such as unmeasured system states, model uncertainties, parameter perturbations, and disturbances. First of all, the continuous-time dynamical models of both the NR and the SG in the PWR-based NSSS are described with consideration of unknown dynamics and then are transformed into discrete-time forms using the Euler approximation method. Two TDEs capable of estimating the unknown dynamics existing in the NR and the SG, respectively, are developed, which rely merely on the measurements of the PWR-based NSSS without the upper bounds of the uncertain dynamics being known. After that, a CDTSTSMC strategy, based on the discrete-time dynamical models describing both the NR and the SG, is proposed, allowing the core thermal power to be driven to a desired value while at the same time maintaining the desired water level in the SG with the help of TDEs. It is proved from stability analysis using a Lyapunov approach that under the proposed CDTSTSMC strategy coupled with the TDEs, the stability of the controlled PWR-based NSSS can be ensured in a wide range of load, where the control errors of both the NR and the SG are driven to a neighbor of zero. Finally, the proposed CDTSTSMC strategy coupled with the TDEs is compared with the previous discrete-time optimized proportional-integral-derivative controller (DTOPIDC) and fuzzy weighting controller (FWC). The simulation results reveal that the proposed CDTSTSMC strategy coupled with the TDEs outperforms the DTOPIDC and the FWC, particularly in rejecting unknown dynamics while maintaining both the core thermal power in the NR and the water level in the SG in their desired ranges.