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The Reactor Cavity Cooling System (RCCS) in a High Temperature Gas-cooled Reactor (HTGR) provides protection to the concrete structures surrounding the reactor pressure vessel. The RCCS comprises stand pipes circulating water. These pipes may fundamentally be considered as U-tubes. Since the RCCS is critical in case of a Loss of Flow Accident (LOFA), it is very important to characterise the dynamics of such a system both for systems and control engineering purposes. Detailed Computational Fluid Dynamic (CFD) models do exist, but these models are too complex for the purposes mentioned. The majority of thermohydraulic simulation codes utilise a network approach towards representing thermohydraulic systems. This concept is used to extract state space models from graphic representations of such systems. The purpose of this paper is to illustrate the application of a State Space Model Extraction (SSME) method applied to a fundamental thermohydraulic system, namely a U-tube. The solution of the extracted state space model is compared with a validated systems CFD code called Flownex and shows good correlation.

The stability margin of a two degree-of-freedom self-sensing active magnetic bearing (AMB) is estimated by means of μ -analysis. The specific self-sensing algorithm implemented in this study is the direct current measurement method. Detailed black-box models are developed for the main subsystems in the AMB by means of discrete-time system identification. In order to obtain models for dynamic uncertainty in the various subsystems in the AMB, the identified models are combined to form a closed-loop model for the self-sensing AMB. The response of this closed-loop model is then compared to the original AMB’s response and models for the dynamic uncertainty are empirically deduced. Finally, the system’s stability margin for the modelled uncertainty is estimated by means of μ -analysis. The results show that μ -analysis is ill-equipped to estimate the stability margin of a nonlinear system

Self-sensing permits active magnetic bearings (AMBs) to consolidate the actuation and sensing functions into a single electromagnetic transducer. Eliminating the position sensing device as well as interfacing reduce potential system failure points, costs, and complexity. Self-sensing performance at present faces technical challenges such as magnetic cross-coupling, saturation, eddy currents, and system robustness. This work proposes an integrated self-sensing approach to collectively address mechanisms that contribute to modelling errors and position estimation inaccuracy. The self-sensing approach is based on the amplitude modulation technique and comprises a coupled reluctance network model (RNM) that is embedded in a nonlinear multiple input multiple output parameter estimator. The estimator employs a frequency-shifted model that is solved at a lower frequency to increase system performance. Furthermore, the RNM incorporates air gap fringing, complex permeability, and magnetic material nonlinearity terms. Magnetic saturation is accounted for using current scaling weights in the position estimation scheme. Basic functionality of the integrated self-sensing approach is demonstrated using an experimentally verified transient simulation model of the magnetic bearing. Verification and refinement of the RNM is accomplished through an iteration process using finite element method (FEM) results and experimental measurements. The simulation results show that the 40 node RNM can be accurate compared to an 80 000 node FEM analysis. Evaluation of the system stability margin indicates that the robustness of the magnetic bearing control is suitable for unrestricted long-term operation. Transactions of the SA Institute of Electrical Engineers

A design process comprising aspects of modelling and analysis is developed, implemented and verified for a flexible rotor active magnetic bearing system. The system is specified to experience the first three critical frequencies up to an operating speed of 10,000 rpm. Rotor stability at critical frequencies places specific constraints on the equivalent stiffness and damping parameters of the active magnetic bearing. An iterative design process is then initiated by an electromagnetic design of the radial active magnetic bearings resulting in parameters used in the detailed modelling of the system. Stiffness and damping parameters as well as system dynamic response are verified and used to design a flexible rotor. The magnetic bearing locations, displacement sensor locations and rotordynamic response are verified using finite element analysis. The design of the rotor stands central to the iterative design process since it impacts on the forces experienced by the active magnetic bearings as well as the critical frequencies of the active magnetic bearing system. Once constructed the actual active magnetic bearing system stiffness and damping parameters as well as dynamic response are compared to modelled results. The rotordynamic response is characterised by measuring the rotor displacement at pre-defined locations as the rotor traverses the critical frequencies. These results are compared with the predicted rotordynamic response