State space model extraction of thermohydraulic systems
Uren, Kenneth Richard
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Many hours are spent by systemand control engineers deriving reduced order dynamicmodels portraying the dominant systemdynamics of thermohydraulic systems. A need therefore exists to develop a method that will automate the model derivation process. The model format preferred for control system design and analysis during preliminary system design is the state space format. The aim of this study is therefore to develop an automated and generic state space model extraction method that can be applied to thermohydraulic systems. Well developed system identiﬁcation methods exist for obtaining state space models from input-output data, but these models are not transparent, meaning the parameters do not have any physical meaning. For example one cannot identify system parameters such as heat or mass transfer coefﬁcients. Another approach is needed to derive state space models automatically. Many commercial thermohydraulic simulation codes follow a network approach towards the representation of thermohydraulic systems. This approach is probably one of the most advanced approaches in terms of technical development. It would therefore be useful to develop a state space extraction algorithm that would be able to derive reduced order state space models from network representations of thermohydraulic systems. In this regard a network approach is followed in the development of the state space extraction algorithm. The advantage of using a network-based extraction method is that the extracted state space model is transparent and the algorithm can be embedded in existing simulation software that follow a network approach. In this study an existing state space extraction algorithm, used for electrical network analysis, is modiﬁed and applied in a new way to extract state space models of thermohydraulic systems. A thermohydraulic system is partitioned into its respective physical domains which, unlike electrical systems, have multiple variables. Network representations are derived for each domain. The state space algorithm is applied to these network representations to extract symbolic state spacemodels. The symbolic parametersmay then be substitutedwith numerical values. The state space extraction algorithm is applied to small scale thermohydraulic systems such as a U-tube and a heat exchanger, but also to a larger, more complex system such as the Pebble Bed Modular Reactor Power Conversion Unit (PBMR PCU). It is also shown that the algorithm can extract linear, nonlinear, time-varying and time-invariant state space models. The extracted state space models are validated by solving the state space models and comparing the solutions with Flownex results. Flownex is an advanced and extensively validated thermo-ﬂuid simulation code. The state space models compared well with Flownex results. The usefulness of the state space model extraction algorithm in model-based control system design is illustrated by extracting a linear time-invariant state space model of the PBMR PCU. This model is embedded in an optimal model-based control scheme called Model-Predictive Control (MPC). The controller is compared with standard optimised control schemes such as PID and Fuzzy PID control. The MPC controller shows superior performance compared to these control schemes. This study succeeded in developing an automated state space model extraction method that can be applied to thermohydraulic networks. Hours spent on writing down equations from ﬁrst principles to derive reduced order models for control purposes can now be replaced with a click of a button. The need for an automated state space model extraction method for thermohydraulic systems has therefore been resolved.
- Engineering