An accurate estimate of the gasturbine inlet air temperature is essential to the stability of the engine since its control depends on it. Most supersonic military aircrafts have a design with the engine integrated in the fuselage which requires a rather long inlet duct from the inlet opening to the engine face. Such duct can affect the temperature measurement because of the heat flow between the inlet air and the duct skin. This is especially true when the temperature sensor is mounted close to the duct skin, which is the case for most engines. This master thesis project therefore revolved around developing a method to better estimate the engine inlet temperature and to compensate for the disturbances which a temperature sensor near the duct skin can be exposed to. A grey box model of the system was developed based on heat transfer equations between different components in the inlet, as well as predictions of temperature changes based on a temperature model of the atmosphere and thermodynamic laws. The unknown parameters of the grey box model were estimated using flight data and tuned to minimize the mean square of the prediction error. The numerical optimization of the parameters was performed using the Matlab implementations of the BFGS and SQP algorithms. An extended Kalman filter based on the model was also implemented. The two models were then evaluated in terms of how much the mean squared error was reduced compared to just using the sensor measurement to estimate the inlet air temperature. It was also analyzed how much the models reduced the prediction errors. A cross-correlation analysis was also done to see how well the model utilized the input signals. The results show that the engine inlet temperature can be estimated with good accuracy. The two models were shown to reduce the mean square of the prediction error by between 84 % and 89 % if you compare with just using the temperature sensor to estimate the temperature. The model which utilized the Kalman filtering was shown to perform slightly better than the other model. The relevance of different subcomponents of the model were investigated in order to see if the model could be simplified and maintain similar accuracy. Some investigations were also done with the relationship between different temperatures of the inlet to further understand the flow patterns of the inlet and to perhaps improve the model even more in the future. / En korrekt uppskattning av lufttemperaturen vid inloppet till turbofläktmotorer är väsentlig för stabil motorfunktion eftersom den direkt påverkar motorregleringen. För militära flygplan där motorn är integrerad i flygplansskrovet krävs ofta en relativt lång luftkanal för att leda luften till motorn. En sådan kanal kan påverka temperaturmätningen på grund av det värmeutbyte som sker mellan luften i kanalen och kanalväggen, speciellt då temperaturgivaren placeras nära kanalväggen eftersom den då kan påverkas av temperaturgränsskiktet nära kanalväggen. Det här examensarbetet handlade därför om att utveckla en metod för att bättre skatta temperaturen i motorinloppet och kompensera för de störningar som en temperaturgivare nära kanalväggen kan utsättas för. En fysikalisk model av systemet togs fram baserat på värmeöverföringen mellan olika komponenter i luftintagskanalen, samt ett sätt att förutse temperaturändringar baserat på en generell temperaturmodell för atmosfären och termodynamiska lagar. Många parametrar i den fysikaliska modellen av systemet var dock okända så dessa skattades baserat på flygdata. Parametrarna anpassades till modellen på ett sådant sätt att den genomsnittliga kvadraten av modellens skattningsfel minimerades. Den numeriska optimeringen av parametrarna utfördes med hjälp av Matlabs implementation av BFGS- och SQP-algoritmerna. Ett utökat kalmanfilter baserat på modellen implementerades också. De två modellerna utvärderades i termer av hur mycket de reducerade kvadraten av skattningsfelet och jämfördes med att endast använda temperaturmätningarna för att skatta temperaturen. Det undersöktes även hur mycket skattningsfelen reducerades. Korskorrelationen mellan skattningsfelet och insignalerna undersöktes även för att se om modellen hade utnyttjat insignalerna på ett bra sätt. Resultaten visar att det går att skatta temperaturen i motorinloppet med god noggrannhet. De två modellerna visade sig reducera den genomsnittliga kvadraten av skattningsfelet med mellan 84 % och 89 % om man jämför med att bara använda temperaturgivaren för att skatta temperaturen. Den modell som utnyttjade kalmanfiltrering visade sig ge något bättre resultat än den andra modellen. Olika delmodellers relevans undersöktes för att se om modellen kunde förenklas utan att modellens noggrannhet äventyrades. Några tester utfördes även för att undersöka förhållandet mellan olika temperaturer i intaget. Detta för att få en bättre förståelse för strömningen i intaget och resultatet skulle eventuellt kunna användas för att förbättra modellen ytterligare i framtiden.

Over the last decades, the frequency on the Nordic electrical power grid has deteriorated. Therefore, new stricter requirements are developed for the hydropower delivering regulating active power on the Frequency Containment Reserve market (FCR). This thesis aims to investigate the possibility of modeling two double-regulated hydropower plants, referred to as Unit 1 and 2, to evaluate their compliance with the new FCR-requirements.  By modeling the hydropower plants, the first goal was to find a model structure that captures the essential dynamics of the systems. A second goal was to evaluate whether the two units currently fulfill the new FCR-requirements, and investigate how the turbine governors’ settings could be optimized to fulfill the new requirements. Data obtained from FCR-tests was used in MATLAB to evaluate the two stations’ dynamic stability and performance requirements. Through system identification in MATLAB, grey-box modeling was used to create linear and non-linear turbine and waterways models for Unit 1 and Unit 2. The non-linear turbine and waterways models were implemented in Simulink, together with corresponding turbine governors, to find optimal parameter settings to fulfill the FCR-requirements.  The evaluation of the new FCR-requirements shows that none of the two units fulfills the dynamic stability requirement. However, Unit 1 fulfills the performance requirement. The results imply that double-regulated turbines will most likely have difficulties fulfilling the new requirements, which will cause major consequences in improving the frequency regulation quality. The results from the grey-box modeling present that the linear models are not validated with the step response data, due to not capturing the system dynamics when compared with provided data from the units. On the other hand, the non-linear models are validated with step response data as the model captures the system dynamics more accurately. However, the non- linear Simulink models cannot capture the dynamics of the hydropower systems for sinusoidal signals with varying frequencies which are used in the new FCR-requirement test. Consequently, the thesis has no result of the optimal parameter setting of the turbine governors to fulfill the new FCR-requirements. In conclusion, the grey-box models, with the level of detail presented in this thesis, are inadequate in capturing the system’s dynamics to evaluate the new FCR-requirements. Thus, the thesis contributes to filling a knowledge gap within the area of modeling for frequency regulation.

<p>This thesis considers the problem of making dynamic models for industrial processes by combining physical modelling with experimental data. The focus is on distributed parameter systems, that is, systems for which the model structure involves partial differential equations (PDE). Distributed parameter systems are important in many applications, e.g., in chemical process systems and in intracellular biochemical processes, and involve for instance all forms of transport and transfer phenomena. For such systems, the postulated model structure usually requires a finite dimensional approximation to enable identification and validation using experimental data. The finite dimensional approximation involves translating the PDE model into a set of ordinary differential equations, and is termed model reduction.</p><p>The objective of the thesis is two-fold. First, general PDE model reduction methods which are efficient in terms of model order for a given level of accuracy are studied. The focus here is on a class of methods called moving mesh methods, in which the discretization mesh is considered a dynamic degree of freedom that can be used for reducing the model reduction error. These methods are potentially highly efficient for model reduction of PDEs, but often suffer from stability and robustness problems. In this thesis it is shown that moving mesh methods can be cast as standard feedback control problems. Existing moving mesh methods are analyzed based on tools and results available from control theory, and plausible explanations to the robustness problems and parametric sensitivity experienced with these methods are provided. Possible remedies to these problems are also proposed. A novel moving finite element method, Orthogonal Collocation on Moving Finite Elements (OCMFE), is proposed based on a simple estimate of the model reduction error combined with a low order linear feedback controller. The method is demonstrated to be robust, and hence puts only small demands on the user.</p><p>In the second part of the thesis, the integration of PDE model reduction methods with grey-box modelling tools available for finite dimensional models is considered. First, it is shown that the standard approach based on performing model reduction using some ad hoc discretization method and model order, prior to calibrating and validating the reduced model, has a number of potential pitfalls and can easily lead to falsely validated PDE models. To overcome these problems, a systematic approach based on separating model reduction errors from discrepancies between postulated model structures and measurement data is proposed. The proposed approach is successfully demonstrated on a challenging chromatography process, used for separation in biochemical production, for which it is shown that data collected at the boundaries of the process can be used to clearly distinguish between two model structures commonly used for this process.</p>

This thesis considers the problem of making dynamic models for industrial processes by combining physical modelling with experimental data. The focus is on distributed parameter systems, that is, systems for which the model structure involves partial differential equations (PDE). Distributed parameter systems are important in many applications, e.g., in chemical process systems and in intracellular biochemical processes, and involve for instance all forms of transport and transfer phenomena. For such systems, the postulated model structure usually requires a finite dimensional approximation to enable identification and validation using experimental data. The finite dimensional approximation involves translating the PDE model into a set of ordinary differential equations, and is termed model reduction. The objective of the thesis is two-fold. First, general PDE model reduction methods which are efficient in terms of model order for a given level of accuracy are studied. The focus here is on a class of methods called moving mesh methods, in which the discretization mesh is considered a dynamic degree of freedom that can be used for reducing the model reduction error. These methods are potentially highly efficient for model reduction of PDEs, but often suffer from stability and robustness problems. In this thesis it is shown that moving mesh methods can be cast as standard feedback control problems. Existing moving mesh methods are analyzed based on tools and results available from control theory, and plausible explanations to the robustness problems and parametric sensitivity experienced with these methods are provided. Possible remedies to these problems are also proposed. A novel moving finite element method, Orthogonal Collocation on Moving Finite Elements (OCMFE), is proposed based on a simple estimate of the model reduction error combined with a low order linear feedback controller. The method is demonstrated to be robust, and hence puts only small demands on the user. In the second part of the thesis, the integration of PDE model reduction methods with grey-box modelling tools available for finite dimensional models is considered. First, it is shown that the standard approach based on performing model reduction using some ad hoc discretization method and model order, prior to calibrating and validating the reduced model, has a number of potential pitfalls and can easily lead to falsely validated PDE models. To overcome these problems, a systematic approach based on separating model reduction errors from discrepancies between postulated model structures and measurement data is proposed. The proposed approach is successfully demonstrated on a challenging chromatography process, used for separation in biochemical production, for which it is shown that data collected at the boundaries of the process can be used to clearly distinguish between two model structures commonly used for this process. / QC 20101020