The contents of this thesis can be divided into two main parts. The first one is the development of an identification methodology for the modelling of complex industrial processes. The second one is the application of this methodology to the curl and twist problem. The main purpose behind the proposed methodology is to provide a schematic planning, together with some suggested tools, when confronted with the challenge of building a complex model of an industrial process. Particular attention has been placed to outlier detection and data analysis when building a model from old, or historical, process data. Another aspect carefully handled in the proposed methodology is the identifiability analysis. In fact, it is rather common in process modelling that the model structure turns out to be weakly identifiable. Consequently, the problem of variable selection is treated at length in this thesis, and a new algorithm for variable selection based on regularization has been proposed and compared with some of the classical methods, yielding promising results. The second part of the thesis is about the development of a curl predictor. Curl is the tendency of paper of assuming a curved shape and is observed mainly during humidity changes. Curl in paper and in paperboard is a long-standing problem because it may seriously affect the processing of the paper. Unfortunately, curl cannot be measured online, but only in the laboratory after that an entire tambour has been produced. The main goal of this project is then to develop a model for curl and twist, and eventually to implement it as an on-line predictor to be used by the operators and process engineers as a tool for decision/control. The approach we used to tackle this problem is based on grey-box modelling. The reasons for such an approach is that the physical process is very complex and nonlinear. The influence of some inputs is not entirely understood, and besides it depends on a number of unknown parameters and unmodelled/unmesurable disturbances. Simulations on real data show a good agreement with the measurement, particularly for MD and CD curl, and hence we believe that the model has an usable accuracy for being implemented as an on-line predictor. / QC 20100928

The purpose of this thesis work was to develop an automatic fault detection system for surveillance of bearing temperature in hydropower turbines. The parameters used except the bearing temperature were cooling water temperature and cooling water flow. A simple static model based on data sampled every minute was developed to estimate the bearing temperature. Then a detector for detection of change in bearing temperature based on the CUSUM-algorithm was designed. Since the amount of data was very small the developed model was too uncertain to be used in a working system. The designed fault detection system showed to work well for the available data. It is, however, recommended that the performance of the system should be evaluated using more data. Another model based on data sampled once every minute for at least a year has to be developed before the system can be fully evaluated. The results shown were: • The fault detection system can discover fast and slow changes in bearing temperature. • No false alarms were given for measuring faults and sensor faults of the types used in this thesis. If a measuring fault occurs for too long there will be an alarm. The fault detection algorithm was also implemented in Delphi to be used in a working system over the Internet where for example trends and alarms will be presented. / Syftet med examensarbetet var att utveckla ett automatiskt feldetekteringssystem för övervakning av bärlagertemperaturen i vattenkraftturbiner. De ingående parametrarna förutom bärlagertemperaturen var kylvattentemperaturen och kylvattenflödet. En enkel statisk modell baserad på data samplat en gång per minut togs fram för att estimera bärlagertemperaturen. Därefter utvecklades en detektor för att upptäcka avvikelser i bärlagertemperaturen baserad på CUSUM-algoritmen. På grund av en för liten mängd data var den framtagna modellen alltför osäker för att kunna implementeras i ett fungerande system. Det framtagna feldetekteringssystemet visade sig fungera bra för de data som fanns tillgängliga. Det är däremot rekommenderat att utvärdera systemets prestanda med längre dataserier. En ytterligare modell baserad på minutdata över ett år måste tas fram innan systemet kan fungera på riktigt. De resultat som erhölls var: • Feldetekteringssystemet klarar av att upptäcka abrupta och långsamma avvikelser av bärlagertemperaturen. • Inga falsklarm ges då det är enstaka mätfel eller givarfel av sådan typ som tagits upp i arbetet. Pågår ett mätfel alltför länge ges dock ett larm. Feldetekteringsalgoritmen implementerades även i Delphi för att kunna användas i ett fungerande system över Internet där t.ex. trendkurvor och larmsignaler skall kunna presenteras.

I Australien är vattenresurserna begränsade. För lantbrukare är tillgängligheten på vatten mycket viktig. På grund av det torra klimatet kan inte de Australiensiska bönderna förlita sig på nederbörden. Bevattningssystemen är därför en viktig del i jordbrukningsindustrin. Bevattningsområdet i Coleambally ligger i södra New South Wales nära gränsen till staten Victoria. Bevattningsnätet i Coleambally förser ofta bevattningskanalerna med för mycket vatten för att vara säker på att lantbrukarna får den mängd vatten de behöver. På grund av denna tillförsel av överskottvatten går stor mängd av vatten förlorad. Design av ett bättre reglersystem skulle kunna minska den stora förlusten av vatten. En matematisk modell beskrivande dynamiken av bevattningssystemet är ett bra redskap vid en design av ett bättre reglersystem. Syftet med det här projektet var att genom systemidentifiering bygga en matematisk modell av bevattningssystemet. Modellen syftade till att beskriva vattennivån i en sträcka av bevattningskanalerna, sträckan i kanalen skulle ha två olika typer av luckor, en typ där vattnet strömmar över luckan och en annan typ där vattnet strömmar under luckan. En modell byggdes genom att parametrar från en vald modellstruktur estimerades från experimentella data. Data samlades under ett experiment som utfördes på en bevattningskanal i Coleambally. Resultatet från systemidentifieringen blev en första ordningens output error grey box modell. Modellen visar goda resultat vid validering och bör kunna användas vid design av ett bättre reglersystem. Modellen visar så god överensstämmelse med valideringsdata att den även kan användas för olika fall av simulering. / Water resources in Australia are limited. For a farmer the access to water is crucial and due to the dry climate the farmers in Australia can not rely on precipitation. Irrigation is therefore a very important part of the farming industry. The Coleambally Irrigation Area is situated in the southern parts of New South Wales close to the border of Victoria. The Irrigation Network often supplies the irrigation channels with too much water to be sure that the demand of water is satisfied. Due to this over supply a great amount of water gets wasted. Design of a bettercontrol system would be able to reduce the water wastage. A mathematical model describing the dynamics of the irrigation system can be used as a tool for the control system design. The aim of this project was to build a mathematical model with the system identification approach. The model should be able to describe the downstream water level of a single pool of an irrigation channel which has both undershot and overshot gates. A model was built by estimating unknown parameters of a chosen model structure from a set of experimental data. The data was collected from an experiment performed on the real irrigation system in Coleambally. The result of the system identification was a first order output error grey box model. The model performs well on validation data and may therefore be used for design of a more efficient control system. The model gave such good results that it additionally may be used for various simulation purposes.

No description available.

In this thesis a quadrotor is studied and a linear model is derived using grey-box estimation, a discipline in system identification where a model structure based on physical relations is used and the parameters are estimated using input-output measurements. From IMU measurements and measured PWM signals to the four motors, a direct approach using the prediction-error method is applied. To investigate the impact of the unknown controller the two-stage method, a closed-loop approach in system identification,  is applied as well. The direct approach was enough for estimating the model parameters. The resulting model manages to simulate the major dynamics for the vertical acceleration and the angular rates well enough  for future control design.

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.

Today’s power systems are based on a centralised system and distribution networks that are considered as passive terminations of transmission networks. The high penetration of Distributed Generation (DG) at the distribution network level has created many challenges for this structure. New tools and simulation approaches are required to address the subject and to quantify the dynamic characteristics of the system. A distribution network or part of it with DG, Active Distribution Network Cell (ADNC), can no longer be considered as passive. An equivalent dynamic model of ADNC is therefore extremely important, as it enables power system operators to quickly estimate the impact of disturbances on the power system’s dynamic behaviour. A dynamic equivalent model works by reducing both the complexity of the distribution network and the computation time required to run a full dynamic simulation. It offers a simple and low-order representation of the system without compromising distribution network dynamic characteristics and behaviour as seen by the external grid. This research aims to develop a dynamic equivalent model for ADNC. It focuses on the development of an equivalent model by exploiting system identification theory, i.e. the grey-box approach. The first part of the thesis gives a comprehensive overview and background of the dynamic equivalent techniques for power systems. The research was inspired by previous work on system identification theory. It further demonstrates the theoretical concept of system identification, system load modelling and the modelling of major types of DG. An equivalent model is developed, guided by the assumed structure of the system. The problem of equivalent model development is then formulated under a system identification framework, and the parameter estimation methodology is proposed. The validation results of the effectiveness and accuracy of the developed model are presented. This includes the estimation of the parameter model using a clustering algorithm to improve the computational performance and the analysis of transformer impedance effects on the ADNC responses. The evaluation of probability density function, eigenvalue analysis and parameter sensitivity analysis for the model parameters are also presented. Typical model parameters for different network topologies and configurations are identified. Finally, the developed equivalent model is used for a large power system application. The accuracy and robustness of the developed equivalent model are demonstrated under small and large disturbance studies for various types of fault and different fault locations.

This thesis presents a grey-box model of the temperature and moisture content for each layer of the multi-ply paperboard inside the drying section of a paper mill. The distribution of the moisture inside the board is an important variable for the board quality, but is unfortunately not measured on-line. The main goal of this work is a model that predicts the moisture evolution during the drying, to be used by operators and process engineers as an estimation of the unmeasurable variables inside the drying section. Drying of carton board is a complex and nonlinear process. The physical phenomena are not entirely understood and the drying depends on a number of unknown parameters and unmodelled or unmeasurable features. The grey-box modelling approach, which consists in using the available measurements to estimate the unknown disturbances, is therefore a suitable approach for modelling the drying section. A major problem encountered with the modelling of the drying section is the lack of measurements to validate the model. Consequently, the correctness and uniqueness of the estimated variables and parameters are not guaranteed. We therefore carry out observability and identifiability analyses and the results suggest that the selected model structure is observable and identifiable under the assumption that specific measurements are available. Based on this analysis, static measurements in the drying section are carried out to identify the parameters of the model. The parameters are identified using one data set and the results are validated with other data sets. We finally simulate the model dynamics to investigate if predicting the final board properties on-line is feasible. Since only the final board temperature and moisture content are measured on-line, the variables and parameters are neither observable nor identifiable. We therefore regard the predictions as an approximation of the estimated variables. The semiphysical model is complemented with a nonlinear Kalman filter to estimate the unmeasured inputs and the unmodelled disturbances. Data simulations show a good prediction of the final board temperature and moisture content at the end of the drying section. The model could therefore possibly be used by operators and process engineers as an indicator of the board temperature and moisture inside the drying section. / QC 20101112

<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