<p>The purpose of this thesis was to investigate how different subspace identification methods cope with closed loop data, and how the controller parameters affect the quality of the acquired models. Three different subspace methods were subject for investigation; the MOESP method, the N4SID method and the DSR_e method. It is shown through a simulation example that all three subspace methods will identify the correct open-loop model from closed-loop data if the data record is noise-free (deterministic identification with perfect data). This result is not a new one, but a confirmation of the results from other researchers. Among the three different subspace methods that were investigated, the DSR_e method developed by dr. David Di Ruscio gave the best overall results. This method is especially designed to cope with closed-loop data, different from the MOESP and N4SID methods. Controller gain is shown to have a significant effect on the quality of the identified model when there is noise present in the loop. It is shown by simulations that up to a point, higher controller gain during the identification experiment actually gives more accurate open-loop models than models identified with lower controller gain. One of the reasons for this is that high gain tuning provides a higher signal to noise ratio through amplification of the reference signal, rendering the noise in the data used for identification less significant. Another reason may be that frequencies in the input signals will be more concentrated around the achievable bandwidth of the controller, which produces system outputs with more information of the frequency response around this bandwidth frequency. This is turn will reveal frequency information from the system that is important for control purposes.</p>

<p>The objective of this master thesis is to design, implement, and evaluate sliding mode control (SMC) applied to stabilize slugging using only the downhole pressure as measurement. The pros and cons of the resulting output-feedback sliding mode controller are to be evaluated against the conventional PI controller. The thesis is based on, and a continuation of the work and conclusions of my project thesis, where the conclusion was that the SMC might have a significant potential for increased oil production and recovery. The clear limitation was however the uncertainty regarding the validity of the van Der Pol model used, and the fact that the SMC was provided the real time-derivative states. Therefore the original main tasks of this thesis was to implement a high fidelity simulation model of severe riser slugging, and to design (and test) differentiators with the purpose of evaluating the output-feedback performance of the SMC. As it turn out that I was not able to achieve the task of stabilizing the pressure with SMC on the chosen OLGA model, the focus of this thesis has in agreement with my supervisors been changed quite a lot from the task requested in the project description. Possible reasons for the lack of results, and the chosen focus of the thesis is presented in the introduction chapter. The thereby chosen focus became the task of designing testing differentiators for the SMC, but with testing on the van Der Pol model. Before presenting and arguing for this change of focus in the section about task and limitation, the introduction chapter starts by giving a brief overview of the environment or setting the controlling challenge is a part of, and follows up by presenting the work and conclusion of that project thesis. In the end of the chapter, the structure of the thesis is shortly listed. The introduction is followed up by giving a further insight to the slug problematic. An overview of the historical development, and a description of some research within the field are provided. The last part of the chapter gives a quite thorough description on the riser slugging phenomenon. Thereby the sliding mode controller (SMC) is presented in chapter 3. The challenge concerning chattering is also discussed, and the approach of using boundary layer to suppress the chattering is introduced. In chapter 4, the empirical van der Pol based model is derived, and the model is augmented to use the valve rate as control input. Chapter 6 gives a discussion on why the SMC should be performed on the choke rate and not directly on the choke opening. This section also designs the SMC that will be used for testing, and the needed time-derivatives for testing the SMC are derived. The chosen main focus of this thesis is to evaluate if there is possible to design observers (differentiators) that meets the requirements for the designed SMC to stabilize slugging. The tests are performed on the van Der Pol model. This task is introduced through chapter 7, that present general observer theory, theory about using observers combined with SMC, and finally the two observers chosen for further testing; the high gain observer (HGO) and the robust high-order sliding mode differentiator (RHOSMD). The first stage in evaluating the HGO and RHOSMD is open loop testing, and is described in chapter 8. The observers perform well for the ideal case of no disturbance, but in the presence of measurement noise the conclusion is that estimations of the higher order time-derivatives do likely not meet the very demanding requirements of the SMC. The biggest problem is probably the time-delay of the estimation, but the correctness of the amplitude might also be a problem. In chapter 9 the observers was tested further in a SMC controlled closed loop system to get a more precise indication on how well the observers are fitted for their intended task of providing the SMC with the required estimations. As for the open loop tests, the 'isolated' estimation performance of the required states was considered, but the main focus was the performance of the output-feedback SMC compared to the performance of manual choking, the PI controller, and the performance of the state-feedback SMC. This chapter confirmed the assumption from the open loop testing that in presence of measurement noise, the observers is not able to meet the demanding requirements of the designed SMC. For the theoretical ideal case of no disturbance the results is very good, especially for the HGO. In the case of measurement noise, the RHOSMD perform slightly better. In both chapter 8 and 9, tuning is considered and discussed. However, since the conclusions of the observer testing is negative, the SMC is not tested further. The results will be negative for output-feedback testing, and a quite extensive state-feedback testing of the SMC is performed in the project thesis. The main results and conclusions throughout the thesis, are presented in chapter 10. The chapter also contain a short discussion where it is concluded that the alternative designs, SMC with direct choke rate control and SMC of the choke acceleration, will not be a solution on the state-feedback SMC problems described in this thesis. There is also a short discussion regarding CPU and system requirements for the observers and the controller. At the very end, further work is discussed.</p>

<p>The purpose of this thesis was to study the use of adjoint methods for gradient calculations in Model Predictive Control (MPC) applications. The goal was to find and test efficient optimization methods to use in MPC on oil reservoir models. Handling output constraints in the optimization problem has been studied closer since they deteriorate the efficiency of the MPC applications greatly. Adjoint- and finite difference approaches for gradient calculations was tested on reservoir models to determine there efficiency on this particular type of problem. Techniques for reducing the number of output constraints was also utilized to decrease the computation time further. The results of this study shows us that adjoint methods can decrease the computation time for reservoir simulations greatly. Combining the adjoint methods with techniques that reduces the number of output constraints can reduce the computation time even more. Adjoint methods require some more work in the modeling process, but the simulation time can be greatly reduced. The principal conclusion is that more specialized optimization algorithms can reduce the simulation time for reservoir models.</p>

<p>The topic of this thesis is modeling and simulation of anchor handling vessels. Computer simulations of anchor handling vessels can be used to evaluate the forces acting on them, and to gain valuable insight into their operational limitations. Introductorily, an overview containing important aspects of anchor handling operations is presented. The objective is to highlight important subjects that must be considered before a simulator is developed. A simulator of an anchor handling vessel is successfully implemented in Matlab and Simulink. The simulator contains modules for ballast tanks, anti-roll tanks, cables, seabed and anchor interaction, winch systems and guide pins. The vessel model is matched up against a real anchor handling vessel to give realistic thrust characteristics. The simulator is capable of simulating both anchor deployment and anchor recovery operations in real time. Catenary equations are used to model cables. A quasi-static polynomial approach with look-up tables is used for implementation. The method allows the use of different catenary models to simulate different phases of the anchor handling operation. A catenary model of two cables with a point load, imitating the effect of an anchor, is developed based on existing catenary models in the literature. The simulator is verified through simulations. A set of case studies is used to evaluate the vessel performance during anchor deployment and recovery. The case studies consider operation in ideal and rough weather conditions, and it is shown how equipment failures and poor vessel configuration can lead to decreased vessel stability and loss of maneuvering capabilities.</p>

<p>Real-world stock markets exhibit periods of increased volatility and bursts in stock prices. This thesis is about creating similar dynamics in a model to gain insight into these potentially dangerous phenomena. A transaction tax able to stabilize the markets is briefly discussed. The relationship between rational and speculative traders is found to be crucial. If the speculative mindsets are allowed to dominate the markets, chaos is inevitable. Simulations show a direct relation between speculation and violent price movements. The discussed transaction tax is found to make the market more robust by targeting the most destabilizing form of trading - short-term speculation.</p>

Summary: In this thesis work, mathematical models required to simulate an offshore ploughing operation has been derived. This includes a surface vessel model, a model of the plough and its friction force due to seabed sediment and a towline model. A Dynamic Positioning control system has been derived in order to regulate the vessel to a desired location based on the plough’s desired position. A supervisor module has been derived in order to generate the vessel’s reference position in a smooth manner. And finally the total system has been implemented and simulated in the Simulink_TM environment. The surface vessel model derived in this assignment is based on an offshore supply vessel from the ”MatLab Marine GNC Toolbox” in Simulink_TM. The vertical motion of the vessel has been kept constant during simulations, based on the assumption that the buoyancy force of the vessel is large compared to the vertical towline force. The plough’s friction force due to penetration of the seabed sediment has been modeled, based on the content in reference [5], to get a realistic picture of the sediment forces involved in ploughing operations. It was found that the plough’s friction force profile changed with different operational boundaries. The boundaries are the ocean depth and the ploughing speed. For the boundaries in this assignment the resulting ploughing force equation were found to be nonlinear and shaped as a sigmoid function. In this assignment the lumped mass model has been derived for the towline’s motion and proven to give reasonably good numerical results when implemented in the Simulink TM environment. To get a realistic towline motion in seawater, a hydrodynamic quadratic damping force has been added to the equations. This hydrodynamic damping had effect on the towline’s tangential and normal motion components. The DP controller derived in this assignment consists of a PD-controller with feed forward signal from the horizontal towline tension. Feed forward signals are often influenced by noise and must be filtered to obtain low-frequency signals. In this assignment a ordinary 1st-order low-pass filter has been used in order to damp out oscillations from the towline. This filter has been proven to give a good damping effect when the towline was exposed to underwater currents. The DP controller provides good position tracking quality. The supervisor module designed in this assignment consists of a reference generator an a reference model. The supervisor module is responsible for converting input signals for the plough’s desired path into a smooth tracking signal for the vessel’s control system. The reference generator produces smaller intermediate reference signals, as input to the reference model, from a final desired vessel position. A circle of acceptance has been introduced in order to change reference values at a convenient vessel location. This has been proven to give a nice effect on the vessel’s and the plough’s behavior. The reference model has been designed with a speed saturation element, in order to bound the speed of the ploughing operation. During the case simulations it was found that by defining the operation over a longer distance, a more efficient operation is gained. When crossing longer distances the plough will reach the vessel’s speed and underwater current disturbances are small compared to the ploughing force that has gotten time to be built up. Underwater currents has great influence on the towline when the towline’s pulling force is small. In appendix A a CD can be found. On this CD this report can be found, the original work schedule, pictures and the Simulink program for the ploughing operation.

In the autumn of 2006 a satellite project was started at NTNU. The goal of the project is two-folded, first it seeks to create more interest and expertise around the field of space technology, secondly to create a satellite platform which can be modified and equipped with different payloads to perform selected tasks in a Low Earth Orbit. For a satellite to be able to complete missions involving sensory and imaging, an attitude determination and control system is needed to give the satellite a stable attitude. In order to create a good attitude control system, a Gauss-Newton improved extended Kalman filter is used together with reference models to supply the controller with estimates of both satellite angular velocity and orientation. This report focuses on the Attitude Determination System, ADS, realized by implementing the improved extended Kalman filter on a microcontroller. The challenge is to create an estimator that will provide the control system with adequate estimates without requiring to much computational power, as this is a limiting factor on board a micro satellite. The need for good computational power comes from the multidimensional matrix mathematical operations performed on float numbers. Based on previous work, an improved Extended Kalman filter has been developed and implemented on a microcontroller for further testing. A new filter, the Unscented Kalman Filter has also been explored but not implemented.

Electric motors with metal graphite brushes experience a change in contact resistance depending on current load. This varying resistance leads to varying gain in the motor, since the proportion of power dissipated due to the resistance changes. This investigation is concerned with a servomechanism, which uses such motors for position and force control. Force control with electric motors is typically accomplished by controlling the current. The servomechanism utilizes a discrete controller, and discretization renders the system unstable for any practical sampling times and controller gains when using current feedback. Feedforward is therefore used to control the current, and is thus sensitive to the variation in the motor's resistance. To counter the sensitivity, a parameter estimator using least mean squares is presently used to learn the value of the resistance. An alternative to the parameter estimator might be a gain-scheduler based on a model of the resistance attenuation phenomenon. It should be possible to find such a model because of the deterministic quality of the resistance attenuation. In the course of this investigation, an extended Kalman filter has been developed to estimate current and resistance with accuracy. Estimated current and resistance data from a series of experiments has been fitted to a rational model using nonlinear regression. The obtained model was used as a gain-scheduler. The estimated resistance from the extended Kalman filter, the least mean squares estimator, and the gain-scheduler were used in conjunction with the feedforward controller and compared for their ability to control the current. The extended Kalman filter provided the most accurate results, but at the expense of being more complex than the least mean squares estimator. The gain scheduler was the worst performer, most likely due to unmodeled effects. With some modifications, it was made to perform on par with the least mean squares estimator, but more work is required before it can be recommended for use.

This thesis describes an experimental programming language called TIME/occam. TIME/occam, like occam, is based on Communicating Sequential Processes (CSP), a branch of process algebra that allows computer programs to be modelled and verified mathematically and mechanically. TIME/occam uses synchronous channel communication as the only legal communication between parallel threads, and prohibits shared variables. Simple statements allow programs to specify parallelism directly. The main innovation in TIME/occam is the TIME statement, which allows the deadline and timing requirements of a task to be specified directly in the language. The TIME statement takes a block and a deadline, and tells the scheduler that the block must be completed within the deadline. It also states that the statement following the TIME block is not allowed to start until the timer expires. This can be used with a loop to create periodic tasks. Statements that have no timing requirements will never be executed. Because channel communication is synchronous, channels allow timing requirements to pass on from one task to another dependent task. The use of channels and timing requirements allow execution of a program to be planned some time in advance. It is assumed that execution time estimates can be found on line, although no viable solution for this exists at this time. Planning execution opens up new possibilities for dealing with missed deadlines. A compiler and scheduler have been implemented for the language. The scheduler is not complete; in particular it lacks the re-planning and execution algorithm. The thesis also contains an introduction to real-time and concurrent programming, and describes some of the difficulties that arise from pre-emptive scheduling of dependent threads. There is also a discussion on worst-case execution time analysis and related hardware issues. An example implementation of dining philosophers is presented, and it is explained how such a program is scheduled and executed in TIME/occam. Finally, the limitations of such a concept are discussed. In particular, there is a question whether or not a very heavy scheduler like the TIME/occam scheduler can be used in practice.

Rotifers are used extensively as start feed for many cultured marine fish species and commercial size hatcheries require stable daily supply of high quality rotifers of substantial volumes. This is often done relying on some employees whose knowledge and experience of the process and procedures ensures a stable production. Control techniques have been used in many other industries during many years improving the quality, reliability, predictability and reducing the costs of the production. However, control engineering is not as widely used as in other industries yet and this is the objective of this thesis, study the possibilities of using such techniques in the area of rotifer production at large scale. The benefits of their application will be an increment in the quality and predictability of the production as it becomes less dependant on the experience of people, but on their experience combined with monitoring and control techniques that will maintain the best conditions possible for the cultivation all the time. And also a better use of the resources will be achieved, that leading probably to a reduction of the costs of the production. This thesis makes a study of the biology and cultivation conditions of the rotifers, which is necessary previous to the application of control techniques, and then studies and proposes to different strategies for controlling the growth of the population, one based on the control of the feed density in the cultivation tank and the other based on the egg ratio control. In this work it is mainly done running simulations over a model, but an experiment is also performed for testing the second of the control strategies proposed.