<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.

A thrust allocation system is used to determine how the desired forces, computed by a high level control sytem, can be distributed among the thrusters. The main goal of the thrust allocation is to obtain the desired force, but other objectives can also be included. Such secondary goals can be to minimize fuel consumption, keep wear and tear of the thruster to a minimum and avoid overloading the power systems. The thrust allocation should also take forbidden sectors and actuator rate constraints into account. It is essential to safe operation that the allocation system provides a solution, and provides the solution in time. In this thesis MPC (Model predictive control) is suggested as a method to solve the control allocation problem for CyberRig I (a scaled model of a semi-submersible drilling unit). 3 MPC algorithms are simulated in matlab, and the most complete are chosen for on-line implementation. The algorithm is based on an extended thrust formulation, and allows for rotatable thrusters. The cost function penalizes change in thust magnitude and in the azimuth angle. Forbidden sector constraints and rate constrains, both for thrust magnitude and angle, are implemented. It is shown in simulations that the MPC algorithm performs well in comparison with an existing quasi-static method. Its main benefit over the quasi-static method is the ability to handle constraints. The cost of using MPC is increased computational efforts.

This report addresses the stabilization problem of a marine structure (i.e. cable/riser), connected to a surface vessel at one end and to a thruster unit at the other. Here, only motion in the lateral direction has been considered. Stabilization control laws are designed for position and velocity control of the robot system. The passivity of the control system is analyzed, and the closed loop system is shown to be asymptotically stable. Simulation results are presented.