This thesis contains a steady state simulation model of a multistage crude oil production plant. The unstable reservoir fluid is separated into crude oil and gas in a three stage gas oil separation plant. Peng Robinson Equation of State and successive substitution is used to model the separators. The liquid output for the third stage separators is stable crude oil and the crude oil is sold on the international market. The gas liberated in the separators is compressed by centrifugal compressors and injected into the reservoir. Several methods for modelling centrifugal compressors are discussed. The discussion concludes that Dimensionless Parameters is the best suited method for this case and this method is therefore used. The plant studied has three separation stages at decreasing pressure and the standard control method is to use fixed separator pressure. This is not optimal and brute force optimization is used to find the optimal pressure set-points. Adaptive pressure set-points will improve product separation and therefore increase the profit. The profit is calculated as the income from crude oil sale minus the energy cost. Using this new method, the optimum separator pressures for Snorre A are determined. As a result, the profit is increased with 0.17, 0.11 and 0.07 present for three different inlet conditions. For one year this small increase in profit gives an extra two million dollars in income. The adaptive pressure set-points give an extension of the plant’s maximum capacity for a reservoir fluid with a high gas oil ratio.

The control solution is a crucial part of Managed Pressure Drilling. Existing solutions are often based on Proportional plus Integral (PI) control and have several drawbacks, mainly poor performance for some common drilling operations and a large need for retuning. Better control solutions will reduce costs and improve safety. This thesis presents a comparison of two adaptive control solutions versus a PI benchmark. Both complexity, tuning, performance and robustness will be compared. The two adaptive solutions considered are the well-known Model-Reference Adaptive Control method, and the recently developed $Lone$ adaptive control method. The control solutions are tested on a wide range of common drilling operations, some common controller issues, changing parameters and for two different control setpoints. The adaptive control solutions are shown to give better performance and to have less need for retuning, but not without costs. The main issues of the $mathcal{L}_1$ adaptive controller is low time-delay margins and high computational demands, but the performance is much better than for the benchmark controller. The most important recommendation for future work is evaluation of higher order filter designs for the $mathcal{L}_1$ adaptive controller, because of the potential to both reduce computational needs and to optimize time-delay margins.

Today's Basel-type banking system is compared with a 100% reserve banking system. Furthermore, negative interest rate on deposits is introduced for these two systems thus two new models are introduced. Eventually all four models are compared with each other in terms of debt crisis mechanisms and if they are prone to enter a liquidity trap. The comparing is done for debt to GDP ratio around a certain ratio of 60% thought to give neutral confidence, thus the effect from confidence dynamics can be excluded for these simulations.

In many ways, the simple act of walking is one of the most complex modes of locomotion there is. For control-system scientists the periodic hybrid dynamical nature of walking systems presents a number of unique challenges, many of which still lack satisfying solutions. This thesis applies fairly recent concepts of motion generation and control to generate steps and gaits for such a walking robotic system. The robot, SemiQuad, developed and built at '{E}cole de Nantes in France, is a five degree of freedom, underactuated periodic hybrid dynamical system. This text presents a generic method of reparametrizing a given smooth motion by the use of virtual holonomic constraints, and comments on the conditions required for the method to succeed. It is then shown how virtual holonomic constraints can be generated from scratch, and certain properties of holonomically constrained systems are investigated. From the generated constraints and associated motion, a controller based on the principle of transverse linearization is created, and closed loop characteristics of the system are observed.

The increasing demand for oil and gas in the world, and the fact that most of the easily accessible reservoirs are in production or already abandoned, result in a need to develop new resources. These may be new reservoirs that have previously been considered uneconomical or impossible to develop, or extended operation of existing fields. Developing smaller reservoirs, means that more wells have to be drilled per barrel, which gives both more and eventually greater challenges as more and more wells are drilled because the wells has to be drilled further and into more difficult formations. Mature fields are drained, which leads to lowering of reservoir pressure and therefore tighter pressure margins for drilling. Because of the challenges with deep water drilling and depleted reservoirs, there is a need to precisely control the pressure profile in the well during drilling in such formations. Some of the parameters that are needed to control the well precisely are not easily obtained during drilling, and an estimation of these will therefore be crucial to be able to use a model to control the well. The transmission of measurements from a well is also often either delayed or absent during periods of drilling, which will cause problems for the control of the well. It is therefore required that an estimation scheme is able to estimate the pressure in the well for the time interval between the updates of the measurements from the well. The conventional method for transmitting measurements from the bottom of the well is by mud pulse telemetry which is pressure waves transmitted through the drilling mud. These measurements will be delayed, so accurate real-time measurements will never be available. To estimate the bottom hole pressure, a extended kalman filter was evaluated. This filter is based on a simple mathematical model derived for the drilling process. The states in the filter is height of mud in the riser, mud weight and different friction factors for the well. The filter is tested when the measurements are continuous available, with delayed update of the bottom hole measurement, and for cases where one of the measurements are absent. A simple controller to control the bottom hole pressure is implemented to control the pressure for reference tracking and during a simulated pipe connection. During simulations, it was not possible to achieve convergence for the friction factor for normal flows, and this led to errors in the other states. The friction factor would only converge to its true value during very high flows during the nominal testing, which led to the other states also achieving their correct values. The problem in estimating the friction factor applied to all different forms for friction parameters. The kalman filter was tested against an artificial well simulated in WeMod, and gave decent estimates of the bottom hole pressure except for at low flows.

Model predictive control (MPC) of a Kaibel distillation column is the main focus of this thesis. A model description together with a model extension is also considered. The motivation of using a Kaibel distillation column is primarily its energy saving potential. There is no reason for using such an energy saving column if the product purities are below some acceptable values. These purities can be kept above these acceptable values by sufficient control of the column. The simulation model of the Kaibel column was extended to include an efficiency parameter which describes an insufficient vapor mixing effect that occurs in distillation columns. This insufficient mixing leads to increased impurity flows in open-loop, but this is counteracted by increased reflux flow in closed-loop. The column can obtain sufficient purities for increasing insufficient mixing until the reflux flow reaches its maximum value. A single layer MPC and a supervisory MPC approach have been described, implemented and tested on the simulation model of the column. These MPCs show improved dynamic responses compared to the existing decentralized control approach. These MPCs have also been compared in a sensitivity analysis part. The sensitivity analysis shows a clear improvement in the robustness properties for a supervisory MPC compared to decentralized control in terms of input uncertainty. The supervisory MPC has also shown to be more robust than the single layer MPC. A brief qualitative discussion regarding alternative MPC approaches has been done, where inferential control is suggested as an alternative MPC approach for the Kaibel column. An MPC implementation has been done for use at the existing laboratory column at Department of Chemical Engineering. Also here, based on implementation issues, the supervisory MPC is preferable compared to a single layer MPC. A parameter adjusted version of the developed simulation model is recommended as the MPC's internal prediction model.

Adjoint based gradient calculation for Nonlinear Model Predictive Control.

In this report we will model a heat system consisting of a heat storage tank and an application. The heat storage tank is supplied by a heating element and heated water from a solar collector. The main objective of the heat system is to mainatian a reference temperature in the application (a house). Weather forecasts will be used as weather data affecting the heat system. We will assume that the weather forecasts and the actual weather will be the same. The heat sytem will consist of simplified nonlinear differential equations and be controlled by a model predictive controller (mpc). The mpc controller will use a linearized model of the nonlinear process. The average predicted outside temperature from the weather forecasts will be used as nominal value for the same temperature in the linearized model in the mpc controller. The mpc controller will measure some disturbances to make more efficient control. The most imortant disturbance will be the temperature of the water coming out of the solar collector, that will flow into the heat storage. By measuring this temperature, the mpc controller can apply it to its predictor and make sure that the power of the heating element in the heat storage is reduced when solar collector heated water is available. This is to make sure that the heat storage has enough capacity to receive the heated water from the solar collector, while still maintaining a reasonable temperature in the heat storage. Simulation with different weighting of the inputs in the mpc controller will show that heating element power consumption is influenced by these weights.

A snake robot will be defined herein as any multilink robot for whose shape and motion capabilities are reminiscent of a snake like PiKo [1]. PiKo is a five links snake robot with active wheels designed by SINTEF in collaboration with the Norwegian University of Science and Technology (NTNU). Researchers have been greatly interested in the development of robots like PiKo because of its shape versatility and motion capacity in difficult terrains. These skills and properties are useful for rescue teams working in earthquakes, pipe inspection operations and other utilities where access and movement in the terrain are typically difficult. When a working team decides to develop a snake robot, an important point to consider is the development of an efficient navigation system that reaches an accurate position of the robot. Technically speaking, it is prudent to design at the same time a state observer that gives us at least the real time position and velocity information of the robot body to be controlled. The relevance of this information is derived from every control action applied to the robot will require some information about the situation of the robot over time. The controller will need feedback about the robot dynamics and the effect that the control actions have caused. Typically this information has three sources: the information that comes from external sensors, that from internal sensors that transmitting to the control place the measurements from the sensors in the robot body and estimated data from a physical model. All of these feedback sources have some advantages and disadvantages. Implementing an external observer, with external sensors, will not cause space problem with sensors location in the robot body, but when the robot is working inside a pipe, underground or in another hard environment where the optical, magnetic or radio frequency contact is difficult or impossible, the information reception from an external observer is too difficult and expensive or simply impossible. Locating internal sensors in the body of the robot may solve has the problem with the measurements reception, but still pose some difficulties which must be considered by the designer. Many times space becomes a problem when locating some sensors inside the robot body due to size and weight constraints within the robot body. Basing the navigation system instead on a physical model that simulates the robot motion invites the possibility of error due to simplifications taken during the mathematical and physical development. It is impossible to develop a perfect physical model since all the variables, forces, and parameters that depend on the nature characteristics usually are random process and we can just raise a useful factor estimating the average of these effects in our concrete situation. In this thesis a navigation system with a GPS (Global Positioning System) and IMU (Inertial Measurement Unit) fusion was achieved. This navigation system will be work as long the GPS signal is available. The application of the fusion technique further reduces one order the potential errors inherent in using only the GPS navigation system. When the robot will encounter locations where the GPS signal is impossible, this thesis will present a set of tools that not being a universal solution, it will be a set of mathematical tools that depending on the case could give us an accurate navigation system. During the time the GPS signal reception is impossible, this thesis presents the development and implementation of a physical model for a snake robot with active wheels which simulates the snake robot running behavior and studies the possibility to use the trajectory estimated by the model for reaching an accurate navigation system.

The main focus of this thesis is aspects in the development of a system for prevention of stick-slip oscillations in drill strings that are used for drilling oil wells. Stick-slip is mainly caused by elasticity of the drill string and changing frictional forces at the bit; static frictional forces are higher than the kinetic frictional forces which make the bit act in a manner where it sticks and then slips, called stick-slip. Stick-slip leads to excessive bit wear, premature tool failures and a poor rate of penetration. A model predictive controller (MPC) should be a suitable remedy for this problem; MPC has gained great success in constrained control problems where tight control is needed. Friction is a highly nonlinear phenomenon and for that reason is it obvious that a nonlinear model is preferred to be used in the MPC to get prime control. Obviously it is of great importance that the internal model used in the MPC is of a certain quality, and as National Oilwell Varco (NOV) has developed a nonlinear drill string model in Simulink, it will be useful to check over this model. This model was therefore verified with a code-to-code comparison and validated using logging data provided from NOV. As the model describing the dynamics of the drill string is somewhat large, a nonlinear model reduction is needed due to the computational complexity of solving a nonlinear model predictive control problem. This nonlinear model reduction is based on the technique of balancing the empirical Gramians, a method that has proven to be successful for a variety of systems. A nonlinear drill string model has been reduced and implemented to a nonlinear model predictive controller (NMPC) and simulated for different scenarios; all proven that NMPC is able to cope with the stick-slip problem. Comparisons have been made with a linear MPC and an existing stick-slip prevention system, SoftSpeed, developed by National Oilwell Varco.