In this thesis, we investige the applicability of the certain numerical methods for the solution of certain systems of partial differential equations. Numerical methods for this purpose are studied, in particular the finite element method. These systems arise from the study of extending performance analysis to general convergent nonlinear systems. It is argued that, for simplex meshes, the finite element method is not applicable to the systems. Further, it is argued that the finite element method should not be pursued as an alternative to the solution of these systems, as far better alternatives have recently been developed.

The focus of the work shall be on DVB-T PBR issues of range and Doppler migration of targets (of opportunity) in resolution cells due to high signal bandwidth and long integration time.

Piezoelectric tubes are commonly used as scanning actuators in nano precision microscopes. They can achieve precision down to sub-nanometer scale, but their vibrational dynamics and nonlinear properties hamper their ability to achieve higher bandwidths. In order to deal with this, further research is needed. This thesis is a first look into the field of piezoelectric tube actuators, intended to lay the groundwork for further research on the subject at NTNU. It details the construction of a laboratory setup for actuation and nanometer displacement measurement of a piezoelectric tube. Needed specifications are found and a mechanical setup is designed. Basic theory on piezoelectricity is presented, along with the setup and equipment used for the thesis. Several experiments are designed and conducted in order to identify the linear dynamics and nonlinear properties of the piezoelectric tube. The results are discussed and related to current literature. This includes the linear frequency responses from applied voltage to displacement of the piezoelectric tube, noise levels and nonlinear properties such as displacement creep and hysteresis. Generally, the results are found to closely match what has been found in similar research, although there are some notable differences, such as a somewhat smaller low frequency gain and a much lower resonant peak frequency of the system. Several possible explanations for these disparities are discussed. Both a capacitive sensor and a piezoelectric strain voltage sensor are utilized for measuring displacement. It is found that the capacitive sensor has a higher noise level but is more accurate at lower frequencies than the strain voltage sensor. The two measurements are then combined into an improved estimate of the displacement of the piezoelectric tube.

In this thesis, the compressor characteristics, being representations of the compressor pressure ratio as a function of the gas flow through the compressor, have been studied. Three different types of representations of the compressor characteristics are presented, implemented and tested with respect to simulation friendliness and effectiveness. These are based on a physical model, a 4th-order polynomial approximation method and a table lookup method. In addition, two different types of active surge controllers have been critically reviewed, i.e. the Close Coupled Valve (CCV) and the Drive Torque Actuation, and subsequently implemented and tested in SIMULINK. Based on the tests carried out on the compressor characteristics it is concluded that the 4th-order polynomial approximation method works best in an online environment. On the other hand, the table lookup method provides better representation of the actual data, but the method is somewhat slower compared to the other one. The usefulness of the physical model is limited, but together with parameter identification its applicability can be extended. Moreover, the active surge controllers have proved to be mathematically stable and shown to perform adequately. However, both face a problem with regard to measurement delay. Based on simulations and other considerations, the indications are that the drive torque actuation is the most promising solution for active surge control and should thus be the focus for further investigations. A possible solution for the measurement delay problem is to use a state observer. As a part of the thesis, two state observers have been implemented and tested, but with limited success.

The capture of gestures in order to use them as input for intuitive control has been investigated exhaustively in recent years. However, for the most part this has resulted in relatively expensive devices. The contribution of this report is the investigation on the feasibility of the development of a low-cost vision based input device for the tracking of head movements, concerning the use of them for motion control. The input device relies on the infrared camera, along with the built-in image analysis tools, present on a Nintendo Wii remote for the measurement of the location and orientation of a head-mountable marker. The marker consists of a set of optical feature points which are easily detectable, and organized in a fashion which allows for the determination of its position and orientation in space. The developed input device was then evaluated in order to determine the operating range, accuracy and robustness, and was shown to be feasible for its intended use. Finally, the implemented device was utilized to control a mechanical output device, being a unit capable of panning and tilting.

Updating the model parameters of the control system of an oil and gas production system for the reasons of cost-effectiveness and production optimization, requires a data set of input and output values for the system identification procedure. A requirement for the system identification to provide a well performing model is for this data set to be informative. Traditionally, the way of obtaining an informative data set has normally been to take the production system out of normal operational order, in the interest of performing experiments specificially designed to produce informative data. It is however desirable to use segments of process data from normal operation in the system identification procedure, as this eliminates the costs connected with a halt of operation. The challenge is to identify segments of the process data that give an informative data set. Dynamic Identifiability Analysis (DYNIA) is an approach to locating periods of high information content and parameter identifiability in a data set. An introduction to the concepts of data mining, system identification and parameter identifiability lay the foundation for an extensive review of the DYNIA method in this context. An implementation of the DYNIA method is presented. Examples and a case study show promising results for the practical functionality of the method, but also raise awareness to elements that should be improved. A discussion on the industrial applicability of DYNIA is presented, as well as suggestions towards modifications that may improve the method.

The topic of this paper is to control and synchronize sphere-shaped spacecrafts in a leader-follower synchronization scheme. In order to achieve this objective, a nonlinear mathematical model of the vehicles has been developed. The design is based on rigid body dynamics where the vessel is actuated by means of three orthogonally mounted reaction wheels. The attitude dynamics is derived using Euler parameters. In the pursuit of reaching the main goal of controlling and synchronizing the satellites, it is natural to rst develop control algorithms for single vehicle control. A sliding mode controller and a backstepping controller have been derived for this matter, and are compared for optimality. Both controllers are based on nonlinear control theory and are designed to control the angular velocity of the satellite. The system in combination with both the controllers is proven to be asymptotically stable. Due to cases where the spacecraft does not have angular velocity measurements, an estimator for the angular velocity is derived. Using LaSalle's theorem, asymptotic stability is proven for the observer in the time-invariant case, while Matrosov's theorem is utilized for system explicitly dependent on time. For operational assignments where it is not sufficient with only one satellite, a synchronizing scheme for several satellites has been proposed. The scheme is based on a leader-follower synchronization design, and is derived assuming that none of the satellites are equipped with angular velocity measurements. It is therefore possible to implement and utilize the nonlinear observer for angular velocity estimation in each vehicle. The controllers are designed in a similar manner for both the leader and the follower using backstepping control. The leader is set to follow an arbitrarily smooth trajectory, while the follower's objective is to track the leader's attitude, given by measurements and estimations. The various systems are tested in a lab setup with the AUVSAT. The AUVSAT is a sphere shaped, autonomous underwater satellite actuated by means of three orthogonally reaction wheels. The experiments are performed when the AUVSAT is submerged in a water tank, making it possible to emulate a gravity free environment equal to what a satellite traveling in space is experiencing. The AUVSAT build up is presented where hardware and software components are chosen with respect to simplicity, cost and space restrictions. Several experiments are carried out using the AUVSAT to evaluate the performance of the controllers, observer and the synchronization scheme. For all cases, the system tracks a time-varying sinusoidal reference signal in addition to a squareshaped sequence. In this way, one can truly validate transient responses, steady-state and tracking maneuvers to determine the performance of the various systems. The experiments show that the sliding mode controller and backstepping controller works quite similar and with a satisfactorily behavior throughout the experiments. However, there are some lack of performance of the combined observer and controller system when tracking the sinusoidal time-varying reference. In the synchronization scheme, the leader follows the desired trajectory and the follower tracks the leader's attitude to some extent. Comments on the results are presented in addition to proposed strategies and thoughts on how to improve the overall performance of the various systems.

Natural gas from organic rich shales has become an important part of the supply of natural gas in the United States. Modern drilling and stimulation techniques have increased the potential and profitability of shale gas reserves that earlier were regarded as unprofitable resources of natural gas. The most prominent property of shale gas reservoirs is the low permeability. This is also the reason why recovery from shale gas wells is challenging and clarifies the need for stimulation with hydraulic fracturing. Shale gas wells typically exhibit a high initial peak in the production rate with a successive rapid decline followed by low production rates. Liquid accumulation is common in shale wells and is detrimental on the production rates. Shut-ins of shale gas wells is used as a means to prevent liquid loading and boost the production. This strategy is used in a model-based production optimization of one and multiple shale gas well with the objective of maximizing the production and long-term recovery. The optimization problem is formulated using a simultaneous implementation of the reservoir model and the optimization problem, with binary variables to model on/off valves and an imposed minimal production rate to prevent liquid loading. A reformulation of the nonlinear well model is applied to transform the problem from a mixed integer nonlinear program to a mixed integer linear program. Four numerical examples are presented to review the potential of using model-based optimization on shale gas wells. The use of shut-ins with variable duration is observed to result in minimal loss of cumulative production on the long term recovery. For short term production planning, a set of optimal production settings are solved for multiple wells with global constraints on the production rate and on the switching capacity. The reformulation to a mixed integer linear program is shown to be effective on the formulated optimization problems and allows for assessment of the error bounds of the solution.

The problem of performing accurate path maneuvering tasks in planar space is investigated in thesis. The purpose is to utilize limited knowledge about the vehicle's maneuverability constraints to output feasible reference signals. Acceleration limitations of the vehicle have been used in an algorithm that determines forward speeds in such way that a predefined path can be followed at high speeds. The algorithm ensures that the speed is reduced before acute turns. Furthermore, an existing steering law has been modified to dynamically take the limitations of the vehicle into consideration when determining the desired course. This modified steering law exhibits desirable convergence characteristics toward the desired path. A complete guidance system, which combines the path convergence algorithm with the path speed algorithm, has been proposed. This system is able to rapidly converge to the desired path and follow this path, even for paths where the curvature is large. The modified steering law has been combined with a path-tracking speed controller. The path-tracking speed controller makes sure the vehicle can track a target on a predefined path. The resulting path-tracking system is able to follow a leader vehicle's path by creating accurate paths online from periodically sampled positions. A method for creating feasible U-turns in a lawn-mower pattern has been proposed. For a given vehicle speed, the resulting path obeys angular speed and angular acceleration constraints. Finally, the proposed algorithms are tested in simulations to illustrate their behavior and usefulness.

In many complex applications an accurate model of the plant is not known. Consequently, complementary methods are needed to automatically achieve accurate dynamical positioning of a robot in relation to its surroundings. This thesis describes the development of a control strategy on vision-based object tracking for a robot manipulator. To ensure necessary robustness we assume that four distinct, circular shapes are visible on the face of the object to inspect. Based on this information, along with knowledge of the camera parameters, the position and the orientation of the object are estimated. The developed system relies on the use of an open-source vision library, ViSP. A Kalman filter is used to predict future states of the moving object, in order to reduce tracking errors introduced by the response time of the system.