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.

Model Predictive Control of Brobekk waste incineration plant is the main focus of this master thesis. The motivation for using MPC at Brobekk is primarily to improve the control of the temperature towards the combustion furnace and towards Oslo. The Brobekk plant is connected to Hafslund Fjernvarme through heat exchangers, and where temperature and flow from Hafslund heavily affects the temperatures within the Brobekk Plant. Based on temperature, flow and demand from Hafslund, the control region was divided into two distinct regions, where one of the regions could be divided in to four sub regions. Four separate Model Predictive Control structures were devised and they were all able to successfully control the temperatures towards the combustion furnace and towards Oslo. The transition between the two main regions was also investigated, and the control structure developed seemed to give promising results. For simulations, a model developed in an earlier master thesis was used. This model had to be modified, because some physical modification had been made at Brobekk the last year.

This thesis illustrates different control structures and tries to demonstrate how feedforward control can be used in stabilizing an unstable ammonia reactor with heat integration. The demonstration of feedforward is done under very special circumstances. While feedback control is necessary for stabilization of the reactor system, feedforward control can be used to avoid input constraints which would otherwise make the input saturate and thereby make the system unstable. It turned out that the ammonia reactor was not the best system to apply the feedforward strategies in question. The main reason is a combination of; the existence of the lower (undesired) steady-state operating point (corresponds to extinction of reaction), positive feedback from the heat exchanger and the manipulated variable range of actuation. The reason is that there are trade offs between making more of the (cold stream) mass flow go through the heat exchanger and making the cold stream mass flow get mixed with the reactor flow between the beds at the quench points. Letting more mass flow entering the heat exchanger will reduce the heat exchanger efficiency. Lowering the efficiency means that the hot stream mass flow through the heat exchanger can not liberate enough heat to the cold stream mass flow entering the heat exchanger. As a result of this, the reactor inlet temperature will decrease because of the positive feedback from the heat exchanger. Thus, it does not exist a range of actuation where the system can be stabilized when influenced by disturbance.

This thesis is about Model Predictive Control (MPC) method for process control. It describes how this method could be implemented using some different open source software components, describing functionalities of each one and showing how the implementation has been done. Finally the code is tested to demonstrate effectiveness of this software in front of this kind of problems and to demonstrate MPC main characteristics. The main goals of this thesis are these last ones, code development and tests, so all mathematical and theoretical background are described but not as in detail as development and tests. Globally describing, MPC is a process control method where a previous knowledge of the plant is needed, so the controller have a model to simulate and predict the behavior of the system to calculate the best command signal. It has an optimization algorithm determining the optimal trajectory to bring system from initial state to desired state. Optimization is done by iterative simulation and solved online periodically at each sample time, initializing values at each time with measured feedback.

The main objective of this thesis was to combine the theory on synchronization of robot manipulators with the concept of hybrid force/motion control; resulting in a controller capable of following both the trajectory of another robot and a desired force trajectory at the same time. This report includes a short introduction to synchronization theory for robot manipulators, and a more thorough summary of existing hybrid control schemes. An intuitive method for describing constraints caused by the environment is presented, and this leads to a straightforward way to separate the interaction control problem into two subproblems. When the manipulator end-effector is in contact with a surface, the hybrid controller tracks a position reference along the surface and a force reference normal to the surface. The contribution of this thesis is a proposed hybrid controller, incorporating ideas from previous hybrid schemes. The closed loop system is shown to be globally asymptotically stable in the position controlled degrees of freedom, and bounded in the force controlled degrees of freedom. The performance of the proposed hybrid control concept is demonstrated by simulations. The proposed hybrid controller easily reduces to a pure position controller when desired.

This thesis addresses the problem of robot synchronization with obstacle avoidance. While these two fields have been studied extensively on their own, they have not yet been considered together as one problem. This thesis is divided roughly into four parts which are to some extent self contained. The theory is presented in a narrative that culminates with the stability proof of the proposed controller. Examples and figures are used in order to keep the material manageable and readable. The introductory part of the thesis consists of chapters 1 and 2. We present the notation and some mathematical background which is necessary for the theoretical analysis. We go on to review the diversity of ways in which one may approach this problem from a control design standpoint. We derive the robot dynamical model in chapter 3 as well as solve other modeling specific problems. This chapter is of little theoretical interest, but is needed to implement a simulator on which we may test our controller. This chapter contains no new contributions but can be read as a guide to robot modeling. The first contributions in this thesis are found in chapter 4 where we propose a real time implementable solution for solving the shortest distance estimation problem. It is important to know the distance to an obstacle in order to avoid it. The solution is a dynamic implementation of a steepest descent optimization scheme which is suitable to run on-line. Chapter 5 is an introduction to the involved control design found in chapter 6. We review results from obstacle avoidance literature and argue for our choice of using the task space control design method. The main contribution of this thesis is found in chapter 6. A controller is developed and is shown to produce a stable closed loop system. We first develop a controller considering only collision for the end effector, and then we extend this to work with full robot collision. The response of the robot is such that it will track a reference trajectory whenever it is locally possible. When one cannot track the reference trajectory because of obstacles hindering the movement, then the trajectory is tracked in all directions in which the robot can move freely. The controller is simple and elegant, and does not rely on heuristics common in traditional solutions to obstacle avoidance control.