The main topics of this master’s project are control theory, system identification and convex optimization. The objective is to develop, implement and test methods for optimal input signal design and for control of a nonlinear dynamical system using MPC. The thesis begins with a theoretical part, in which some known results in these fields are summarized. In the applied part of the thesis, methods are developed and exemplified in MATLAB. Optimal input signal design is performed on specific FIR, ARX and DCmotor systems which are all controlled by an MPC. The implementation works very well for the FIR and ARX systems. The estimates of the true parameters fulfill the pre-specified requirements when using the optimal input signal constructed. An unexpected behavior is obtained of the estimates for the DC-motor system. Some additional approximations which were made in the design of the optimal input signal are thought to be the cause. Although, the source of the odd behavior were never confirmed. To be able to have a user-friendly environment for optimal input signal design, further work is necessary to overcome numerical problems in the implementation. A general method of implementing MPC of nonlinear dynamical systems is constructed. It is problematic to use MPC to control a nonlinear system. The reason for this is that a nonlinear system in general corresponds to a non-convex optimization problem in the MPC algorithm. Our method is based on making the problem convex through a linearization of the nonlinear system dynamics. The method is tested on simulations of a reaction wheel pendulum and a two link robot arm. It works very well and the systems fulfill the control objectives. Each optimization problem takes about 0.3-1 second to solve when using cvx. This is in some situations too slow to be able to control a system in reality. Further work is recommended on implementing our method with another solver so that it can be tested on an actual system which requires new updates every milli- or microsecond. / Design av optimal insignal och MPC för ickelinjära dynamiska system Detta examensarbete berör områden som reglerteknik, systemidentifiering och konvex optimering. Syftet är att utveckla metoder för design av en optimal insignal och för att använda MPC på ickelinjära dynamiska system. Rapporten börjar med en teoretisk del som sammanfattar kända resultat inom dessa områden. Därefter följer beskrivningar av de metoder som har utvecklats och de exemplifieras genom simulering i MATLAB. En metod för att designa en optimal insignal för specifika FIR-, ARX och DC-system har utvecklats. Systemen styrs med hjälp av en MPC regulator. Metoden fungerar utmärkt för FIR- och ARX-system. Ett oväntat resultat erhålls för fallet med DC-motorn. Vi tror att det beror på de approximationer som har gjorts särskilt för detta system men det har inte kunnat bekräftas. För att skapa en användarvänlig miljö för design av en optimal insignal givet ett system och en regulator så krävs ytterligare arbete. Det bör fokusera på att eliminera de numeriska problem som uppstår när metoden implementeras i MATLAB. En allmän metod för att använda MPC på ickelinjära dynamiska system har implementerats. Ett ickelinjärt system ger generellt upphov till ett ickekonvext optimeringsproblem i MPC algoritmen. Det är därför problematiskt att använda MPC för att reglera ickelinjära system. Vår metod bygger på att göra problemet konvext genom att linjärisera det icke linjära systemet. Metoden har testats på simuleringar av en pendel och en två-länkad robotarm. Den presterar väldigt bra och systemen uppnår önskat beteende. Optimeringsproblemet tar cirka 0,3-1 sekund att lösa när vi använder cvx. Detta är i vissa fall för långsamt för att kunna reglera ett verkligt system. Ytterligare arbete där metoden implementeras med en annan lösare rekommenderas. Detta skulle möjliggöra att man kan testa den på ett verkligt system som kräver uppdateringar varje milli- eller mikrosekund.

We consider the problem of selecting k sensors out of m available (linear) sensors, so that the error in estimating some parameters is minimized. When the sensor noises are uncorrelated, the sensor selection problem can be (approximately) solved by a method recently suggested by Joshi and Boyd, which relies on a convex relaxation of the underlying combinatorial optimization problem. This thesis describes a non-trivial extension of the relaxation method to the case when the measurement noises are correlated, as occurs, for example, in a sensor scheduling problem in a dynamic system. We develop several new semidenite programming (SDP) relaxations for the problem, which give provable bounds on the attainable performance, as well as suboptimal sensor selections. Numerical experiments for sensor scheduling suggest that the methods work well.

In a world where there are about 7 billion people living and this number is continuously increasing, it is necessary to reduce the resource consumption to achieve a sustainable situation. In this work, a system to detect water and electricity consumption is introduced to identify resource waste and inform the consumers about it. For this purpose, many sensors are deployed in the kitchen of the department in order to gather data of the consumption. These sensors are an alternative to other ways of getting this information that are usually considered as invasive, like a camera. Even though, as far as there are many sensors deployed, the way to put all data together will be using wireless communication. Then, a treatment is performed in order to obtain some statistics about the consumption. These networks can also be accessed by people external to the department, who would be able to get information about their consumption and, consequently, their expenditures. Because all of this, a privacy problem of the enterprise appears, in this case the Electrical Engineering Automatic Control Department. Regarding the wireless communication, dierent protocols will be tested to check their reliability. Furthermore, the data from the dierent sensors makes possible to determine behaviour patterns of the people working there. By using this system, not environmentally friendly actions that lead to resource waste can be easily identied and corrected. Again, this opens a discussion about privacy, concerning the dierent people and their habits. To sum up, the system would enable the consumers to decrease their resource consumption, which would lead to an important energy saving in large scale and a reduction in costs in small scale.

In this master thesis, an extension of the interaction matrix formulation to the discrete-time bilinear state-space model is derived. Several identication techniques are presented from this formulation to identify the bilinear state-space matrices using a superstate vector, derived from a single set of su-ciently rich input-output measurements. The initial state can be non-zero and unknown. Unlike other approaches, no specialized inputs are required, such as sinusoidal or white inputs, or duration-varying unit pulses involving multiple experiments. For that reason, the bilinear state-space identication problem is di-cult to solve, since it can be seen as a linear time-varying system with input-dependent system matrix or state-dependent input-influence matrix. The resultant input-output map from this state-space formulation can be used for output prediction. A relationship between the coe-cients of this input-output map and the bilinear state-space model matrices is obtained via two interaction matrices, corresponding to the linear and bilinear portions of the model, respectively. Numerical examples are provided to illustrate these bilinear state-space model identication techniques and the input-output model identication method. It is concluded that the proposed identication algorithms can correctly identify the original bilinear state-space model, and the identied input-output map correctly predict its system output response, despite the fact that the interaction matrices are only implicitly assumed to exist.

Transportation-cost is an important factor in the price of products, from groceries to industrial products. These products are conventionally transported using road carriers, both domestic and international. The two largest parts of the transportation-costs using this method are fuel and driver costs. Research has shown that by using platoons, traffic flow is increased and fuel cost is reduced. The aim of this thesis is to study different disturbances and their effect on platoons to enable platooning. Two types of disturbances have been identified; internal and external. The internal disturbance is delay in the radar of the adaptive cruise control, and external disturbances are different road and traffic scenarios. Throughout this thesis, the disturbances identified have been modeled and implemented on a heavy-duty vehicle platoon of five vehicles. These disturbances have been implemented single and in combinations, trying to identify the properties of a robust adaptive cruise control and platoon. The simulations show that the adaptive cruise control can manage external disturbances resulting in a robust platoon. But by implementing radar delay, increase of relative velicity and decrease of relative distance are amplified through the platoon. Further using the vehicle’s collision warning system a correlation has been found, resulting in identification of a robust area for a platoon. This identification could be used to help avoiding collision warnings and collisions in the platoons.

Syftet med detta examensarbetet är att ta fram en modell av ett segelinställande system hos en segelbåt. Detta för att ställa in storseglet hos båten per automatik. Anledningen till ett segelinställande system kan vara att man vill hålla nere vikten hos båten då manskap väger mer än systemet. Andra aspekter är att personer med segelbåtar som saknar kunskaper, eller tycker det är besvärligt att ställa in seglen vid turer med båten, kan använda systemet för att underlätta seglingen. Man undviker då att använda motorn på segelbåten och kan då spara bränslekostnader. Segelinställningen görs genom att en sensor mäter varifrån vinden blåser i förhållande till skrovet, samt efter vilken hastighet vinden har. Information har insamlats för att kunna modellera en segelbåt med dess komponenter. En matematisk modell för segelbåtens komponenter har tagits fram för att veta hur storseglet ställs in för en viss insignal till elvinschen, samt för hur krafterna påverkar vinsch med segel. Till sist har båtens komponenter och skrovets tröghetsmoment modellerats, detta för att få fram dynamik för att mer exakt beskriva rörelser i systemet. Den matematiska modellen av det segelinställande systemet skapades i delsystem. I programmet Simulink sattes delsystemen ihop till en komplett modell. Modellen som är olinjär linjäriserades av anledningen att linjär reglerteori användes vid framtagandet av en lead-lag regulator. Den framtagna linjära regulatorn implementerades i den olinjära modellen, och flera simuleringar med olika störningar och laster gjordes. Regulator med system uppfyllde de ställda kraven enligt kravspecikationen. / The purpose of this thesis work is to construct a model of a sail setting system of a sailboat. This system will automatically adjust the setting of the mainsail of the boat. The reason of having an automatic sail setting system could be to keep the weight down of the boat as the crew weighs more than the system. Other aspects are that sailboat owners, who lack the knowledge or think that it is di-cult to adjust the sails, can use the system to ease the sailing when taking trips with their boat. You will then avoid using the boat's engine and can then save on fuel costs. The setting of the sail is made by measuring with a sensor from where the wind is blowing relative to the hull and due to the wind velocity. Information has been collected to be able to model a sailboat with its components. A mathematical model of the sailboats components has been constructed to know how the mainsail is set for a given input signal to the electric winch as well as how the forces will aect the winch. Finally, the moment of inertia of the components of the boat and its hull has been modeled to capture the dynamics and to more accurately describe motions in the system. The mathematical model of the sail setting system was created in subsystems. In the software Simulink the subsystems were put together to a complete model. The model that is non-linear was linearized due to the reason that linear control theory was used when constructing a leadlag controller. The constructed linear controller was implemented in the non-linear model and several simulations were made with dierent disturbances and loads. The controller and the system fulfillled all the requirements that were specied.

The aim of this thesis project is to implement a vision based surveillance system in a wireless sensor network running the Contiki operating system. After a comparative review of experimental cameras the decision fell on the Cmucam3. Hardware and software to integrate the camera with a Tmote Sky mote were created. In this way, the camera can be controlled with the Contiki operation system and images can be transferred to the sensors memory for further processing and forwarding to other network nodes. Due to the lack of memory on the sensor nodes, the prospect of image compression was investigated. To save energy, the system uses an energy efficient onboard light sensor to detect ambivalent changes that would occur in the presence of, for instance, intruders or fire. When these sensors detect changes, the more energy consuming camera gets activated. The detection mechanism uses a Cusum algorithm which filters out irrelevant disturbances while maintaining high sensitivity to unexpected changes. An evaluation of the system using multiple motes running the energy efficient detection algorithm demonstrates rapid detection and transmission times of about 2 seconds.

To be able to monitor forces acting on objects is important for a lot of dierent applications. In this case the object is a big steel disc and the forces to be monitored are those acting on the rim of the disc. This is done with strain gauges that register changes in the internal strain eld. This is then run through a system model that outputs the equivalent force for that strain eld. The system model is created through a static system identication consisting of a series of test pushes on the rim of the disc. This method of system identication has a series of problem mainly that it is time consuming. The thesis presents a proof-of-concept of a dynamic system identication method. Instead of pressure applied while stationary the pressure is applied by rotating the disc against another smaller steel disc and performing the system identication on this continuous data. An algorithm to use the data is tested in simulation and the results are analyzed and proven successful. Then a experiment is performed, recording data and running the algorithm. The dynamic system identication is shown to give almost equal results to the static one. The dierence can be accounted for as problems with the force measuring or that the dynamic system identication is actually more accurate than the static one. The algorithm is concluded to work and give an advantage over the old algorithm in form of the time it takes to perform it. It has a possibility to be more accurate and also to be able to identify forces in more directions than straight into the disc.

Ett nytt koncept för separering av jäst från öl har tagits fram på Alfa Laval i Tumba. Jästen matas nu ut kontinuerligt istället for att skjutas ut då separatorn har fyllts med för mycket jäst, konceptet gör att man kan spara öl som annars försvinner i samband med skott. För att konceptet skall vara lönsamt måste den utmatade jästen ha tillräckligt hög densitet trots att indensiteten ständigt sjunker, samtidigt som man måste ha bra separering. I det här examensarbetet har en reglerstrategi för denna höghastighets centrifugal separationsprocess utvecklats. Genom experimentella studier av systemet kunde en matematisk modell av separationsprocessen skapas. Modellen användes sedan som grund for en MPC-regulator där densiteten styrdes genom att styra flödena i processen. En implementering av styrningen genomfördes sedan i processlaboratoriet i Tumba. Separeringen antogs vara bra så länge massflödet in var relativt lågt och trycknivåerna var bra. Med MPC-regulatorn gick det att hålla densiteten över en satt gräns i laboratorieexperiment. Det visas också att en ervariabel regulator i det här fallet har fördelar över envariabla. Förutsättningar för att i ett nästa steg även reglera separeringseffektiviteten anses finnas. / A new concept for separating yeast from beer has been developed at Alfa Laval in Tumba. The yeast is now continuously fed out from the separator instead of discharged when too much yeast have collected in the separator. The concept makes it possible to save beer which otherwise would have been wasted at discharges. For the concept to be protable, the density of out yeast must be high enough even though the inlet density is steadily declining, and at the same time have good separation eency. In this thesis a control strategy has been developed for this high speed centrifugal separation process. Through experimental studies a mathematical model of the separation process could be made. This model was then used for a MPC-controller where the density was controlled by controlling the ows of the process. An implementation of the control strategy was carried out in the process laboratory in Tumba. The separation was assumed to be good as long as the mass inow was relatively low and the pressure levels were steady. With the MPC-controller it was possible to maintain the density over the set limit in laboratory experiments. It is also shown that a multivariable controller has benets compared to a single variable controller. Controlling the separation efficiency is deemed possible and is the next step.

Wireless sensor networks (WSNs) are utilized for ubiquitous and pervasive computing to detect contextual information as well as represent a new monitoring and control ability for applications in industries, transportation and health care. A user is able to gain the effective use of captured context by the sensor network. The WSN software application is an important tool to visualize the information for the different applications. This research provides how to design WSN software application for visual user interface and how to develop WSN system in order to use it in practice. We apply a graphical user interface (GUI) to enhance the intuitiveness of the interactive system. Activity Theory (AT) helps WSN software application make user-centered design. WSN GUI application is implemented with Java Swing on TinyOS, an operating system for WSNs. Furthermore, Java Web Start and the web database support WSN system to provide the GUI software applications via the internet.