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A model (NONLINRK) was developed for a closed tank system under feedback control by an ideal proportional-integral-derivative controller. Under servo action the fluid level in the tank is altered from its equilibrium set point. Under regulatory action the feed pressure to the inlet valve and/or the outlet valve percentage opening are varied from equilibrium settings. The numerical model uses Gill’s fourth-order Runge-Kutta algorithm to solve the system equation. The equation was made separable by approximating an exponential factor by the tangent at the beginning of each time step in the numerical solution. NONLINRK simulation trials exhibited many characteristics of linear system including unequal offset under proportional control for the setpoint changes equal in magnitude but opposite in sign, harmonics in the response to a sine wave input on fluid level setpoint and bounded response in spite of increased gain settings. In addition, further simulation trials showed the system response converges to that of a linear system for sufficiently small setpoint of load variations. A second model using the modeling language TUTSIM provided corroboration of the results produced by NONLINRK. Proportional and proportional-integral control simulations differed by less than .1% and the models showed the same rates of convergence as the time step was decreased. Under PID control TUTSIM simulations developed severe instabilities, but NONLINRK exhibited the expected trends in the increased ability to react to a ramp function disturbance and the decrease in phase lag in response to a sinusoidal setpoint function.

There is a constant demand to use more advanced control methods in a wider field of applications. Model Predictive Control (MPC) is one such control method, based on recurrently solving an optimization problem for determining the optimal control signal. To solve an optimization problem can be a complex task, and it is difficult to determine beforehand how long time it will take. For a high-speed application with limited computational power, it is necessary to have an efficient algorithm to solve the optimization problem and an accurate estimation of the longest solution time. Recent research has given methods both to solve quadratic programs efficiently and to find an upper limit on the solution times. These methods are in this thesis applied to a control system based on linear MPC for the Crazyflie 2.0 nano quadcopter. The implementation is made completely online on the processor of the quadcopter, with limited computational power. A problem with the size of 36 optimization variables and 60 constraints is solved at a frequency of 100 Hz on the quadcopter. Apart from implementing MPC, a framework for computing an upper limit to the solution time has been tested. This gives a possibility to certify the formulation for real-time applications up to a well-defined maximum frequency. An implementation is shown where the framework has been used in practice to control a quadcopter flying with a real-time certified implementation of MPC. / Det finns en ständig efterfrågan för mer avancerade metoder för reglering. Modellprediktiv reglering (MPC) är en sådan avancerad metod som kräver att ett optimeringsproblem löses varje gång en ny styrsignal ska beräknas. Att lösa optimeringsproblem kan vara en komplicerad uppgift, och det är svårt att på förhand veta hur lång beräkningstid som krävs. För att MPC ska kunna användas i tillämpningar i hög hastighet och med begränsad beräkningskraft är det nödvändigt att ha en effektiv lösningsalgoritm, och även en korrekt uppskattning av den längsta lösningstiden som behövs. Aktuell forskning har gett metoder både för att effektivt lösa kvadratiska optimeringsproblem, samt för att kunna hitta en övre gräns på beräkningstiden. I den här rapporten appliceras dessa metoder på ett styrsystem baserat på MPC i en Crazyflie 2.0, vilket är en nanodrönare. Styrsystemet är implementerat helt och hållet på drönarens processor, med den begränsade datorkraft som det innebär. Ett problem med en storlek på 36 optimeringsvariabler och 60 bivillkor lösesmed en frekvens på 100 Hz. Förutom att implementera MPC har även en metod för att bestämma en övre gräns på beräkningstiden testats. Det ger en möjlighet att certifiera styrstytemetför att garanterat kunna beräkna en ny styrsignal inom den övre tiden, vilket i sin tur innebär att styrsytemet kan certificeras för realtidsanvändning i långsammare frekvenser än den övre gränsen. I rapporten visas en certifierad implementation, och data från flygning med en certifierad regulator finns med i resultatet.

The main focus of this study is on the active and semi-active control of civil engineering structures subjected to seismic excitations. Among different candidate control strategies, the sliding mode control approach emerges as a convenient alternative, because of its superb robustness under parametric and input uncertainties. The analytical developments and numerical results presented in this dissertation are directed to investigate the feasibility of application of the sliding mode control approach to civil structures. In the first part of this study, a unified treatment of active and semi-active sliding mode controllers for civil structures is presented. A systematic procedure, based on a special state transformation, is also presented to obtain the regular form of the state equations which facilitates the design of the control system. The conditions under which this can be achieved in the general case of control redundancy are also defined. The importance of the regular form resides in the fact that it allows to separate the design process in two basic steps: (a) selection of a target sliding surface and (b) determination of the corresponding control actions. Several controllers are proposed and extensive numerical results are presented to investigate the performance of both active and semi-active schemes, examining in particular the feasibility of application to real size civil structures. These numerical studies show that the selection of the sliding surface constitutes a crucial step in the implementation of an efficient control design. To improve this design process, a generalized sliding surface definition is used which is based on the incorporation of two auxiliary dynamical systems. Numerical simulations show that this definition renders a controller design which is more flexible, facilitating its tuning to meet different performance specifications. This study also considers the situation in which not all the state information is available for control purposes. In practical situations, only a subset of the physical variables, such as displacements and velocities, can be directly measured. A general approach is formulated to eliminate the explicit effect of the unmeasured states on the design of the sliding surface and the associated controller. This approach, based on a modified regular form transformation, permits the utilization of arbitrary combinations of measured and unmeasured states. The resulting sliding surface design problem is discussed within the framework of the classical optimal output feedback theory, and an efficient algorithm is proposed to solve the corresponding matrix nonlinear equations. A continuous active controller is proposed based only on bounding values of the unmeasured states and the input ground motion. Both active and semi-active schemes are evaluated by numerical simulations, which show the applicability and performance of the proposed approach. / Ph. D.

A method utilizing H2 control concepts and the numerical method of Polynomial Chaos was developed in order to create a novel robust probabilistically optimal control approach. This method was created for the practical reason that uncertainty in parameters tends to be inherent in system models. As such, the development of new methods utilizing probability density functions (PDFs) was desired. From a more theoretical viewpoint, the utilization of Polynomial Chaos for studying and designing control systems has not been very thoroughly investigated. The current work looks at expanding the H2 and related Linear Quadratic Regulator (LQR) control problems for systems with parametric uncertainty. This allows solving deterministic linear equations that represent probabilistic linear differential equations. The application of common LTI (Linear Time Invariant) tools to these expanded systems are theoretically justified and investigated. Examples demonstrating the utilized optimization process for minimizing the H2 norm and parallels to LQR design are presented. The dissertation begins with a thorough background section that reviews necessary probability theory. Also, the connection between Polynomial Chaos and dynamic systems is explained. Next, an overview of related control methods, as well as an in-depth review of current Polynomial Chaos literature is given. Following, formal analysis, related to the use of Polynomial Chaos, is provided. This lays the ground for the general method of control design using Polynomial Chaos and H2. Then an experimental section is included that demonstrates controller synthesis for a constructed probabilistic system. The experimental results lend support to the method. / Ph. D.

Rapid mixing is crucial for the efficient and environment-friendly operation of many industrial and propulsion devices involving jet flows. In this dissertation, two methodologies, self-excited nozzles and radially lobed nozzles, are studied and presented in order to enhance mixing in the near field of coflowing, subsonic, turbulent, free jet flows. The characteristics of the concentration field and the mixing performance are examined, mainly in quantitative manner. Two new parameters, mixing index and mixing efficiency index, are defined for free jets, allowing quantitative analysis of the mixing performance and efficiency. The flow fields are studied with hot wire anemometry, and with CFD simulation for some of the radially lobed nozzles. Due to the large vectoring angle of the jet flows from these nozzles, a new definition for the entrainment ratio is also adopted in order to take the large radial velocity component into consideration. Self-excited nozzles, rectangular and square shaped, are examined at Reynolds numbers of 17,000 and 31,000. The self-excited square jet has fastest mixing and highest mixing efficiency, with 400% higher mixing index at 4 diameters downstream than the unexcited square jet. The mixing is improved as the excitation frequency or coflow velocity increases. The study of flow field shows the presence of one pair of periodic, coherent array of large-scale, streamwise, counter-rotating inviscid vortices shedding from each of the two flaps which dominate the mean flow and the mixing process. The coflow is primarily entrained into the jet in the minor plane while the jet fluid vectors in the major plane. Significant increase in turbulent kinetic energy immediately downstream the nozzle exit improves small-scale mixing. Radially lobed nozzles, a cross-shaped and a clover-shaped with four lobes each, are analyzed in comparison to a conical nozzle. In addition, a few modified radially lobe nozzles, including a 6-lobe nozzle and an 8-lobe nozzle, two type of fully penetrating nozzles, and a cross-shaped nozzle with centerbody, are examined in order to achieve better mixing than the cross-shaped nozzle. At 4 diameters downstream, the mixing index of the cross-shaped nozzle is 650% higher than that of the conical nozzle. The cross-shaped nozzle with centerbody, the 6- lobe and 8-lobe nozzles have slower mixing and lower efficiency than the cross-shaped nozzle,but the fully-penetrating nozzles are generally better than the cross-shaped nozzle, especially at low coflow velocities and in the far field. The flow field study shows that parallel lobe walls and deep penetration of the coflow are importance factors responsible for the observed mixing enhancement. / Ph. D.