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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.

This dissertation aims to reduce urban traffic congestion with street traffic signal control. The traffic signal controllers in the U.S. follow the National Electrical Manufacturing Association Standards (NEMA Standards). In a NEMA controller, the control parameters for a coordinated control are cycle, green splits, and offset. This dissertation proposed a virtual phase-link concept and developed a macroscopic model to describe the dynamics of a traffic network. The coordinated optimal splits control problem was solved using model predictive control. The outputs of the solution are the green splits that can be used in NEMA controllers. I compared the proposed method with a state-of-the-practice signal timing software under coordinated-actuated control settings. It was found that the proposed method significantly outperformed the benchmarking method. I compared the proposed NEMA-based virtual phase-link model and a Max Pressure controller model using Vissim. It was found that the virtual phase-link method outperformed two control strategies and performed close, but not as good as, the Max Pressure control strategy. The disadvantage of the virtual phase-link method stemmed from the waste of green time during a fixed control cycle length and the delay which comes from the slowing down of platoon during a road link to allow vehicles to switch lanes. Compared to the Max Pressure control strategy, the virtual phase-link method can be implemented by any traffic controller that follows the NEMA standards. The real-time requirement of the virtual phase-link method is not as strict as the Max Pressure control strategy. I introduced the offsets optimization into the virtual phase-link method. I modeled the traffic arrival pattern based on the optimization results from the virtual phase-link control method. I then derived a phase delay function based on the traffic arrival pattern. The phase delay function is a function of the offset between two consecutive intersections. This phase delay function was then used for offsets optimization along an arterial. I tested the offsets optimization method against a base case using microscopic simulations. It was found that the proposed offset optimization method can significantly reduce vehicle delays. / Doctor of Philosophy / The goal of this work is to reduce traffic congestion by providing optimized signal timing plans to controllers. Knowing that the controllers in the U.S. follow National Electrical Manufacturing Association (NEMA) Standards, I proposed a virtual phase-link concept and modeled the road traffic network under NEMA controllers’ control as a set of virtual phase-links. Each virtual phase-link corresponds to a NEMA phase at an intersection. I then proposed a NEMA-based virtual phase-link street traffic model. The control variables are the green time allocated to each phase. I compared the proposed NEMA-based virtual phase-link control method with a state-of-the-practice signal timing software using simulation experiments. It was found that the proposed control methods significantly outperformed the signal timing software. I implemented a state-of-the-art adaptive control strategy, Max Pressure control. I compared the proposed NEMA-based virtual phase-link control method with the Max Pressure control strategy. I found that the virtual phase-link control method performed close, but not as good as, the Max Pressure control strategy. The disadvantage of the virtual phase-link method stemmed from the waste of green time during a fixed control cycle length and the delay which comes from the slowing down of platoon during a road link to allow vehicles to switch lanes. The Max Pressure control needs non-conventional controllers which can potentially switch to any phase at any time. Compared to the Max Pressure control strategy, the virtual phase-link method can be implemented by any traffic controller that follows the NEMA standards. The real-time requirement of the virtual phase-link method is not as strict as the Max Pressure control strategy. I then augmented the virtual phase-link method with optimal offsets control. The offsets are the time differences of the coordinated phases comparing to a reference point in a control cycle. I derived a phase delay function and used that function to optimize the offsets by minimizing the associated delays. The simulation experiments showed that the proposed offsets optimization method could reduce the delay along the coordinated path significantly.

Traditional generators have been decommissioned or replaced by renewable energy generation due to utility long-standing goals. However, instead of flattening the entire plant, the rotating mass of generator can be utilized as a storage unit (inertia resource) to mitigate the frequency swings during transient caused by the renewables. The goal of this work is to design a control strategy utilizing the decommissioned generator interfaced with power grid via a back-to-back converter to provide inertia support. This is referred to as decoupled synchronous machine system (DSMS). On top of that, the grid-side converter is capable of providing reactive power as an auxiliary voltage controller. However, in a practical setting, for power utilities, the detailed state equations of such device as well as the complicated nonlinear power system are usually unobtainable making the controller design a challenging problem. Therefore, a model free, purely data-driven strategy for the nonlinear controller design using Koopman operator-based framework is proposed. Besides, the time delay embedding technique is adopted together with Koopman operator theory for the nonlinear system identification. Koopman operator provides a linear representation of the system and thereby the classical linear control algorithms can be applied. In this work, model predictive control is adopted to cope with the constraints of the control signals. The effectiveness and robustness of the proposed system are demonstrated in Kundur two-area system and IEEE 39-bus system. / Doctor of Philosophy / Power system is facing an energy transformation from the traditional fuel to sustainable renewable such as solar, wind and so on. Unlike the traditional fuel energized generators, the renewable has very little inertia to maintain frequency stability. Therefore, this work proposes a new system referred to as decoupled synchronous machine system (DSMS) to support the grid frequency. DSMS consists of the rotating mass of generator and a back-to-back converter which can be utilized as an inertia resource to mitigate the frequency oscillations. In addition, the grid-side converter can provide reactive power to improve voltage performance during faults. This work aims to design a control strategy utilizing DSMS to support grid frequency and voltage. However, an explicit mathematical model of such device is unobtainable in a practical setting making data-driven control the only option. A data-driven technique which is Koopman operator-based framework together with time delay embedding algorithm is proposed to obtain a linear representation of the system. The effectiveness and robustness of the proposed system are demonstrated in Kundur two-area system and IEEE 39-bus system.

Spacecraft relative motion modeling and control promises to enable or augment a wide range of missions for scientific research, military applications, and space situational awareness. This dissertation focuses on the development of novel, optimization-based, control design for some representative relative-motion-enabled missions. Spacecraft relative motion refers to two (or more) satellites in nearly identical orbits. We examine control design for relative configurations on the scale of meters (for the purposes of proximity operations) as well as on the scale of tens of kilometers (representative of science gathering missions). Realistic control design for satellites is limited by accurate modeling of the relative orbital perturbations as well as the highly constrained nature of most space systems. We present solutions to several types of optimal orbital maneuvers using a variety of different, realistic assumptions based on the maneuver objectives. Initially, we assume a perfectly circular orbit with a perfectly spherical Earth and analytically solve the under-actuated, minimum-energy, optimal transfer using techniques from optimal control and linear operator theory. The resulting open-loop control law is guaranteed to be a global optimum. Then, recognizing that very few, if any, orbits are truly circular, the optimal transfer problem is generalized to the elliptical linear and nonlinear systems which describe the relative motion. Solution of the minimum energy transfer for both the linear and nonlinear systems reveals that the resulting trajectories are nearly identical, implying that the nonlinearity has little effect on the relative motion. A continuous-time, nonlinear, sliding mode controller which tracks the linear trajectory in the presence of a higher fidelity orbit model shows that the closed-loop system is both asymptotically stable and robust to disturbances and un-modeled dynamics. Next, a novel method of computing discrete-time, multi-revolution, finite-thrust, fuel-optimal, relative orbit transfers near an elliptical, perturbed orbit is presented. The optimal control problem is based on the classical, continuous-time, fuel-optimization problem from calculus of variations, and we present the discrete-time analogue of this problem using a transcription-based method. The resulting linear program guarantees a global optimum in terms of fuel consumption, and we validate the results using classical impulsive orbit transfer theory. The new method is shown to converge to classical impulsive orbit transfer theory in the limit that the duration of the zero-order hold discretization approaches zero and the time horizon extends to infinity. Then the fuel/time optimal control problem is solved using a hybrid approach which uses a linear program to solve the fuel optimization, and a genetic algorithm to find the minimizing time-of-flight. The method developed in this work allows mission planners to determine the feasibility for realistic spacecraft and motion models. Proximity operations for robotic inspection have the potential to aid manned and unmanned systems in space situational awareness and contingency planning in the event of emergency. A potential limiting factor is the large number of constraints imposed on the inspector vehicle due to collision avoidance constraints and limited power and computational resources. We examine this problem and present a solution to the coupled orbit and attitude control problem using model predictive control. This control technique allows state and control constraints to be encoded as a mathematical program which is solved on-line. We present a new thruster constraint which models the minimum-impulse bit as a semi-continuous variable, resulting in a mixed-integer program. The new model, while computationally more expensive, is shown to be more fuel-efficient than a sub-optimal approximation. The result is a fuel efficient, trajectory tracking, model predictive controller with a linear-quadratic attitude regulator which tracks along a pre-computed ``safe'' trajectory in the presence of un-modeled dynamics on a higher fidelity orbital and attitude model. / Ph. D.

This thesis aims at investigating numerical methods through which the accuracy in landing of a Mars entry-descent-landing (EDL) vehicle can be improved. The methods investigated include the collocation method and model predictive control (MPC). The primary control variable utilized in this study is the bank angle of the spacecraft, which is the angle between the lift vector and the vertical direction. Modulating this vector affects the equations of system of equations and the seven state variables, namely altitude, velocity, latitude, longitude, flight path angle, heading angle and total time taken. An optimizer is implemented which utilizes the collocation method, through which the optimal bank angle is found at every discretized state along the trajectory which are equally separated through a definite timestep, which is a function of the end time state. A 3-sigma wind disturbance model is introduced to the system, as a function of the altitude, which introduces uncertainties to the system, resulting in a final state deviating from the targeted location. The trajectory is split into two parts, for better control of the vehicle during the end stages of flight. The MPC aims at reducing the end state deviation, through the implementation of a predictor-corrector algorithm that propagates the trajectory for a certain number of timesteps, followed by running the optimizer from the current disturbed state to the desired target location. At the end of this analysis, a new set of optimal bank angle are found, which account for the wind disturbances and navigates the EDL vehicle to the desired location. / M.S. / Landing on Mars has always been a process of following a set of predetermined instructions by the spacecraft, in order to reach a calculated landing target. This work aims to take the first steps towards autonomy in maneuvering the spacecraft, and finding a method by which the vehicle navigates itself towards the target. This work determines the optimal control scheme a Mars reentry vehicle must have through the atmosphere to reach the target location, and employs method through which the uncertainty in the final landing location is mitigated. A model predictive controller is employed which corrects the disturbed trajectory of the vehicle at certain timesteps, through which the previously calculated optimal control is changed so as to account for the disturbances. The control is achieved by means of changing the bank angle of the spacecraft, which in turn affects the lift and drag experienced by the vehicle. Through this work, a method has been demonstrated which reduces the uncertainty in final landing location, even with wind disturbances present.

The Hybrid Electric Vehicle Team (HEVT) of Virginia Tech is partaking in the 4-Year EcoCar Mobility Challenge organized by Argonne National Labs. The objective of this competition is to modify a stock 2019 traditional internal combustion engine Chevrolet Blazer and to transform the vehicle into a P4 hybrid. Due to the P4 Hybrid architecture, the HEVT vehicle has an internal combustion engine on the front axle and an electric motor on the rear axle. The goal of this competition is to create a vehicle that achieves better fuel economy and increases customer appeal. The general target market of hybrids is smaller vehicles. As a midsize sport utility vehicle (SUV), the Blazer offers a larger vehicle with the perk of better fuel economy. In the competition, the vehicle is assessed on the ability to integrate advanced vehicle technology, improve consumer appeal, and provide comfort for the passenger. The research of this paper is centered around the design of a full range longitudinal Adaptive Cruise Control (ACC) algorithm. Initially, research is conducted on various linear and nonlinear control strategies that provide the necessary functionality. Based on the ability to predict future time instances in an optimal method, the Model Predictive Control (MPC) algorithm is chosen and combined with other standard control strategies to create an ACC system. The main objective of this research is the implementation of Adaptive Cruise Control features that provide comfort and energy savings to the rider while maintaining safety as the priority. Rider comfort is achieved by placing constraints on acceleration and jerk. Lastly, a proper energy analysis is conducted to showcase the potential energy savings with the implementation of the Adaptive Cruise Control system. This implementation includes tuning the algorithm so that the best energy consumption at the wheel is achieved without compromising vehicle safety. The scope of this paper expands on current knowledge of Adaptive Cruise Control by using a simplified nonlinear vehicle system model in MATLAB to simulate different conditions. For each condition, comfort and energy consumption are analyzed. The city 505 simulation of a traditional ACC system show a 14% or 42 Wh/mi reduction in energy at the wheel. The city 505 simulation of the environmentally friendly ACC system show a 29% or 88 Wh/mi reduction in energy at the wheel. Furthermore, these simulations confirm that maximum acceleration and jerk are bounded. Specifically, peak jerk is reduced by 90% or 8 m/s3 during a jerky US06 drive cycle. The main objective of this analysis is to demonstrate that with proper implementation, this ACC system effectively reduces tractive energy consumption while improving rider comfort for any vehicle. / Master of Science / The Hybrid Electric Vehicle Team (HEVT) of Virginia Tech is partaking in the 4-Year EcoCar Mobility Challenge organized by Argonne National Labs. The objective of this competition is to modify a stock 2019 Chevrolet Blazer into a hybrid. This modification is accomplished by creating a vehicle that burns less gasoline and increases customer appeal. The general target market of hybrids is smaller vehicles. As a midsize sport utility vehicle (SUV), the Blazer offers a larger vehicle with the perk of better fuel economy. In the competition, the vehicle is assessed on the ability to integrate advanced technology, improve consumer appeal, and provide comfort for the passenger. The research of this paper is centered around the design of Adaptive Cruise Control (ACC). Initially, research is conducted on various control strategies that provide the necessary functionality. A controller that predicts future events is selected for the Adaptive Cruise Control. The main objective of this research is the implementation of Adaptive Cruise Control features that provide comfort and energy consumption savings to the rider while maintaining safety as the priority. Rider comfort is achieved by creating a smoother ride. Lastly, a proper energy analysis showcases the potential energy savings with the implementation of the Adaptive Cruise Control system. The scope of this paper expands on current knowledge of Adaptive Cruise Control by using a simplified vehicle model to simulate different conditions. The city simulations of a traditional ACC system show a 14% reduction in energy at the wheel. City simulations of the environmentally friendly Adaptive Cruise Controller show a 29% reduction in energy. Both of these simulations allow for comfortable ride. Specifically, maximum car jerk is reduced by 90%. The main objective of this analysis is to demonstrate that with proper implementation, this ACC system effectively reduces energy consumption at the wheel while improving rider comfort.

Yes / A milk pasteurization process, a nonlinear process and multivariable interacting system, is difficult to control by the conventional on-off controllers since the on-off controller can handled the temperature profiles for milk and water oscillating over the plant requirements. The multi-variable control approach with model predictive control (MPC) is proposed in this study. The proposed algorithm was tested for control of a milk pasteurization process in three cases of simulation such as set point tracking, model mismatch, difference control and prediction horizons, and time sample. The results for the proposed algorithm show the well performance in keeping both the milk and water temperatures at the desired set points without any oscillation and overshoot and giving less drastic control action compared to the cascade generic model control (GMC) strategy.

Networked control systems (NCSs) present many advantages such as easy installation and maintenance, flexible layouts and structures of components, and efficient allocation and distribution of resources. Consequently, they find potential applications in a variety of emerging industrial systems including multi-agent systems, power grids, tele-operations and cyber-physical systems. The study of NCSs with nonlinear dynamics (i.e., nonlinear NCSs) is a very significant yet challenging topic, and it not only widens application areas of NCSs in practice, but also extends the theoretical framework of NCSs with linear dynamics (i.e., linear NCSs). Numerous issues are required to be resolved towards a fully-fledged theory of industrial nonlinear NCS design. In this dissertation, three important problems of nonlinear NCSs are investigated: The robust filtering problem, the robust model predictive control (MPC) problem and the robust distributed MPC problem of large-scale nonlinear systems. In the robust filtering problem of nonlinear NCSs, the nonlinear system model is subject to uncertainties and external disturbances, and the measurements suffer from time delays governed by a Markov process. Utilizing the Lyapunov theory, the algebraic Hamilton-Jacobi inequality (HJI)-based sufficient conditions are established for designing the H_infty nonlinear filter. Moreover, the developed results are specialized for a special type of nonlinear systems, by presenting the HJI in terms of matrix inequalities. For the robust MPC problem of NCSs, three aspects are considered. Firstly, to reduce the computation and communication load, the networked MPC scheme with an efficient transmission and compensation strategy is proposed, for constrained nonlinear NCSs with disturbances and two-channel packet dropouts. A novel Lyapunov function is constructed to ensure the input-to-state practical stability (ISpS) of the closed-loop system. Secondly, to improve robustness, a networked min-max MPC scheme are developed, for constrained nonlinear NCSs subject to external disturbances, input and state constraints, and network-induced constraints. The ISpS of the resulting nonlinear NCS is established by constructing a new Lyapunov function. Finally, to deal with the issue of unavailability of system state, a robust output feedback MPC scheme is designed for constrained linear systems subject to periodical measurement losses and external disturbances. The rigorous feasibility and stability conditions are established. For the robust distributed MPC problem of large-scale nonlinear systems, three steps are taken to conduct the studies. In the first step, the issue of external disturbances is addressed. A robustness constraint is proposed to handle the external disturbances, based on which a novel robust distributed MPC algorithm is designed. The conditions for guaranteeing feasibility and stability are established, respectively. In the second step, the issue of communication delays are dealt with. By designing the waiting mechanism, a distributed MPC scheme is proposed, and the feasibility and stability conditions are established. In the third step, the robust distributed MPC problem for large-scale nonlinear systems subject to control input constraints, communication delays and external disturbances are studied. A dual-mode robust distributed MPC strategy is designed to deal with the communication delays and the external disturbances simultaneously, and the feasibility and the stability conditions are developed, accordingly. / Graduate / 0548 / 0544

Platooning is an interesting area which involve the possibility of decreasing the fuel consumption of heavy-duty vehicles. By reducing the inter-vehicle spacing in the platoon we can reduce air drag, which in turn reduces fuel consumption. Two fuel-efficient model predictive controllers for HDVs in a platoon has been formulated in this master thesis, both utilizing road grade preview information. The first controller is based on linear programming (LP) algorithms and the second on quadratic programming (QP). These two platooning controllers are compared with each other and with generic controllers from Scania. The LP controller proved to be more fuel-efficient than the QP controller, the Scania controllers are however more fuel-efficient than the LP controller.