Browsing by Subject "Optimal control"
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Item A homotopic approach to solve the fuel optimal spacecraft proximity operations problem(2017-05) Gulino, Marco; Akella, Maruthi Ram, 1972-This report focuses on finding the low-thrust fuel optimal solution to a class of spacecraft proximity operations subject to path constraints. The mission is for a service spacecraft to perform a surveying orbit relative to a reference within a prescribed period, without violating a no fly zone represented by a sphere centered on the reference vehicle. Clohessy-Wiltshire equations are used, together with the controllability Gramian of the resulting linear system, to obtain an analytical solution to the energy optimal problem. A homotopic approach is subsequently shown to serve as an effective bridge from the energy optimal solution toward the fuel optimal solution.Item Battery energy storage control : modeling, uncertainty, and applications(2020-05) Rosewater, David Martin; Santoso, Surya; Baldick, Ross; Zhu, Hao; Huang, Qin (Alex); Hanasusanto, Grani; Byrne, RaymondBattery energy storage systems (BESS) can restore flexibility to power systems that grow increasingly constrained from proliferation of variable renewable power and retirement of fossil-fuel based generation. BESS are often controlled through an energy management system (EMS), which may not have access to detailed, physical models developed by battery manufacturers. The research outlined in this dissertation makes substantive contributions to quantify, reduce, and ultimately account for the effects of battery system modeling uncertainty on energy management and control. Battery models for optimal control are reviewed in detail and metrics for their accuracy and uncertainty are derived. Optimal parameter identification and adaptive modeling methods are developed to reduce model uncertainty as much as possible. As some uncertainty always remains, a method for risk-averse model predictive control for BESS is developed to account for uncertainty and hedge control decisions to reduce optimistic shortfall. Lastly, the potential for controller performance improvement to bolster the value of BESS on the grid is demonstrated. Together, more accurate, adaptive models working in conjunction with risk-adverse control algorithms dismantle the impacts of model uncertainty on energy storage grid integration. These contributions represent an advance to the state-of-the-art in the engineering methods for addressing molding uncertainty in BESS control.Item Brushless DC motor modeling and optimal control: a cardiovascular application(2016-08) Rapp, Ethan Stewart; Longoria, Raul G.; Chen, DongmeiThe increasing use of Ventricular Assist Devices (VADs) in patients with weak or failing hearts has driven a need for more thorough analysis of VAD design, control methods, and cardiovascular dynamic effects. In recent years, studies have shown the potential of applying formal optimization methods to VAD actuation in order to reduce power consumption or improve pump output. This thesis continues the use of formal optimization methods as well as digital analysis using the brushless DC (BLDC) motors within the TORVAD(TM), designed by Windmill Cardiovascular Systems, Inc. (WCS), as a basis. To begin the optimization, a parameterized model of the BLDC motor system has been developed and combined with a lumped parameter model of the cardiovascular system. The combined system is then digitally analyzed under varying rates of TORVAD(TM) motor controller frequencies to determine the minimum frequency at which the system will remain stable and minimize detrimental physiological effects. Formal optimization methods are then introduced and implemented on the combined motor and cardiovascular system model. The output of the optimization is a reference trajectory that minimizes average motor power consumption. This trajectory, along with the results from the digital analysis, provides a more robust examination on the combined motor and cardiovascular system.Item Collision avoidance techniques and optimal synthesis for motion planning applications(2019-05-09) Marchidan, Andrei; Bakolas, Efstathios; Akella, Maruthi; Humphreys, Todd; Sentis, Luis; Longoria, RaulThis dissertation focuses on the problem of motion planning for autonomous agents that are required to perform fast and reactive maneuvers. In realistic situations, this problem needs to be solved in real-time for environments that are both dynamic and partially known. The success of the provided motion plans also relies on the agent’s ability to accurately perform the prescribed maneuvers and, as such, consideration of the input constraints is often times necessary. The problem can be posed in two different ways: as a controllability problem, where trajectory generation is only concerned with satisfying the given boundary conditions, system constraints (dynamic and input constraints) and state constraints (forbidden areas in the state space); or as an optimal control problem, where the trajectory is also required to optimize some performance measure. The main contributions of this dissertation are two-fold. First, a new numerical technique is proposed for solving time-optimal control problems for an agent moving in a spatiotemporal drift field. The solution technique computes the minimum time function and the corresponding time-optimal feedback control law, while using an extremal front expansion procedure to filter out sub-optimal solutions. This methodology can be applied for a rich class of time-optimal control problems where the control input structure is determined by a parameter family of differential equations. To demonstrate its applicability, the numerical technique is implemented for the Zermelo navigation problem on a sphere and for the steering problem of a self-propelled particle in a flow field. Next, in the second part of this dissertation, the controllability problem in the presence of obstacles can be solved using local reactive collision avoidance vector fields. The proposed approach uses the concept of local parametrized guidance vector fields that are generated directly from the agent model and encode collision avoidance behaviors. Their generation relies on a decomposition of agent kinematics and on a proximity-based velocity modulation determined by specific eigenvalue functions. Further exploiting the modulation properties arising from the nature of these eigenvalue functions, curvature constraints can be guaranteed. Closed-form steering laws are determined in accordance with the computed collision avoidance vector fields and can provide the necessary avoidance maneuvers to guarantee problem feasibility. Throughout this dissertation, examples and simulation results in different types of environments are presented and discussed. In the final part of this dissertation, the motion planning problem is tackled for more complex environments. The two proposed methodologies for optimal control and for collision avoidance are combined to yield a hybrid controller that generates near-optimal feasible plans in the presence of multiple static and moving obstacles and of spatiotemporal drift fields.Item Controlled self-assembly of charged particles(2010-05) Shestopalov, Nikolay Vladimirovic; Rodin, G. J. (Gregory J.); Henkelman, GraemeSelf-assembly is a process of non-intrusive transformation of a system from a disordered to an ordered state. For engineering purposes, self-assembly of microscopic objects can benefit significantly from macroscopic guidance and control. This dissertation is concerned with controlling self-assembly in binary monolayers of electrically charged particles that follow basic laws of statistical mechanics. First, a simple macroscopic model is used to determine an optimal thermal control for self-assembly. The model assumes that a single rate-controlling mechanism is responsible for the formation of spatially ordered structures and that its rate follows an Arrhenius form. The model parameters are obtained using molecular dynamics simulations. The optimal control is derived in an analytical form using classical optimization methods. Two major lessons were learned from that work: (i) isothermal control was almost as effective as optimal time-dependent thermal control, and (ii) neither electrostatic interactions nor thermal control were particularly effective in eliminating voids formed during self-assembly. Accordingly, at the next stage, the focus is on temperature-pressure control under isothermal-isobaric conditions. In identifying optimal temperature and pressure conditions, several assumptions, that allow one to relate the optimal conditions to the phase diagram, are proposed. Instead of verifying the individual assumptions, the entire approach is verified using molecular dynamics simulations. It is estimated that under optimal isothermal-isobaric conditions the rate of self-assembly is about five time faster than that under optimal temperature control conditions. It is argued that the proposed approach of relating optimal conditions to the phase diagram is applicable to other systems. Further, the work reveals numerous and useful parallels between self-assembly and crystal physics, which are important to exploit for developing robust engineering self-assembly processes.Item Design and control of a variable ratio gearbox for distributed wind turbine systems(2012-08) Hall, John Francis, 1968-; Chen, Dongmei, Ph. D.; Longoria, Raul G.; Masada, Glenn Y.; Pratap, Siddharth B.; Traver, Alfred E.Wind is one of the most promising resources in the renewable energy portfolio. Still, the cost of electrical power produced by small wind turbines impedes the use of this technology, which can otherwise provide power to millions of homes in rural regions worldwide. To encourage their use, small wind turbines must convert wind energy more effectively while avoiding increased equipment costs. A variable ratio gearbox (VRG) can provide this capability to the simple low-cost fixed-speed wind turbine through discrete operating speeds. The VRG concept is based upon mature technology taken from the automotive industry and is characterized by low cost and high reliability. A 100 kW model characterizes the benefits of integrating a VRG into a fixed-speed stall-regulated wind turbine system. Simulation results suggest it improves the efficiency of the fixed-speed turbine in the partial-load region and has the ability to limit power in the full-load region where pitch control is often used. To maximize electrical production, mechanical braking is applied during the normal operation of the wind turbine. A strategy is used to select gear ratios that produce torque slightly above the maximum amount the generator can accept while simultaneously applying the mechanical brake, so that full-load production may be realized over greater ranges of the wind speed. Dynamic programming is used to establish the VRG ratios and an optimal control design. This optimization strategy maximizes the energy production while insuring that the brake pads maintain a predetermined service life. In the final step of the research, a decision-making algorithm is developed to find the gears that emulate the ratios found in the optimal control design. The objective is to match the energy level as closely as possible, minimize the mass of the gears, and insure that tooth failure does not occur over the design life of the VRG. Recorded wind data of various wind classes is used to quantify the benefit of using the VRG. The results suggest that an optimized VRG design can increase wind energy production by roughly 10% at all of the sites in the study.Item Evidence of intelligent neural control of human eyes(2011-05) Najemnik, Jiri; Geisler, Wilson S.; Cormack, Lawrence K.; Hayhoe, Mary; Huk, Alex; Bovik, Alan C.Nearly all imaginable human activities rest on a context-appropriate dynamic control of the flow of retinal data into the nervous system via eye movements. The brain’s task is to move the eyes so as to exert intelligent predictive control over the informational content of the retinal data stream. An intelligent oculomotor controller would first model future contingent upon each possible next action in the oculomotor repertoire, then rank-order the repertoire by assigning a value v(a,t) to each possible action a at each time t, and execute the oculomotor action with the highest predicted value each time. We present a striking evidence of such an intelligent neural control of human eyes in a laboratory task of visual search for a small target camouflaged by a natural-like stochastic texture, a task in which the value of fixating a given location naturally corresponds to the expected information gain about the unknown location of the target. Human searchers behave as if maintaining a map of beliefs (represented as probabilities) about the target location, updating their beliefs with visual data obtained on each fixation optimally using the Bayes Rule. On average, human eye movement patterns appear remarkably consistent with an intelligent strategy of moving eyes to maximize the expected information gain, but inconsistent with the strategy of always foveating the currently most likely location of the target (a prevalent intuition in the existing theories). We derive principled, simple, accurate, and robust mathematical formulas to compute belief and information value maps across the search area on each fixation (or time step). The formulas are exact expressions in the limiting cases of small amount of information extracted, which occurs when the number of potential target locations is infinite, or when the time step is vanishingly small (used for online control of fixation duration). Under these circumstances, the computation of information value map reduces to a linear filtering of beliefs on each time step, and beliefs can be maintained simply as running weighted averages. A model algorithm employing these simple computations captures many statistical properties of human eye movements in our search task.Item Fluid and queueing networks with Gurvich-type routing(2015-08) Sisbot, Emre Arda; Hasenbein, John J.; Bickel, James Eric; Cudina, Milica; Djurdjanovic, Dragan; Khajavirad, AidaQueueing networks have applications in a wide range of domains, from call center management to telecommunication networks. Motivated by a healthcare application, in this dissertation, we analyze a class of queueing and fluid networks with an additional routing option that we call Gurvich-type routing. The networks we consider include parallel buffers, each associated with a different class of entity, and Gurvich-type routing allows to control the assignment of an incoming entity to one of the classes. In addition to routing, scheduling of entities is also controlled as the classes of entities compete for service at the same station. A major theme in this work is the investigation of the interplay of this routing option with the scheduling decisions in networks with various topologies. The first part of this work focuses on a queueing network composed of two parallel buffers. We form a Markov decision process representation of this system and prove structural results on the optimal routing and scheduling controls. Via these results, we determine a near-optimal discrete policy by solving the associated fluid model along with perturbation expansions. In the second part, we analyze a single-station fluid network composed of N parallel buffers with an arbitrary N. For this network, along with structural proofs on the optimal scheduling policies, we show that the optimal routing policies are threshold-based. We then develop a numerical procedure to compute the optimal policy for any initial state. The final part of this work extends the analysis of the previous part to tandem fluid networks composed of two stations. For two different models, we provide results on the optimal scheduling and routing policies.Item Forward optimization and real-time model adaptation with applications to portfolio management, indifference valuation and optimal liquidation(2018-12) Wang, Haoran, Ph. D.; Zariphopoulou, Thaleia, 1962-; Sirbu, Mihai; Zitkovic, Gordan; Muthuraman, KumarThe goal of this thesis is to introduce a new, alternative approach to deal with model uncertainty and “real-time” model revisions and, in turn, develop a comparative study with existing approaches in the context of various applications in financial mathematics. This new approach is based on the forward performance criteria which adapt in a time-consistent way to “real-time” model revisions. The novelty is that these revisions are genuinely “model-free” in that they occur in “real-time”, without any modeling pre-commitment. For example, in the context of optimal liquidation (see Chapter 3 and Chapter 4), there is no a priori model for the evolution of the market impact parameter λ. It is rather assumed that this parameter switches at predictable times, to values only observable at the switching times. As such, the model revisions capture the evolving reality and allow for considerable flexibility. This forward approach thus incorporates “real-time” model revisions and is, therefore, close to adaptive optimization. On the other hand, it produces, by construction, time-consistent policies and is, thus, close to the classical optimization with model(s) pre-commitment. In other words, it can be thought as a hybrid approach that accommodates dynamic model changes while preserving time-consistency. We apply the forward approach with “real-time” model revisions in four distinct problems: portfolio management in discrete and continuous settings (binomial and lognormal, respectively), indifference valuation in lognormal models and optimal liquidation in the continuous time Almgren-Chriss model. We produce closed form solutions and characterize the optimal policies and optimal criteria. As the analysis shows, one needs to solve various sequential “inverse” optimal investment problems with random coefficients, corresponding to model revisions in real-time. We develop a comparative study with the classical settings. A main novelty is the introduction of two performance metrics which measure the discrepancies between the actual performance, and the projected or the true optimal performances under the various criteria and behavior. We study these metrics for various scenaria, related to favorable and non-favorable market changes, and compare their performance. These metrics resemble the notion of “regret”, which is now considered in a more dynamic and “real-time” manner. Among others, we show that the regret of the forward decision maker is always zero, independently of the upcoming model changes. In what follows, we describe each application separately. For each application, we introduce the model, the forward and classical criteria, construct the corresponding solutions and policies, and compare them in detailItem GaN enabled high step-down bidirectional ac-dc converter for grid-tied battery energy storage system(BESS)(2022-05-06) Chen, Tianxiang (Ph. D. in electrical and computer engineering); Huang, Alex Q.; Santoso, Surya; Zhu, Hao; Hanson, Alex J; Subramanian, VenkatWith the increasing penetrations of renewable energy resources, the energy storage system (ESS) is becoming necessary to minimize the impact of the variable power generation on the grid operation. Among many different types of storage, the battery energy storage system (BESS), mostly based on the Li-ion battery, is the fastest-growing due to the decreased system cost, and fast real and reactive power dispatch capabilities, which can be used for various applications such as voltage and frequency support, as well as for economic dispatch applications. BESS requires a bidirectional power electronics converter between the dc battery and the ac grid while having the capability to handle a wide range dc battery voltage. For interfacing with a three-phase ac grid, a single-stage configuration is used. The single-stage design can eliminate the ac grid side contactor, as it has a small ac-link capacitor and the inrush current is small. The three-phase single-stage design can also minimize the bulky dc-link capacitor. The proposed design includes three identical single-phase modules. Each module includes an unfolding bridge and a single-stage bidirectional (DAB) or series-resonant dual-activebridge (SR-DAB). This modular topology can also be used for both the single-phase and three-phase grid-connected BESS. The unfolding bridge will rectify the ac voltage to twice the line frequency in ac-dc operation (charging of the battery), or invert the voltage to the ac grid for dc-ac operation (discharging of the battery). In the meantime, DAB can convert ac energy with the absolute value of the sinusoidal voltage to the battery side or converter dc energy to the ac side with a high-frequency transformer, while providing zero voltage switching (ZVS) for the whole ac voltage range. A single-stage DAB topology is proposed in Chapter 2. The power flow for both directions is introduced and the novel combined dual phase shift modulation and variable frequency modulation are explained with advantages over the single phase shift modulation and fixed frequency modulation in terms of the inductor rootmean-square (rms) current. The power factor circuit (PFC) requirement and the ZVS constraints are investigated for the single-stage DAB with dual phase shift and variable frequency modulation. A novel online calculation control algorithm for the single-stage DAB is explained in Chapter 3. The control is proposed to minimize the dc low voltage side maximum turn-off current. A detailed explanation is provided for the control algorithm with the variable frequency and with a fixed frequency range. The extended ZVS ranges are proposed for the control algorithm to guarantee the ZVS over a wide range of the dc battery voltage and loads. A dual loop close loop control is introduced with its capability of dealing with the transit charging/discharging current response. An adaptive deadtime method is utilized to optimize the deadtime loss while working with a varying switching current over line period. A single-stage SR-DAB is proposed to further optimize the turn-off current and (rms) current of the single-stage topology, and is included in Chapter 4. The operation principle of a single-stage SR-DAB is proposed and its numerical expression of the equivalent model is analyzed with its PFC requirement and ZVS constraint investigated. The advantage of the dual phase shift and variable frequency control modulation is explained with its comparison over the single phase shift and fixed frequency modulation. An optimization algorithm is proposed aiming to minimize the system overall loss for the single-stage SR-DAB. A range of comparisons over the switching current and rms current between the single-stage DAB and SR-DAB are made, and the advantage of a single-stage SR-DAB is verified. A comprehensive loss model including a transistor loss such as conduction loss, switching loss, driving loss and deadtime loss, and magnetic loss such as transformer and inductor loss is introduced and well analyzed in Chapter 5. An optimization algorithm aimed to optimize the system loss is introduced based on the comprehensive loss model. With this algorithm, hardware optimizations are conducted and the optimal values of the transformer turns ratio, auxiliary inductor for a single-stage DAB, a resonant inductor and capacitor for a single-stage SR-DAB, the snubber capacitor for the dc low voltage side transistors are determined to ensure optimal performance of the converter. The ac side input capacitance and inductance are also determined to ensure a small switching voltage ripple and guarantee relay-less operation. In Chapter 6, the hardware that is utilized to verify the single-stage DAB and single-stage SR-DAB is explained in detail. Advanced implementation and switching performance of the power stage are presented. The system operation parameters as well as the major components used are included. Experimental results for single-stage DAB and single-stage SR-DAB at 1 kW and 2 kW single phase operation, and three-phase operation are displayed to verify the single-stage concept and present its performance. Thermal image, loss breakdown, and efficiency map/curve are presented. The single-stage DAB and single-stage SR-DAB provide a good solution for three-phase ac to dc battery with bidirectional power flow and requirement of isolation. The operation principle, PFC requirement, and ZVS constraint for both converters is well analyzed in the main content. A loss model is established and a hardware optimization is conducted to ensure the converter is operating at optimal efficiency. Experimental verification is included to verify the capability of the single-stage DAB and single-stage SR-DAB.Item Harnessing demand flexibility to minimize cost, facilitate renewable integration, and provide ancillary services(2014-08) Kefayati, Mahdi; Baldick, RossRenewable energy is key to a sustainable future. However, the intermittency of most renewable sources and lack of sufficient storage in the current power grid means that reliable integration of significantly more renewables will be a challenging task. Moreover, increased integration of renewables not only increases uncertainty, but also reduces the fraction of traditional controllable generation capacity that is available to cope with supply-demand imbalances and uncertainties. Less traditional generation also means less rotating mass that provides very short term, yet very important, kinetic energy storage to the system and enables mitigation of the frequency drop subsequent to major contingencies but before controllable generation can increase production. Demand, on the other side, has been largely regarded as non-controllable and inelastic in the current setting. However, there is strong evidence that a considerable portion of the current and future demand, such as electric vehicle load, is flexible. That is, the instantaneous power delivered to it needs not to be bound to a specific trajectory. In this thesis, we focus on harnessing demand flexibility as a key to enabling more renewable integration and cost reduction. We start with a data driven analysis of the potential of flexible demands, particularly plug-in electric vehicle (PEV) load. We first show that, if left unmanaged, these loads can jeopardize grid reliability by exacerbating the peaks in the load profile and increasing the negative correlation of demand with wind energy production. Then, we propose a simple local policy with very limited information and minimal coordination that besides avoiding undesired effects, has the positive side-effect of substantially increasing the correlation of flexible demand with wind energy production. Such local policies could be readily implemented as modifications to existing "grid friendly" charging modes of plug-in electric vehicles. We then propose improved localized charging policies that counter balance intermittency by autonomously responding to frequency deviations from the nominal frequency and show that PEV load can offer a substantial amount of such ancillary services. Next, we consider the case where real-time prices are employed to provide incentives for demand response. We consider a flexible load under such a pricing scheme and obtain the optimal policy for responding to stochastic price signals to minimize the expected cost of energy. We show that this optimal policy follows a multi-threshold form and propose a recursive method to obtain these thresholds. We then extend our results to obtain optimal policies for simultaneous energy consumption and ancillary service provision by flexible loads as well as optimal policies for operation of storage assets under similar real-time stochastic prices. We prove that the optimal policy in all these cases admits a computationally efficient form. Moreover, we show that while optimal response to prices reduces energy costs, it will result in increased volatility in the aggregate demand which is undesirable. We then discuss how aggregation of flexible loads can take us a step further by transforming the loads to controllable assets that help maintain grid reliability by counterbalancing the intermittency due to renewables. We explore the value of load flexibility in the context of a restructured electricity market. To this end, we introduce a model that economically incentivizes the load to reveal its flexibility and provides cost-comfort trade-offs to the consumers. We establish the performance of our proposed model through evaluation of the price reductions that can be provided to the users compared to uncontrolled and uncoordinated consumption. We show that a key advantage of aggregation and coordination is provision of "regulation" to the system by load, which can account for a considerable price reduction. The proposed scheme is also capable of preventing distribution network overloads. Finally, we extend our flexible load coordination problem to a multi-settlement market setup and propose a stochastic programming approach in obtaining day-ahead market energy purchases and ancillary service sales. Our work demonstrates the potential of flexible loads in harnessing renewables by affecting the load patterns and providing mechanisms to mitigate the inherent intermittency of renewables in an economically efficient manner.Item Lossless convexification of optimal control problems(2014-05) Harris, Matthew Wade; Açıkmeşe, BehçetThis dissertation begins with an introduction to finite-dimensional optimization and optimal control theory. It then proves lossless convexification for three problems: 1) a minimum time rendezvous using differential drag, 2) a maximum divert and landing, and 3) a general optimal control problem with linear state constraints and mixed convex and non-convex control constraints. Each is a unique contribution to the theory of lossless convexification. The first proves lossless convexification in the presence of singular controls and specifies a procedure for converting singular controls to the bang-bang type. The second is the first example of lossless convexification with state constraints. The third is the most general result to date. It says that lossless convexification holds when the state space is a strongly controllable subspace. This extends the controllability concepts used previously, and it recovers earlier results as a special case. Lastly, a few of the remaining research challenges are discussed.Item Model-based controller design and simulation of a marine chiller(2012-08) Salhotra, Gautam Vijay; Kiehne, Thomas M.; Longoria, Raul G.For the past decade, the US Navy has committed to fundamental research and technology development on its next generation of surface ships. The vision is that these warships will be dynamically reconfigurable, energy-efficient, and have state-of-the-art pulsed energy weapons and sensors onboard. These developments represent a significant increase in highly dynamic on-board electrical systems that will produce correspondingly large amounts of dynamic heat generation, which, if not managed properly, will likely produce significant thermal side effects. In previous work, a highly customizable simulation framework has been developed to address thermal management issues across both the mechanical and electrical domains. This software environment is called the Dynamic Thermal Modeling and Simulation (DTMS) framework. The purpose of the current work is to introduce modern control theory into DTMS, thus providing the framework with the ability to control large-scale system simulations. The research reported in this thesis uses control of a marine chiller as a simulation vehicle. Several control strategies were implemented. These included the well-established PID controller as well as a new controller based on optimal control theory. Results for chiller simulations in the case of no-control, PID control, and optimal control are presented here. The comparative effectiveness of these controls in bringing the chiller to startup equilibrium is investigated. Response of the chiller model and the optimal controller to highly dynamic, varying heat loads was tested. The PID controller in DTMS is modeled as a special case of the transfer function control scheme. A PID controller is simple to implement but responses are inherently local and multiple controls in a system or subsystem simulation can easily lead to conflicts. The optimal control problem has been modeled as an Infinite Horizon Linear Quadratic Regulator (LQR) problem. This formulation is not local and does not create undesirable effects in parts of the system that not controlled directly by controller inputs. Using the York 200-ton marine chiller as an example, specific steps required to formulate the LQR problem are documented in this report. Implementation of the LQR controller was demonstrated for the startup to steady-state function of the chiller at full load. Treatment of the optimal controller ends with simulation of the chiller and its LQR controller under the influence of varying dynamic heat loads in a chilled water loop. The heat load variation examined has highly transient characteristics that affect the temperature of the fresh water entering the chiller, as well as the refrigerant pressure and temperature in the evaporator. The LQR formulation is shown to actively adjust to these varying operating points in a smooth and responsive manner.Item Model-based decentralized optimal control of a microgrid(2019-08) Chu Cheong, Matthew; Chen, Dongmei, Ph. D.; Bakolas, Efstathios; Du, Pengwei; Hall, Matthew J; Seepersad, CarolynPower networks have experienced dramatic changes with the growth of renewable energy and `smart' grids. To accommodate the challenges posed to traditional power system control architectures, the microgrid concept has gained traction. Microgrids are small-scale power networks that can disconnect from the main grid and operate autonomously if necessary. These systems add robustness and facilitate the incorporation of renewable power, but they face control challenges of their own due to the lack of significant inertial generation. Without the main grid to provide balance, the high proportion of electrically-interfaced power resources can cause significant deterioration in microgrid stability. This dissertation proposes designs to improve decentralized control in microgrids; model based information is incorporated into controllers and estimators to more optimally guide control signals, while still only using local data for real-time computation. We outline the role that microgrid topology can have on stability, and how judicious power injection can mitigate instabilities. These results are extended to a decentralized H-infinity control design for microgrid frequency; even with limited model-based information and controller distribution, the design offers significant improvements over traditional controllers. Building upon the idea of microgrid stabilization, we also present a control method by which a wind turbine can be coordinated for microgrid support. The wind turbine is used as a controllable power source by utilizing the rotational energy stored in its rotor; this design incorporates an aerodynamic wind turbine model and a novel optimal blade pitch angle controller to ensure stable turbine operation. This allows for rapid power injection for grid support. This theme concludes with a decentralized estimation scheme to facilitate coordinated control across a microgrid using only local data. We leverage the frequency synchronization and load-sharing intrinsic to the microgrid so that local measurements can provide insight about grid-wide conditions. This allows for effective implementation of optimal filtering techniques so that remote conditions can be estimated using only local data; this allows for grid-wide coordination and optimization. Together these ideas represent the concept that the microgrid model, even in a limited and inaccurate sense, can be manipulated to provide significant benefits for decentralized control across the network.Item Multiple-shooting differential dynamic programming with applications to spacecraft trajectory optimization(2017-09-13) Pellegrini, Etienne; Russell, Ryan Paul, 1976-; Akella, Maruthi R; Bakolas, Efstathios; Cerf, Max; Jones, Brandon AThe optimization of spacecraft trajectories has been, and continues to be, critical for the development of modern space missions. Longer flight times, continuous low-thrust propulsion, and multiple flybys are just a few of the modern features resulting in increasingly complex optimal control problems for trajectory designers to solve. In order to efficiently tackle such challenging problems, a variety of methods and algorithms have been developed over the last decades. The work presented in this dissertation aims at improving the solutions and the robustness of the optimal control algorithms, in addition to reducing their computational load and the amount of necessary human involvement. Several areas of improvement are examined in the dissertation. First, the general formulation of a Differential Dynamic Programming (DDP) algorithm is examined, and new theoretical developments are made in order to achieve a multiple-shooting formulation of the method. Multiple-shooting transcriptions have been demonstrated to be beneficial to both direct and indirect optimal control methods, as they help decrease the large sensitivities present in highly nonlinear problems (thus improving the algorithms' robustness), and increase the potential for a parallel implementation. The new Multiple-Shooting Differential Dynamic Programming algorithm (MDDP) is the first application of the well-known multiple-shooting principles to DDP. The algorithm uses a null-space trust-region method for the optimization of quadratic subproblems subject to simple bounds, which permits to control the quality of the quadratic approximations of the objective function. Equality and inequality path and terminal constraints are treated with a general Augmented Lagrangian approach. The choice of a direct transcription and of an Augmented Lagrangian merit function, associated with automated partial computations, make the MDDP implementation flexible, requiring minimal user effort for changes in the dynamics, cost and constraint functions. The algorithm is implemented in a general, modular optimal control software, and the performance of the multiple-shooting formulation is analyzed. The use of quasi-Newton approximations in the context of DDP is examined, and numerically demonstrated to improve computational efficiency while retaining attractive convergence properties. The computational performance of an optimal control algorithm is closely related to that of the integrator chosen for the propagation of the equation of motion. In an effort to improve the efficiency of the MDDP algorithm, a new numerical propagation method is developed for the Kepler, Stark, and three-body problems, three of the most commonly used dynamical models for spacecraft trajectory optimization. The method uses a time regularization technique, the generalized Sundman transformation, and Taylor Series developments of equivalents to the f and g functions for each problem. The performance of the new method is examined, and specific domains where the series solution outperforms existing propagation methods are identified. Finally, because the robustness and computational efficiency of the MDDP algorithm depend on the quality of the first- and second-order State Transition Matrices, the three most common techniques for their computation are analyzed, in particular for low-fidelity propagation. The propagation of variational equations is compared to the complex step derivative approximation and finite differences methods, for a variety of problems and integration techniques. The subtle differences between variable- and fixed-step integration for partial computation are revealed, common pitfalls are observed, and recommendations are made for the practitioner to enhance the quality of state transition matrices.Item Numerical optimal control of a wind turbine system(2015-08) Yan, Zeyu, Ph. D.; Chen, Dongmei, Ph. D.; Fahrenthold, Eric P.; Hall, Neal A.; Li, Wei; Seepersad, Carolyn C.With the development of wind turbine technology and the need for maximizing wind energy harvesting, more wind turbines operate in the partial load region. Among many control algorithms developed for this region, controllers based on feedback of the global maximum power coefficient have been widely used. These control schemes offer good performance with simple implementations, but they may not be suited for wind turbines with limited rotor speed ranges. In such cases, the controller is challenged because the main feature ---the global maximum power coefficient--- is not achievable due to the turbine speed constraint. It is necessary to develop a controller to seek the achievable maximum power coefficient that leads to optimal wind energy capture. In this dissertation, the development of an optimal control framework to maximize wind energy capture for wind turbines with constrained turbine speed is first presented. Numerical optimal control techniques are applied to search for the achievable maximum power coefficient, with proposed modifications to make this task more computationally feasible. Mitigating the turbine generator torque variation, thus reducing the fatigue loading on turbine generator shaft, is also important for the partial load region operation. Including this aspect in the optimal control is then discussed. Furthermore, an approach of incorporating time-varying weightings into developing the optimal controller is introduced to seek further improvement on turbine generator torque variation reduction, thus fatigue reduction. In addition, the power generated by the wind turbine varies due to variation in the wind speed. Depending on the load demand and the wind speed, the wind turbine's operation switches between two modes: a multi-input-single-output (MISO) mode and a single-input-single-output (SISO) mode. Due to the wind turbine changes its dynamic behavior during the switching process, applying the traditional control methods to each corresponding mode may not be capable of maximizing the overall wind energy capture throughout the entire turbine's operation. Therefore, the development of an optimal control framework to maximize the overall wind energy capture for a switched wind turbine system is subsequently presented.Item Optimal control for a modern wind turbine system(2012) Yan, Zeyu, master of science in engineering; Chen, DongmeiWind energy is the most abundant resource in the renewable energy portfolio. Increasing the wind capture capability improves the economic viability of this technology, and makes it more competitive with traditional fossil-fuel based supplies. Therefore, it is necessary to explore control strategies that maximize aerodynamic efficiency, thus, the wind energy capture. Several control algorithms are developed and compared during this research. A traditional feedback control is adapted as the benchmark approach, where the turbine torque and the blade pitch angle are used to control the wind turbine operation during partial and full load operations, correspondingly. Augmented feedback control algorithms are then developed to improve the wind energy harvesting. Optimal control methodologies are extensively explored to achieve maximal wind energy capture. Numerical optimization techniques, such as direct shooting optimization are employed. The direct shooting method convert the optimal control problem into a parameter optimization problem and use nonlinear programming algorithm to find the optimal solution. The dynamic programming, a global optimization approach over a time horizon, is also investigated. The dynamic programming finds the control inputs for the blade pitch angle and speed ratio to maximize the power coefficient, based on historical wind data. A dynamic wind turbine model has been developed to facilitate this process by characterizing the performance of the various possible input scenarios. Simulation results of each algorithm on real wind site data are presented to compare the wind energy capture under the proposed control algorithms with the traditional feedback control design. The result of the tradeoff analysis between the computation expense and the energy capture is also reported.Item Optimal control of wind turbines for distributed power generation(2015-08) Shaltout, Mohamed Lotfi Eid Nasr; Chen, Dongmei, Ph. D.; Longoria, Raul G.; Crawford, Richard H.; Deshpande, Ashish D.; Malikopoulos, Andreas A.; Pratap, Siddharth B.Wind energy represents one of the major renewable energy sources that can meet future energy demands to sustain our lifestyle. During the last few decades, the installation of wind turbines for power generation has grown rapidly worldwide. Besides utility scale wind farms, distributed wind energy systems contributes to the rise in wind energy penetration. However, the expansion of distributed wind energy systems is faced by major challenges such as the system’s reliability in addition to the environmental impacts. This work is intended to explore various control algorithms to enable the distributed wind energy systems to face the aforementioned challenges. First of all, a stall regulated fixed speed wind turbine augmented with a variable ratio gearbox has been proven to enhance the wind energy capture at a relatively low cost, and considered as an attractive design for small wind energy systems. However, the high reliability advantage of traditional fixed-speed wind turbines can be affected by the integration of the variable ratio gearbox. A portion of this work is intended to develop a control algorithm that extends the variable ratio gearbox service life, thus improves overall system reliability and reduces the expected operational cost. Secondly, a pitch regulated variable speed wind turbines dominates the wind energy industry as it represents a balance between cost and flexibility of operation. They can be used for midsized wind power generation. Optimizing its wind energy capture while maintain high system reliability has been the one of the main focuses of many researchers. Another portion of this work introduces a model predictive control framework that enhances the reliability of pitch regulated variable speed wind turbines, thus improves their operational cost. Finally, one of the major environmental challenges facing the continuous growth of wind energy industry is the noise emitted from wind turbines. The severity of the noise emission problem is more significant for small and medium sized wind turbines installed in the vicinity of residential areas for distributed power generation. Consequently, the last portion of this work is intended to investigate the potential of wind turbine control design to reduce noise emission in different operating conditions with minimal impact on power generationItem Real time optimal control and state estimation for Li-ion batteries(2021-08-12) Gupta, Dhananjay, M.S. in Engineering; Subramanian, Venkat R.; Chen, DongmeiLi-Ion batteries are increasingly being looked at as a major alternative to fossil fuels in the transition towards clean energy. This has made created the necessity to be able to understand and predicted their behaviors – with the goal of elongating their life and ensuring safety of use. This thesis investigates the use of optimization-based state estimation and control methods on first-principle, physics-based models for the monitoring and real time control of batteries. Specifically, Moving Horizon Estimation in conjunction with Nonlinear Model Predictive Control applied to the Single Particle and Tank-in-Series Battery Models are investigated. First principle Li-Ion Battery Models consist of a set of coupled differential and algebraic equations. The constants in these equations are battery design parameters, which have been identified for an LGHG2 Cell by referring to relevant literature and conducting parameter estimation using gradient based methods. The two models’ equations are solved using numerical methods after spatial discretization. The optimization problems for state estimation and control are set up and tested offline. The same real time control framework is then deployed onto hardware application with a real battery. The real time control using this setup is tested on a Raspberry Pi, to gauge and optimally charge an LGHG2 3Ah Cell. The battery voltage and current is measured using a TI BQ40Z50 Battery Fuel Gauge, and the charging is done using a TI BQ25700A Buck Boost Charger. The optimization-based state estimation algorithm (MHE) can converge to the measured voltage and recover the model states based on real time current and voltage measurements received from the fuel gauge. The control algorithm (NMPC) can adjust the charging current as the battery nears the voltage setpoint, to prevent overcharging. The designed algorithm can also be easily modified for several objective functions, cell chemistries, and constraints. The novelty in this work is the application onto hardware, and closed loop, real time implementation of a Nonlinear Model Predictive Control algorithm without the use of any lookup tables, where optimization is conducted at each step to find an optimal control action.Item Stability analysis and optimal control of large-scale stochastic systems(2022-08-11) Hmedi, Hassan; Shakkottai, Sanjay; Caramanis, Constantine; Pang, Guodong; De Veciana, Gustavo; Zitkovic, GordanIn the past years, large-scale stochastic networks have been an intense subject of study due to their use in modelling a variety of systems including telecommunications, service and data centers, patient flows, etc. The optimal control of such systems has found numerous applications such as, but not limited to, finance and cognitive neuroscience. This thesis focuses on the stability analysis and optimal control of stochastic systems. In particular, we study: (1) the ergodic properties of multiclass multi-pool networks in the Halfin-Whitt regime; and (2) the optimal control of stochastic networks assuming a structural property relating the running cost to the solution of the Hamilton-Jacobi-Bellman (HJB) equation. In the first part of this thesis, we introduce a "system-wide safety staffing" (SWSS) parameter for multiclass multi-pool networks in the Halfin-Whitt regime which have any tree topology. This parameter can be regarded as the optimal reallocation of the capacity fluctuations (positive or negative) when each server pool employs a square-root staffing rule. First, we provide an explicit form of the SWSS as a function of the system parameters, which is derived using a graph theoretic approach based on Gaussian elimination. In addition, we give an equivalent characterization of the SWSS parameter via the drift parameters of the limiting diffusion. Then, we show that if the SWSS parameter is negative, the limiting diffusion and the diffusion-scaled queueing processes are transient under any Markov control, and cannot have a stationary distribution when this parameter is zero. If it is positive, we show that the diffusion-scaled queueing processes are stabilizable, that is, there exists a scheduling policy under which the stationary distributions of the controlled processes are tight over the size of the network. Finally, we show that there exists a control under which the limiting controlled diffusion is exponentially ergodic. Thus, we have identified a necessary and sufficient condition for the stabilizability of such networks in the Halfin-Whitt regime. In the second part of this thesis, we examine two problems related to the general topic of optimal control of stochastic systems. In the first problem, we consider a linear system with Gaussian noise observed by multiple sensors which transmit measurements over a dynamic lossy network. We assume that the system is stabilizable, that is, there exists a control such that all states variables are bounded during system's behavior. First, we characterize the stationary optimal sensor scheduling policy for the finite horizon, discounted, and long-term average cost problems. Then, we show that there exists a structural property relating the running cost to the value function which is the solution of the average cost problem. In addition, we show that the value iteration algorithm converges to this solution. Further, we show that the suboptimal policies provided by the rolling horizon truncation of the value iteration also guarantee stability and provide near-optimal average cost. Lastly, we provide qualitative characterizations of the multidimensional set of measurement loss rates for which the system is stabilizable for a static network, thus extending earlier results on intermittent observations. In the second problem and motivated by the results from the previous problem, a multiplicative relative value iteration algorithm (RVI) for infinite-horizon risk-sensitive control of controlled diffusions in [doublestruck R][superscript d] is studied. We assume that the running cost is near-monotone and that it is related to the solution of the multiplicative HJB equation through a structural assumption. We show that this structural assumption implies the existence of a control under which the ground state diffusion is exponentially ergodic. In addition, we show that the multiplicative RVI algorithm converges globally to the solution of the multiplicative dynamic programming equation starting from any positive initial condition; thus extending upon the results in the literature.