Process economic improvement subject to safety, operational and environmental constraints is an ultimate goal of using on-line process optimization and control techniques. The dynamic nature of present-day market conditions motivates the consideration of process dynamics within the economic optimization calculation. Two key paradigms for implementing real-time dynamic economic optimization are a dynamic real-time optimization (DRTO) and regulatory MPC two-layer architecture, and a single-level economic model predictive control (EMPC) con figuration. In the two-layer architecture, the economically optimal set-point trajectories computed in an upper DRTO layer are provided to the MPC layer, while in the single-layer EMPC con figuration the economics are incorporated within the MPC objective function. There are limited studies on a systematic performance comparison between these two approaches. Furthermore, these studies do not simultaneously consider the economic, disturbance rejection and computational performance criteria. Thus, it may not be clear under what conditions one particular method is preferable over the other. These reasons motivate a more comprehensive comparison between the two paradigms, with both open and closed-loop predictions considered in the DRTO calculations. In order to conduct this comparison, we utilize two process case studies for the economic analysis and performance comparison of on-line optimization systems. The first case study is a process involving two stirred-tank reactors in-series with an intermediate mixing point, and the second case study is a linear multi-input single-output (MISO) system. These processes are represented using a fi rst principles model in the form of differential-algebraic equations (DAEs) system for the first case study and a simplified linear model of a polymerization reactor for the second case study problem. Both of the case study processes include constraints associated with input variables, safety considerations, and output quality. In these case study problems, the objective of optimal process operation is net profit improvement. The following performance evaluation criteria are considered in this study: (I) optimal value of the economic objective function, (II) average run time (ART) over a same operating time interval, (III) cumulative output constraint violation (COCV) for each constraint. The update time of the single-layer approach is selected to be equal to that of the control layer in the two-layer formulations, while the update time of the economic layer in the two-layer formulation is bigger than that of the single-layer approach. The nonlinear programing (NLP) problems which result in the single-layer and two-layer formulations and the quadratic programing problem which corresponds to the MPC formulation are solved using the fmincon and quadprog optimization solvers in MATLAB. Performance assessment of the single-layer and two-layer formulations is evaluated in the presence of a variety of unknown disturbance scenarios for the first case study problem. The effect of a dynamic transition in the product quality is considered in the performance comparison of the single-layer and two-layer methods in the second case-study problem. The first case study problem results show that for all unknown disturbance scenarios, the economic performance of the single-layer approach is slightly higher than that of the two layer formulations. However, the average computation times for the DRTO-MPC two-layer formulations are at least one order of magnitude lower than that of the EMPC formulation. Also, comparison results of the COCV for the EMPC formulation for different sizes of update time intervals could justify the necessity of the MPC control layer to reduce the COCV for the economic optimization problems with update times larger than that of the MPC control layer. A similar computational advantage of the OL- and CL-DRTO-MPC over the EMPC is observed for the second case study problem. In particular, it is shown that increasing the economic horizon length in the EMPC formulation to a sufficiently large value may result a higher economic improvement. However, the increase in economic optimization horizon would increase the resulting NLP problem size. The computational burden could limit the use of the EMPC formulation with larger economic optimization horizons in real-time applications. The ART of the dual-layer methods is at least two orders of magnitude lower than that of the EMPC methods with an appropriate horizon length. The CL-DRTO-MPC economic performance is slightly less than that of the EMPC formulation with the same economic optimization horizon. In conclusion, the performance comparison on the basis of multiple criteria in this study demonstrates that the economic performance criterion is not necessarily the only important metric, and the operational constraint limitations and the optimization problem solution time could have an important impact on the selection of the most suitable real-time optimization approach. / Thesis / Master of Applied Science (MASc)

This thesis mainly focuses on parallel hybrid electric vehicle energy management problems considering fueling control and air path dynamics of a diesel engine. It aims to explore the concealed fuel-saving potentials in conventional energy management strategies, by employing detailed engine models. The contributions of this study lie on the following aspects: 1) Fueling control consists of fuel injection mass and timing control. By properly selecting combinations of fueling control variables and torque split ratio, engine efficiency is increased and the HEV fuel consumption is further reduced. 2) A transient engine model considering air path dynamics is applied to more accurately predict engine torque. A model predictive control based energy management strategy is developed and solved by dynamic programming. The fuel efficiency is improved, comparing the proposed strategy to those that ignore the engine transients. 3) A novel adaptive control-step learning model predictive control scheme is proposed and implemented in HEV energy management design. It reveals a trade-off between control accuracy and computational efficiency for the MPC based strategies, and demonstrates a good adaptability to the variation of driving cycle while maintaining low computational burden. 4) Two methods are presented to deal with the conjunction between consecutive functions in the piece-wise linearization for the energy management problem. One of them shows a fairly close performance with the original nonlinear method, but much less computing time. / Thesis / Doctor of Philosophy (PhD)

no / A milk pasteurization process is a nonlinear process and multivariable interacting system. This makes it difficultly to control by the conventional on-off controllers. Even if the on-off controller can managed the milk temperatures in the holding tube and the cooling stage of the plate pasteurizer according to the plant's requirements, the dynamic profiles of the milk temperature are oscillating around a desired value. Consequently, this work is aimed at improving the control performance by a multi-variables control approach with model predictive control (MPC). The proposed algorithm was tested in the case of set point tracking under nominal condition gathered by the real observation. To compare the performance of the MPC controller, a model-based control approach of generic model control (GMC) coupled with cascade control strategy is taken into account. The simulation results demonstrated that a proposed control algorithm performed well in keeping both the milk and water temperatures at the desired set points without any oscillation and overshoot. Because of the predictive control strategy, the control response for MPC was less drastic control action compared to the GMC.

No / A novel threefold optimization algorithm is proposed to simultaneously solve the nonlinear model predictive control and dynamic real-time optimization for batch processes while optimizing the batch operation time. Object-oriented programming and parallel computing are exploited to make the algorithm effective to handle industrial cases. A well-known literature case is selected to validate the algorithm.

This dissertation aims to realize the goal of deploying legged robots that cooperatively walk to transport objects in complex environments. More than half of the Earth's continent is unreachable to wheeled vehicles---this motivates the deployment of collaborative legged robots to enable the accessibility of these environments and thus bring robots into the real world. Although significant theoretical and technological advances have allowed the development of distributed controllers for complex robot systems, existing approaches are tailored to the modeling and control of multi-agent systems composed of collaborative robotic arms, multi-fingered robot hands, aerial vehicles, and ground vehicles, but not collaborative legged agents. Legged robots are inherently unstable, unlike most of the systems where these algorithms have been deployed. Models of cooperative legged robots are further described by high-dimensional, underactuated, and complex hybrid dynamical systems, which complicate the design of control algorithms for coordination and motion control. There is a fundamental gap in knowledge of control algorithms for safe motion control of these inherently unstable hybrid dynamical systems, especially in the context of collaborative work. The overarching goal of this dissertation is to create a formal foundation based on scalable optimization and robust and nonlinear control to develop distributed and hierarchical feedback control algorithms for cooperative legged robots to transport objects in complex environments. We first develop a hierarchical nonlinear control algorithm, based on model predictive control (MPC), quadratic programming (QP), and virtual constraints, to generate and stabilize locomotion patterns in a real-time manner for dynamical models of single-agent quadrupedal robots. The higher level of the proposed control scheme is developed based on an event-based MPC that computes the optimal center of mass (COM) trajectories for a reduced-order linear inverted pendulum (LIP) model subject to the feasibility of the net ground reaction force (GRF). QP-based virtual constraint controllers are developed at the lower level of the proposed control scheme to impose the full-order dynamics to track the optimal trajectories while having all individual GRFs in the friction cone. The analytical results are numerically verified to demonstrate stable and robust locomotion of a 22 degree of freedom (DOF) quadrupedal robot, in the presence of payloads, external disturbances, and ground height variations. We then present a hierarchical nonlinear control algorithm for the real-time planning and control of cooperative locomotion of legged robots that collaboratively carry objects. An innovative network of reduced-order models subject to holonomic constraints, referred to as interconnected LIP dynamics, is presented to study quasi-statically stable cooperative locomotion. The higher level of the proposed algorithm employs a supervisory controller, based on event-based MPC, to effectively compute the optimal reduced-order trajectories for the interconnected LIP dynamics. The lower level of the proposed algorithm employs distributed nonlinear controllers to reduce the gap between reduced- and full-order complex models of cooperative locomotion. We numerically investigate the effectiveness of the proposed control algorithm via full-order simulations of a team of collaborative quadrupedal robots, each with a total of 22 DOFs. The dissertation also investigates the robustness of the proposed control algorithm against uncertainties in the payload mass and changes in the ground height profile. Finally, we present a layered control approach for real-time trajectory planning and control of dynamically stable cooperative locomotion by two holonomically constrained quadrupedal robots. An innovative and interconnected network of reduced-order models, based on the single rigid body (SRB) dynamics, is developed for trajectory planning purposes. At the higher level of the control scheme, two different MPC algorithms are proposed to address the optimal control problem of the interconnected SRB dynamics: centralized and distributed MPCs. The MPCs compute the reduced-order states, GRFs, and interaction wrenches between the agents. The distributed MPC assumes two local QPs that share their optimal solutions according to a one-step communication delay and an agreement protocol. At the lower level of the control scheme, distributed nonlinear controllers are employed to impose the full-order dynamics to track the prescribed and optimal reduced-order trajectories and GRFs. The effectiveness of the proposed layered control approach is verified with extensive numerical simulations and experiments for the blind, robust, and cooperative locomotion of two holonomically constrained A1 robots with different payloads on different terrains and in the presence of external disturbances. It is shown that the distributed MPC has a performance similar to that of the centralized MPC, while the computation time is reduced significantly. / Doctor of Philosophy / Future cities will include a complex and interconnected network of collaborative robots that cooperatively work with each other and people to support human societies. Human-centered communities, including factories, offices, and homes, are developed for humans who are bipedal walkers capable of stepping over gaps, walking up/down stairs, and climbing ladders. One of the most challenging problems in deploying the next generation of collaborative robots is maneuvering in those complex environments. Although significant theoretical and technological advances have allowed the development of distributed controllers for motion control of multi-agent robotic systems, existing approaches do not address the collaborative locomotion problem of legged robots. Legged robots are inherently unstable with nonlinear and hybrid natures, unlike most systems where these algorithms have been deployed. Furthermore, the evolution of legged collaborative robot teams that cooperatively manipulate objects can be represented by high-dimensional and complex dynamical systems, complicating the design of control algorithms for coordination and motion control. This dissertation aims to establish a formal foundation based on nonlinear control and optimization theory to develop hierarchical feedback control algorithms for effective motion control of legged robots. The proposed layered control algorithms are developed based on interconnected reduced-order models. At the high level, we formulate cooperative locomotion as an optimal control problem of the reduced-order models to generate optimal trajectories. To realize the generated optimal trajectories, nonlinear controllers at the low level of the hierarchy impose the full-order models to track the trajectories while sustaining stability. The effectiveness of the proposed layered control approach is verified with extensive numerical simulations and experiments for the blind and stable cooperative locomotion of legged robots with different payloads on different terrains and subject to external disturbances. The proposed architecture's robustness is shown under various indoor and outdoor conditions, including landscapes with randomly placed wood blocks, slippery surfaces, gravel, grass, and mulch.

yes / Batch reactive distillation is aimed at achieving a high purity product, therefore, there is a great deal to find an optimal operating condition and effective control strategy to obtain maximum of the high purity product. An off-line dynamic optimization is first performed with an objective function to provide optimal product composition for the batch reactive distillation: maximum productivity. An inferential state estimator (an extended Kalman filter, EKF) based on simplified mathematical models and on-line temperature measurements, is incorporated to estimate the compositions in the reflux drum and the reboiler. Model Predictive Control (MPC) has been implemented to provide tracking of the desired product compositions subject to simplified model equations. Simulation results demonstrate that the inferential state estimation can provide good estimates of compositions. Therefore, the control performance of the MPC with the inferential state is better than that of PID. In addition, in the presence of unknown/uncertain parameters (forward reaction rate constant), the estimator is still able to provide accurate concentrations. As a result, the MPC with the inferential state is still robust and applicable in real plants.

Today's Cyber-Physical Systems (CPS) are typically distributed over several computing nodes communicating by way of shared buses such as Controller Area Network (CAN). Their control performance gets degraded due to variable delays (jitters) incurred by messages on the shared CAN bus due to contention and network overhead. This work presents a novel online delay prediction approach that predicts the message delay at runtime based on real-time traffic information on CAN. It leverages the proposed method to improve control quality, by compensating for the message delay using the Model Predictive Control (MPC) algorithm in designing the controller. By simulating an automotive Cruise Control system and a DC Motor plant in a CAN environment, it goes on to demonstrate that the delay prediction is accurate, and that the MPC design which takes the message delay into consideration, performs considerably better. It also implements the proposed method on an 8-bit 16MHz ATmega328P microcontroller and measures the execution time overhead. The results clearly indicate that the method is computationally feasible for online usage. / Master of Science

Threat assessment and reliable motion-prediction of surrounding vehicles are some of the major challenges encountered in autonomous vehicles' safe decision-making. Predicting a threat in advance can give an autonomous vehicle enough time to avoid crashes or near crash situations. Most vehicles on roads are human-driven, making it challenging to predict their intentions and movements due to inherent uncertainty in their behaviors. Moreover, different driver behaviors pose different kinds of threats. Various driver behavior predictive models have been proposed in the literature for motion prediction. However, these models cannot be trusted entirely due to the human drivers' highly uncertain nature. This thesis proposes a novel trust-based driver behavior prediction and stochastic reachable set threat assessment methodology for various dangerous situations on the road. This trust-based methodology allows autonomous vehicles to quantify the degree of trust in their predictions to generate the probabilistically safest trajectory. This approach can be instrumental in the near-crash scenarios where no collision-free trajectory exists. Three different driving behaviors are considered: Normal, Aggressive, and Drowsy. Hidden Markov Models are used for driver behavior prediction. A "trust" in the detected driver is established by combining four driving features: Longitudinal acceleration, lateral acceleration, lane deviation, and velocity. A stochastic reachable set-based approach is used to model these three different driving behaviors. Two measures of threat are proposed: Current Threat and Short Term Prediction Threat which quantify present and the future probability of a crash. The proposed threat assessment methodology resulted in a lower rate of false positives and negatives. This probabilistic threat assessment methodology is used to address the second challenge in autonomous vehicle safety: crash avoidance decision-making. This thesis presents a fast, proactive decision-making methodology based on Stochastic Model Predictive Control (SMPC). A proactive decision-making approach exploits the surrounding human-driven vehicles' intent to assess the future threat, which helps generate a safe trajectory in advance, unlike reactive decision-making approaches that do not account for the surrounding vehicles' future intent. The crash avoidance problem is formulated as a chance-constrained optimization problem to account for uncertainty in the surrounding vehicle's motion. These chance-constraints always ensure a minimum probabilistic safety of the autonomous vehicle by keeping the probability of crash below a predefined risk parameter. This thesis proposes a tractable and deterministic reformulation of these chance-constraints using convex hull formulation for a fast real-time implementation. The controller's performance is studied for different risk parameters used in the chance-constraint formulation. Simulation results show that the proposed control methodology can avoid crashes in most hazardous situations on the road. / Master of Science / Unexpected road situations frequently arise on the roads which leads to crashes. In an NHTSA study, it was reported that around 94% of car crashes could be attributed to driver errors and misjudgments. This could be attributed to drinking and driving, fatigue, or reckless driving on the roads. Full self-driving cars can significantly reduce the frequency of such accidents. Testing of self-driving cars has recently begun on certain roads, and it is estimated that one in ten cars will be self-driving by the year 2030. This means that these self-driving cars will need to operate in human-driven environments and interact with human-driven vehicles. Therefore, it is crucial for autonomous vehicles to understand the way humans drive on the road to avoid collisions and interact safely with human-driven vehicles on the road. Detecting a threat in advance and generating a safe trajectory for crash avoidance are some of the major challenges faced by autonomous vehicles. We have proposed a reliable decision-making algorithm for crash avoidance in autonomous vehicles. Our framework addresses two core challenges encountered in crash avoidance decision-making in autonomous vehicles: 1. The outside challenge: Reliable motion prediction of surrounding vehicles to continuously assess the threat to the autonomous vehicle. 2. The inside challenge: Generating a safe trajectory for the autonomous vehicle in case of future predicted threat. The outside challenge is to predict the motion of surrounding vehicles. This requires building a reliable model through which future evolution of their position states can be predicted. Building these models is not trivial, as the surrounding vehicles' motion depends on human driver intentions and behaviors, which are highly uncertain. Various driver behavior predictive models have been proposed in the literature. However, most do not quantify trust in their predictions. We have proposed a trust-based driver behavior prediction method which combines all sensor measurements to output the probability (trust value) of a certain driver being "drowsy", "aggressive", or "normal". This method allows the autonomous vehicle to choose how much to trust a particular prediction. Once a picture is painted of surrounding vehicles, we can generate safe trajectories in advance – the inside challenge. Most existing approaches use stochastic optimal control methods, which are computationally expensive and impractical for fast real-time decision-making in crash scenarios. We have proposed a fast, proactive decision-making algorithm to generate crash avoidance trajectories based on Stochastic Model Predictive Control (SMPC). We reformulate the SMPC probabilistic constraints as deterministic constraints using convex hull formulation, allowing for faster real-time implementation. This deterministic SMPC implementation ensures in real-time that the vehicle maintains a minimum probabilistic safety.

The Hybrid Electric Vehicle Team (HEVT) at Virginia Tech participates in the 4-Year EcoCAR Mobility Challenge organized by Argonne National Laboratory. The objective of this competition is to modify a stock 2019 internal combustion engine Chevrolet Blazer and incorporate a hybrid powertrain and advanced driver assist systems. The Blazer has a P4 hybrid architecture which contains an electric traction motor on the rear axle and an internal combustion engine on the front axle. HEVT seeks to develop a vehicle with advanced driving capabilities to demonstrate energy savings by utilizing existing technologies. The hybrid market has generally been tailored to small compact vehicles however, a Chevrolet Blazer is a midsize utility vehicle that offers additional space with the benefit of increased fuel economy. The research discussed in this paper focuses on the design of a Signalized Intersection Control Strategy. First, research is performed on different methods of intersection control and implementation with an existing Model Predictive Adaptive Cruise Controller. Based on ease of integration into an existing tuned Eco Adaptive Cruise Control System (ACC), a control strategy operating in the background of the main vehicle controllers is chosen. The main topic of this research is the development and simulation of a Signalized Intersection Control Strategy that works through an Eco ACC system to achieve further energy savings during an approach to a connected intersection while ensuring rider safety. This paper expands on the current knowledge of vehicle utilization of Signal Phase and Timing (SPaT) signals through simulated test cases of a vehicle system model using MATLAB. In each case, the tractive energy consumption and travel times are analyzed for both the Eco ACC system with Signalized Intersection Control Strategy (informed) vehicle and an assumed uninformed driver for comparison. In the case of a vehicle approaching a green intersection which turns red several seconds after SPaT information is received, the informed system shows a 92% decrease or 75 Wh/mi reduction in propel energy consumption at when compared to an uninformed driver. However, in a similar case where the vehicle accelerates back to cruising speed after the light turns green, displays only an 11% decrease or 47 Wh/mi reduction in propel energy consumption at the wheel when compared to the uninformed driver. These simulations confirm that the Signalized Intersection Control Strategy reduces the propel energy consumption at the wheel during approaches to signalized intersections without extending the travel time greatly and in some cases at all. The results of this research show that the control strategy reduces tractive energy consumption while maintaining travel time. / Master of Science / The Hybrid Electric Vehicle Team (HEVT) at Virginia Tech participates in the 4-Year EcoCAR Mobility Challenge organized by Argonne National Laboratory. The objective of this competition is to change a stock 2019 internal combustion engine Chevrolet Blazer into a functioning hybrid. This conversion is accomplished with the addition of an electric motor to allow the vehicle to burn less gasoline and increase customer appeal. The hybrid market has generally been tailored to small compact vehicles however, a Chevrolet Blazer is a midsize utility vehicle that offers additional space with the benefit of increased fuel economy. The research discussed in this paper focuses on the design of a Signalized Intersection Control Strategy. First, research is performed on various methods of existing intersection speed control. Based on ease of integration, a background process is chosen to update the set speed of the vehicle. The main topic of this research is the development and simulation of a Signalized Intersection Control Strategy that achieves greater energy savings during approaches to intersections. This paper expands on the current knowledge of vehicle utilization of Signal Phase and Timing (SPaT) signals through simulated test cases of a vehicle system model using MATLAB. In the case of a vehicle approaching a green intersection which turns red several seconds later, the implemented strategy shows a 92% decrease in energy consumption when compared to an uninformed driver. However, a similar case where the vehicle accelerates back to cruising speed after the light turns green displays only an 11% decrease in energy consumption when compared to an uninformed driver. These simulations confirm that the Signalized Intersection Control Strategy successfully reduces energy consumption without significant travel time extensions. The results of this research show that the control strategy reduces tractive energy consumption while maintaining travel time.

<p dir="ltr">The automotive industry has incorporated controls since the 1970s, starting with the pioneering application of an air-to-fuel ratio feedback control carburetor. Over time, significant advancements have been made in control strategies to meet industry standards for reduced fuel consumption, exhaust emissions, and enhanced safety. This thesis focuses on the implementation of advanced control strategies in heavy-duty diesel powertrains and their advantages over traditional control methods commonly employed in the automotive industry.</p><p dir="ltr">The initial part of the thesis demonstrates the utilization of model predictive control (MPC) to generate an optimized velocity profile for class 8 trucks. These velocity profiles are designed to minimize fuel consumption along a given route with known grade conditions, while adhering to the time constraints comparable to those of standard commercial cruise controllers. This methodology is further expanded to include the platooning of two trucks, with the rear truck following a desired gap (variable or fixed), resulting in additional fuel savings throughout the designated route. Through collaborative efforts involving Cummins, Peloton Technology, and Purdue University, these control strategies were implemented and validated through simulation, hardware-in-the-loop testing, and ultimately, in demonstration vehicles.</p><p dir="ltr">MPC is highly effective for vehicle-level controls due to the accurate plant model used for optimization. However, when it comes to engine controls, the plant model becomes highly nonlinear and loses accuracy when linearized [20]. To address this issue, robust control techniques are introduced to account for the inherent inaccuracies in the plant model, which can be represented as uncertainties.</p><p dir="ltr">The second study showcases the application of robust controllers in diesel engine operations, focusing on a 4.5L John Deere diesel engine equipped with an electrified intake boosting system. The intake boosting system is selectively activated during transient operations to mitigate drops in the air-to-fuel ratio (AFR), which can result in smoke emissions. Initially, a two-degree-of-freedom robustsingle-input single-output (SISO) eBooster controller is synthesized to control the eBooster during load transients. Although the robust SISO controller yields improvements, the eBooster alone does not encompass all factors affecting the gas exchange process. Other actuators, such as the exhaust throttle and EGR valve, need to be considered to enhance the air handling system. To achieve this, a robust model-basedmultiple-input multiple-output (MIMO) controller is developed to regulate the desired AFR, engine speed, and diluent air ratio (DAR) using various air handling actuators and fueling strategies. The robust MIMO controller is synthesized based on a physics-based mean value engine model, which has been calibrated to accurately reflect high-fidelity engine simulation software. The robust SISO and MIMO controllers are implemented in simulation using the high-fidelity engine simulation software. Following the simulation, the controllers are validated through experimental testing conducted in an engine dynamometer at University of Wisconsin. Results from these controllers are compared against a non-eBoosted engine, which serves as the baseline. While both the SISO and MIMO controllers show improvements in AFR (Air-Fuel Ratio), DAR (Diluent Air Ratio), and engine speed recovery during the load transients, the robust MIMO controller outperforms them by demonstrating the best overall engine performance. This superiority is attributed to its comprehensive understanding of the coupling between each actuator input and the model output. When the MIMO controller operates alongside the electrified intake boosting system, the engine exhibits remarkable enhancements. Not only does it recover back to a steady state 70% faster than the baseline, but it also reduces engine speed droop by 45%. Consequently, the engine's ability to accept load torque increases significantly.</p><p dir="ltr">As a result, a single robust MIMO controller can efficiently perform the same task instead of employing multiple PIDs or look-up tables for each actuator.</p>