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This dissertation aims to realize the goal of developing robust control solutions that can enable legged robots to navigate complex unknown environments. The idea of creating articulated-legged machines that can mimic animal locomotion has fueled the imagination of many researchers. These legged robots are designed to assist humans in their day-to-day tasks and challenging scenarios such as monitoring remote, inhospitable environments, disaster response, and other dangerous environments. Despite several decades of research, legged robots have yet to reach the dexterity or dynamic stability needed for real-world deployments. A fundamental gap exists in the understanding and development of reliable and scalable algorithms required for the real-time planning and control of legged robots. The overarching goal of this thesis is to formally develop computationally tractable, robust controllers based on nonlinear hybrid systems theory, model predictive control, and optimization for the real-time planning and control of agile locomotion in quadrupedal robots. Toward this objective, this thesis first investigates layered control architectures. In particular, we propose a two-level hierarchical control architecture in which the higher level is based on a reduced-order model predictive control (MPC), and the lower level is based on a full-order quadratic programming (QP) based virtual constraints controller. Specifically, two MPC architectures are explored: 1) An event-based MPC scheme that generates the optimal center of mass (COM) trajectories using a reduced-order linear inverted pendulum (LIP) model, and 2) A time-based MPC scheme that computes the optimal COM and ground reaction forces (GRF) using the reduced-order single rigid body (SRB) dynamics model. The optimal COM trajectories in the event-based MPC and the optimal COM trajectories, along with the ground reaction forces in the time-based MPC, are then tracked by the low-level virtual constraints controller. The event-based MPC scheme is numerically validated on the Vision 60 platform in a physics-based simulation environment. It has significantly reduced the computational burden associated with real-time planning-based MPC schemes. However, owing to the quasi-static nature of the optimal trajectories generated by the LIP model, we explored a time-based MPC scheme using Single Rigid Body Dynamics. This time-based MPC scheme is also numerically validated using the mathematical model of the A1 quadrupedal robot. Most MPC schemes use a reduced-order model to generate optimal trajectories. However, the abstraction and unmodeled dynamics in template models significantly increase the gap between reduced- and full-order models, limiting the robot's full scope and potential. In the second part of the thesis, we aim to develop a computationally tractable robust model predictive control (RMPC) scheme based on convex QPs to bridge this gap. The RMPC framework considers the single rigid body model subject to a set of unmodeled dynamics and plans for the optimal reduced-order trajectory and GRFs. The generated optimal GRFs of the high-level RMPC are then mapped to the full-order model using a low-level nonlinear controller based on virtual constraints and QP. The key innovation of the proposed RMPC framework is that it allows the integration of the hierarchical controller with Reinforcement Learning (RL) techniques to train a neural network to compute the vertices of the uncertainty set numerically. The proposed hierarchical control algorithm is validated numerically and experimentally for robust and blind locomotion of the A1 quadrupedal robot on different indoor and outdoor terrains and at different speeds. The numerical analysis of the RMPC suggests significant improvement in the performance of the rough terrain locomotion compared to the nominal MPC. In particular, the proposed RMPC algorithm outperforms the nominal MPC by over 60% during rough terrain locomotion over 550 uneven terrains. Our experimental studies also indicate a significant reduction in the gap between the reduced full-order models by comparing the desired and actual GRFs. Finally, the last part of the thesis presents a formal approach for synthesizing robust $mathcal{H}_2$- and $mathcal{H}_infty$-optimal MPCs to stabilize the periodic locomotion of legged robots. The proposed algorithm builds on the existing optimization-based control stack. We outline the set of conditions under which the closed-loop nonlinear dynamics around a periodic orbit can be transformed into a linear time-invariant (LTI) system using Floquet theory. We then outline an approach to systematically generate parameterized $mathcal{H}_2$- and $mathcal{H}_infty$- robust controllers using linear matrix inequalities (LMIs). We subsequently established a set of conditions guaranteeing the existence of such robust optimal controllers. The proposed $mathcal{H}_2$- and $mathcal{H}_infty$-optimal MPCs are extensively validated both numerically and experimentally for the robust locomotion of the A1 quadrupedal robot subject to various external disturbances and uneven terrains. Our numerical analysis suggests a significant improvement in the performance of robust locomotion compared to the nominal MPC. / Doctor of Philosophy / Legged robots have always been envisioned to work alongside humans, assisting them in mundane day-to-day tasks to challenging scenarios such as monitoring remote locations, planetary exploration, and supporting relief programs in disaster situations. Furthermore, research into legged locomotion can aid in designing and developing powered prosthetic limbs and exoskeletons. With these advantages in mind, several researchers have created sophisticated-legged robots and even more complicated algorithms to control them. Despite this, a significant gap exists between the agility, mobility, and dynamic stability shown by the existing legged robots and their biological counterparts. To work alongside humans, legged robots have to interact with complex environments and deal with uncertainties in the form of unplanned contacts and unknown terrains. Developing robust control solutions to accommodate disturbances explicitly marks the first step towards safe and reliable real-world deployment of legged robots. Toward this objective, this thesis aims to establish a formal foundation to develop computationally tractable robust controllers for the real-time planning and control of legged robots. Initial investigations in this thesis report on the use of layered control architectures, specifically event-based and time-based Model Predictive Control(MPC) schemes. These layered control architectures consist of an MPC scheme built around a reduced-order model at the high level and a virtual constraints-based nonlinear controller at the low level. Using these layered control architectures, this thesis proposed two robust control solutions to improve the rough terrain locomotion of legged robots. The first proposed robust control solution aims to mitigate one of the issues of layered control architecture. In particular, layered control architectures rely on a reduced order model at the high level to remain computationally tractable. However, the approximation of fullorder models with reduced-order models limits the full scope and potential of the robot. The proposed algorithm aims to bridge the gap between reduced- and full-order models with the integration of model-free Reinforcement Learning (RL) techniques. The second algorithm proposes a formal approach to generate robust optimal control solutions that can explicitly accommodate the disturbances and stabilize periodic legged locomotion. Under some mild conditions, the MPC control solution is analyzed, and an auxiliary feedback control solution that can handle disturbances explicitly is proposed. The thesis also theoretically establishes the sufficient conditions for the existence of such controllers. Both the proposed control solutions are extensively validated using numerical simulations and experiments using an A1 quadrupedal robot as a representative example.

<p>Among all additive manufacturing processes, material jetting, or inkjet 3D printing, builds the product similar to the traditional inkjet printing, either by drop-on-demand or continuous printing. Aside from the common advantages as other additive manufacturing methods, it can achieve higher resolution than other additive manufacturing methods. Combining its ability to accept a wide range of functional inks, inkjet 3D printing is predominantly used in pharmaceutical and biomedical applications. A height profile model is necessary to achieve better estimation of the geometry of a printed product. Numerical height profile models have been documented that can estimate the inkjet printing process from when the droplet hits the substrate till fully cured. Although they can estimate height profiles relatively accurately, these models generally take a long time to compute. A simplified model that can achieve sufficient accuracy while reducing computational complexity is needed for real-time process control. In this work, a layer-to-layer height propagation model that aims to balance computational complexity and model accuracy is proposed and experimentally validated. The model consists of two sub-models where one is dedicated to multi-layer line printing and the other is more broadly applicable for multi-layer 2D patterns. Both models predict the height profile of drops through separate volume and area layer-to-layer propagation. The layer-to-layer propagation is based on material flow and volume conservation. The models are experimentally validated on an experimental inkjet 3D printing system equipped with a heated piezoelectric dispenser head made by Microdrop. There are notable similarities between inkjet 3D printing and inkjet image printing, which has been studied extensively to improve color printing quality. Image processing techniques are necessary to convert nearly continuous levels of color intensities to binary printing map while satisfying the human visual system at the same time. It is reasonable to leverage such image processing techniques to improve the quality of inkjet 3D printed products, which might be more effective and efficient. A framework is proposed to adapt image processing techniques for inkjet 3D printing. Standard error diffusion method is chosen as a demonstration of the framework to be adapted for inkjet 3D printing and this adaption is experimentally validated. The adapted error diffusion method can improve the printing quality in terms of geometry integrity with low demand on computation power. Model predictive control has been widely used for process control in various industries. With a carefully designed cost function, model predictive control can be an effective tool to improve inkjet 3D printing. While many researchers utilized model predictive control to indirectly improves functional side of the printed products, geometry control is often overlooked. This is possibly due to the lack of high quality height profile models for inkjet 3D printing for real-time control. Height profile control of inkjet 3D printing can be formulated as a constrained non-linear model predictive control problem. The input to the printing system is always constrained, as droplet volume not only is bounded but also cannot be continuously adjusted due to the limitation of the printhead.  A specific cost function is proposed to account for the geometry of both the final printed product and the intermediate layers better. The cost function is further adjusted for the inkjet 3D printing system to reduce memory usage for larger print geometries by introducing sparse matrix and scaler cost weights. Two patterns with different parameter settings are simulated using model predictive controller. The simulated results show a consistent improvement over open-loop prints. Experimental validation is also performed on both a bi-level pattern and a P pattern, same as that printed with adapted error diffusion for inkjet 3D printing. The model predictive controlled printing outperforms the open-loop printing. In summary, a set of layer-to-layer height propagation profile models for inkjet 3D printing are proposed and experimentally validated. A framework to adapt error diffusion to improve inkjet 3D printing is proposed and validated experimentally. Model predictive control can also improve geometric integrity of inkjet 3D printing with a carefully designed cost function to address memory usage. It is also experimentally validated.</p>

As vehicles become electrified and more intelligent in terms of sensing, actuation and processing; a number of interesting possibilities arise in controlling vehicle dynamics and driving behavior. Over-actuation with inwheel motors, all wheel steering and active camber is one such possibility, and can facilitate control combinations that push boundaries in energy consumption and safety. Optimal control can be used to investigate the best combinations of control inputs to an over-actuated system. In Part 1, a literature study is performed on the state of art in the field of optimal control, highlighting the strengths and weaknesses of different methods and their applicability to a vehicular system. Out of these methods, Dynamic Programming and Model Predictive Control are of particular interest. Prior work in overactuation, as well as control for reducing tire energy dissipation is studied, and utilized to frame the dynamics, constraints and objective of an optimal control problem. In Part 2, an optimal control problem representing the lateral dynamics of an over-actuated vehicle is formulated, and solved for different objectives using Dynamic Programming. Simulations are performed for standard driving maneuvers, performance parameters are defined, and a system design study is conducted. Objectives include minimizing tire cornering resistance (saving energy) and maintaining the reference vehicle trajectory (ensuring safety), and optimal combinations of input steering and camber angles are derived as a performance benchmark. Following this, Model Predictive Control is used to design an online controller that follows the optimal vehicle state, and studies are performed to assess the suitability of MPC to over-actuation. Simulation models are also expanded to include non-linear tires. Finally, vehicle implementation is considered on the KTH Research Concept Vehicle (RCV) and four vehicle-implementable control cases are presented. To conclude, this thesis project uses methods in optimal control to find candidate solutions to improve vehicle performance thanks to over-actuation. Extensive vehicle tests are needed for a clear indication of the energy saving achievable, but simulations show promising performance improvements for vehicles overactuated with all-wheel steering and active camber.

<p>In this thesis, a human-in-the-loop control system is presented to assist an operator in teleoperation of a mobile robot. In a conventional teleoperation paradigm, the human operator would directly navigate the robot without any assistance which may result in poor performance in complex and unknown task environments due to inadequacy of visual feedback. The proposed method in this thesis builds on an earlier general control framework that systematically combines teleoperation and autonomous control subtasks. In this approach, the operator controls the mobile robot (slave) using a force-feedback haptic interface (master). Teleoperation control commands coordinate master and slave robots while an autonomous control subtask helps the operator avoid collisions with obstacles in the robot task environment by providing corrective force feedback. The autonomous collision avoidance is based on a Model Predictive Control (MPC) philosophy. The autonomous subtask control commands are generated by formulating and solving a constrained optimization problem over a rolling horizon window of time into the future using system models to predict the operator force and robot motion. The goal of the optimization is to prevent collisions within the prediction horizon by applying corrective force feedback, while minimizing interference with the operator teleoperation actions. It is assumed that the obstacles are stationary and sonar sensors mounted on the mobile robot measure the obstacle distances relative to the robot. Two formulation of MPC-based collision avoidance are proposed. The first formulation directly incorporates raw observation points as constraints in the MPC optimization problem. The second formulation relies on a line segment representation of the task environment. This thesis employs the well-known Hough transform method to effectively transform the raw sensor data into line segments. The extracted line segments constitute a compact model for the environment that is used in the formulation of collision constraints. The effectiveness of the proposed model-predictive control obstacle avoidance schemes is demonstrated in teleoperation experiments where the master robot is a 3DOF haptic interface and the slave is a P3-DX mobile robot equipped with eight (8) sonar sensors at the front.</p> / Master of Applied Science (MASc)

This thesis focuses on utilizing the persistent voltage vector injections by finite control set model predictive control (FCSMPC) to enable simultaneous estimations of both position and parameters in order to realize robust sensorless interior permanent magnet synchronous machine (IPMSM) drives valid at the entire operating region including no-load standstill without any additional signal injection and switchover. The system (here, IPMSM) needs to meet certain observability conditions to identify the parameters and position. Moreover, each combination of the parameters and/or position involves different observability requirements which cannot be accomplished at every operating point. In particular, meeting the observability for parameters and position at no-load standstill is more challenging. This is overcome by generating persistent excitation in the system with high-frequency signal injection. The FCSMPC scheme inherently features the persistent excitation with voltage vector injection and hence no additional signal injection is required. Moreover, the persistent excitation always exists for FCSMPC except at the standstill where the control applies the null vectors when the reference currents are zero. However, introducing a small negative d axis current at the standstill would be sufficient to overcome this situation.The parameter estimations are investigated at first in this thesis. The observability is analyzed for the combinations of two, three and four parameters and experimentally validated by online identification based on recursive least square (RLS) based adaptive observer. The worst case operating points concerning observability are identified and experimentally proved that the online identification of all the parameter combinations could be accomplished with persistent excitation by FCMPC. Moreover, the effect of estimation error in one parameter on the other known as parameter coupling is reduced with the proposed decoupling technique. The persistent voltage vector injections by FCSMPC help to meet the observability conditions for estimating the position, especially at low speeds. However, the arbitrary nature of the switching ripples and absence of PWM modulator void the possibility of applying the standard demodulation based techniques for FCSMPC. Consequently, a nonlinear optimization based observer is proposed to estimate both the position and speed, and experimentally validated from standstill to maximum speed. Furthermore, a compensator is also proposed that prevents converging to saddle and symmetrical ( ambiguity) solutions. The robustness analysis of the proposed nonlinear optimization based observer shows that estimating the position without co-estimating the speed is more robust and the main influencing parameters on the accuracy of the position estimation are d and q inductances. Subsequently, the proposed nonlinear optimization based observer is extended to simultaneously estimate the position, d and q inductances. The experimental results show the substantial improvements in response time, and reduction in both steady and transient state position errors. In summary, this thesis presents the significance of persistent voltage vector injections in estimating both parameter and position, and also shows that nonlinear optimization based technique is an ideal candidate for robust sensorless FCSMPC. / Thesis / Doctor of Philosophy (PhD)

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.