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- All Subjects: engineering
- Creators: Berman, Spring
- Member of: Theses and Dissertations
Description
For the last 50 years, oscillator modeling in ranging systems has received considerable
attention. Many components in a navigation system, such as the master oscillator
driving the receiver system, as well the master oscillator in the transmitting system
contribute significantly to timing errors. Algorithms in the navigation processor must
be able to predict and compensate such errors to achieve a specified accuracy. While
much work has been done on the fundamentals of these problems, the thinking on said
problems has not progressed. On the hardware end, the designers of local oscillators
focus on synthesized frequency and loop noise bandwidth. This does nothing to
mitigate, or reduce frequency stability degradation in band. Similarly, there are not
systematic methods to accommodate phase and frequency anomalies such as clock
jumps. Phase locked loops are fundamentally control systems, and while control
theory has had significant advancement over the last 30 years, the design of timekeeping
sources has not advanced beyond classical control. On the software end,
single or two state oscillator models are typically embedded in a Kalman Filter to
alleviate time errors between the transmitter and receiver clock. Such models are
appropriate for short term time accuracy, but insufficient for long term time accuracy.
Additionally, flicker frequency noise may be present in oscillators, and it presents
mathematical modeling complications. This work proposes novel H∞ control methods
to address the shortcomings in the standard design of time-keeping phase locked loops.
Such methods allow the designer to address frequency stability degradation as well
as high phase/frequency dynamics. Additionally, finite-dimensional approximants of
flicker frequency noise that are more representative of the truth system than the
tradition Gauss Markov approach are derived. Last, to maintain timing accuracy in
a wide variety of operating environments, novel Banks of Adaptive Extended Kalman
Filters are used to address both stochastic and dynamic uncertainty.
attention. Many components in a navigation system, such as the master oscillator
driving the receiver system, as well the master oscillator in the transmitting system
contribute significantly to timing errors. Algorithms in the navigation processor must
be able to predict and compensate such errors to achieve a specified accuracy. While
much work has been done on the fundamentals of these problems, the thinking on said
problems has not progressed. On the hardware end, the designers of local oscillators
focus on synthesized frequency and loop noise bandwidth. This does nothing to
mitigate, or reduce frequency stability degradation in band. Similarly, there are not
systematic methods to accommodate phase and frequency anomalies such as clock
jumps. Phase locked loops are fundamentally control systems, and while control
theory has had significant advancement over the last 30 years, the design of timekeeping
sources has not advanced beyond classical control. On the software end,
single or two state oscillator models are typically embedded in a Kalman Filter to
alleviate time errors between the transmitter and receiver clock. Such models are
appropriate for short term time accuracy, but insufficient for long term time accuracy.
Additionally, flicker frequency noise may be present in oscillators, and it presents
mathematical modeling complications. This work proposes novel H∞ control methods
to address the shortcomings in the standard design of time-keeping phase locked loops.
Such methods allow the designer to address frequency stability degradation as well
as high phase/frequency dynamics. Additionally, finite-dimensional approximants of
flicker frequency noise that are more representative of the truth system than the
tradition Gauss Markov approach are derived. Last, to maintain timing accuracy in
a wide variety of operating environments, novel Banks of Adaptive Extended Kalman
Filters are used to address both stochastic and dynamic uncertainty.
ContributorsEchols, Justin A (Author) / Bliss, Daniel W (Thesis advisor) / Tsakalis, Konstantinos S (Committee member) / Berman, Spring (Committee member) / Mittelmann, Hans (Committee member) / Arizona State University (Publisher)
Created2020
Description
The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that techniques for analyzing and controlling the system scale well with the number of agents. One scalable approach to characterizing the behavior of a multi-agent system is possible when the agents' states evolve over time according to a Markov process. In this case, the density of agents over space and time is governed by a set of difference or differential equations known as a {\it mean-field model}, whose parameters determine the stochastic control policies of the individual agents. These models often have the advantage of being easier to analyze than the individual agent dynamics. Mean-field models have been used to describe the behavior of chemical reaction networks, biological collectives such as social insect colonies, and more recently, swarms of robots that, like natural swarms, consist of hundreds or thousands of agents that are individually limited in capability but can coordinate to achieve a particular collective goal.
This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.
This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.
ContributorsBiswal, Shiba (Author) / Berman, Spring (Thesis advisor) / Fainekos, Georgios (Committee member) / Lanchier, Nicolas (Committee member) / Mignolet, Marc (Committee member) / Peet, Matthew (Committee member) / Arizona State University (Publisher)
Created2020
Description
In the last few decades, with the revolution of availability of low-cost microelectronics, which allow fast and complex computations to be performed on board, there has been increasing attention to aerial vehicles, especially rotary-wing vehicles. This is because of their ability to vertically takeoff and land (VTOL), which make them appropriate for urban environments where no runways are needed. Quadrotors took considerable attention in research and development due to their symmetric body, which makes them simpler to model and control compared to other configurations.
One contribution of this work is the design of a new open-source based Quadrotor platform for research. This platform is compatible with both HTC Vive Tracking System (HVTS) and OptiTrack Motion Capture System, Robot Operating System (ROS), and MAVLINK communication protocol.
The thesis examined both nonlinear and linear modeling of a 6-DOF rigid-body quadrotor's dynamics along with actuator dynamics. Nonlinear/linear models are used to develop control laws for both low-level and high-level hierarchical control structures. Both HVTS and OptiTrack were used to demonstrate path following for single and multiple quadrotors. Hardware and simulation data are compared. In short, this work establishes a foundation for future work on formation flight of multi-quadrotor.
One contribution of this work is the design of a new open-source based Quadrotor platform for research. This platform is compatible with both HTC Vive Tracking System (HVTS) and OptiTrack Motion Capture System, Robot Operating System (ROS), and MAVLINK communication protocol.
The thesis examined both nonlinear and linear modeling of a 6-DOF rigid-body quadrotor's dynamics along with actuator dynamics. Nonlinear/linear models are used to develop control laws for both low-level and high-level hierarchical control structures. Both HVTS and OptiTrack were used to demonstrate path following for single and multiple quadrotors. Hardware and simulation data are compared. In short, this work establishes a foundation for future work on formation flight of multi-quadrotor.
ContributorsAltawaitan, Abdullah (Author) / Rodriguez, Armando A (Thesis advisor) / Tsakalis, Konstantinos (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2019
Description
This thesis presents a process by which a controller used for collective transport tasks is qualitatively studied and probed for presence of undesirable equilibrium states that could entrap the system and prevent it from converging to a target state. Fields of study relevant to this project include dynamic system modeling, modern control theory, script-based system simulation, and autonomous systems design. Simulation and computational software MATLAB and Simulink® were used in this thesis.
To achieve this goal, a model of a swarm performing a collective transport task in a bounded domain featuring convex obstacles was simulated in MATLAB/ Simulink®. The closed-loop dynamic equations of this model were linearized about an equilibrium state with angular acceleration and linear acceleration set to zero. The simulation was run over 30 times to confirm system ability to successfully transport the payload to a goal point without colliding with obstacles and determine ideal operating conditions by testing various orientations of objects in the bounded domain. An additional purely MATLAB simulation was run to identify local minima of the Hessian of the navigation-like potential function. By calculating this Hessian periodically throughout the system’s progress and determining the signs of its eigenvalues, a system could check whether it is trapped in a local minimum, and potentially dislodge itself through implementation of a stochastic term in the robot controllers. The eigenvalues of the Hessian calculated in this research suggested the model local minima were degenerate, indicating an error in the mathematical model for this system, which likely incurred during linearization of this highly nonlinear system.
To achieve this goal, a model of a swarm performing a collective transport task in a bounded domain featuring convex obstacles was simulated in MATLAB/ Simulink®. The closed-loop dynamic equations of this model were linearized about an equilibrium state with angular acceleration and linear acceleration set to zero. The simulation was run over 30 times to confirm system ability to successfully transport the payload to a goal point without colliding with obstacles and determine ideal operating conditions by testing various orientations of objects in the bounded domain. An additional purely MATLAB simulation was run to identify local minima of the Hessian of the navigation-like potential function. By calculating this Hessian periodically throughout the system’s progress and determining the signs of its eigenvalues, a system could check whether it is trapped in a local minimum, and potentially dislodge itself through implementation of a stochastic term in the robot controllers. The eigenvalues of the Hessian calculated in this research suggested the model local minima were degenerate, indicating an error in the mathematical model for this system, which likely incurred during linearization of this highly nonlinear system.
ContributorsBaye-Wallace, Lily Catherine (Author) / Berman, Spring (Thesis director) / Marvi, Hamidreza (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School of Music, Dance and Theatre (Contributor) / School for Engineering of Matter,Transport & Enrgy (Contributor) / Barrett, The Honors College (Contributor)
Created2020-12