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- Creators: Prokofiev, Sergey, 1891-1953
Description
In this thesis, different H∞ observers for time-delay systems are implemented and
their performances are compared. Equations that can be used to calculate observer gains are mentioned. Different methods that can be used to implement observers for time-delay systems are illustrated. Various stable and unstable systems are used and H∞ bounds are calculated using these observer designing methods. Delays are assumed to be known constants for all systems. H∞ gains are calculated numerically using disturbance signals and performances of observers are compared.
The primary goal of this thesis is to implement the observer for Time Delay Systems designed using SOS and compare its performance with existing H∞ optimal observers. These observers are more general than other observers for time-delay systems as they make corrections to the delayed state as well along with the present state. The observer dynamics can be represented by an ODE coupled with a PDE. Results shown in this thesis show that this type of observers performs better than other H∞ observers. Sub-optimal observer-based state feedback system is also generated and simulated using the SOS observer. The simulation results show that the closed loop system converges very quickly, and the observer can be used to design full state-feedback closed loop system.
their performances are compared. Equations that can be used to calculate observer gains are mentioned. Different methods that can be used to implement observers for time-delay systems are illustrated. Various stable and unstable systems are used and H∞ bounds are calculated using these observer designing methods. Delays are assumed to be known constants for all systems. H∞ gains are calculated numerically using disturbance signals and performances of observers are compared.
The primary goal of this thesis is to implement the observer for Time Delay Systems designed using SOS and compare its performance with existing H∞ optimal observers. These observers are more general than other observers for time-delay systems as they make corrections to the delayed state as well along with the present state. The observer dynamics can be represented by an ODE coupled with a PDE. Results shown in this thesis show that this type of observers performs better than other H∞ observers. Sub-optimal observer-based state feedback system is also generated and simulated using the SOS observer. The simulation results show that the closed loop system converges very quickly, and the observer can be used to design full state-feedback closed loop system.
ContributorsTalati, Rushabh Vikram (Author) / Peet, Matthew (Thesis advisor) / Berman, Spring (Committee member) / Rivera, Daniel (Committee member) / Arizona State University (Publisher)
Created2018
Description
Human habitation of other planets requires both cost-effective transportation and low time-of-flight for human passengers and critical supplies. The current methods for interplanetary orbital transfers, such as the Hohmann transfer, require either expensive, high fuel maneuvers or extended space travel. However, by utilizing the high velocities of a super-geosynchronous space elevator, spacecraft released from an apex anchor could achieve interplanetary transfers with minimal Delta V fuel and time of flight requirements. By using Lambert’s Problem and Free Release propagation to determine the minimal fuel transfer from a terrestrial space elevator to Mars under a variety of initial conditions and time-of-flight constraints, this paper demonstrates that the use of a space elevator release can address both needs by dramatically reducing the time-of-flight and the fuel budget.
ContributorsTorla, James (Author) / Peet, Matthew (Thesis director) / Swan, Peter (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Prior research has confirmed that supervised learning is an effective alternative to computationally costly numerical analysis. Motivated by NASA's use of abort scenario matrices to aid in mission operations and planning, this paper applies supervised learning to trajectory optimization in an effort to assess the accuracy of a less time-consuming method of producing the magnitude of delta-v vectors required to abort from various points along a Near Rectilinear Halo Orbit. Although the utility of the study is limited, the accuracy of the delta-v predictions made by a Gaussian regression model is fairly accurate after a relatively swift computation time, paving the way for more concentrated studies of this nature in the future.
ContributorsSmallwood, Sarah Lynn (Author) / Peet, Matthew (Thesis director) / Liu, Huan (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School of Earth and Space Exploration (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
A computational framework based on convex optimization is presented for stability analysis of systems described by Partial Differential Equations (PDEs). Specifically, two forms of linear PDEs with spatially distributed polynomial coefficients are considered.
The first class includes linear coupled PDEs with one spatial variable. Parabolic, elliptic or hyperbolic PDEs with Dirichlet, Neumann, Robin or mixed boundary conditions can be reformulated in order to be used by the framework. As an example, the reformulation is presented for systems governed by Schr¨odinger equation, parabolic type, relativistic heat conduction PDE and acoustic wave equation, hyperbolic types. The second form of PDEs of interest are scalar-valued with two spatial variables. An extra spatial variable allows consideration of problems such as local stability of fluid flows in channels and dynamics of population over two dimensional domains.
The approach does not involve discretization and is based on using Sum-of-Squares (SOS) polynomials and positive semi-definite matrices to parameterize operators which are positive on function spaces. Applying the parameterization to construct Lyapunov functionals with negative derivatives allows to express stability conditions as a set of LinearMatrix Inequalities (LMIs). The MATLAB package SOSTOOLS was used to construct the LMIs. The resultant LMIs then can be solved using existent Semi-Definite Programming (SDP) solvers such as SeDuMi or MOSEK. Moreover, the proposed approach allows to calculate bounds on the rate of decay of the solution norm.
The methodology is tested using several numerical examples and compared with the results obtained from simulation using standard methods of numerical discretization and analytic solutions.
The first class includes linear coupled PDEs with one spatial variable. Parabolic, elliptic or hyperbolic PDEs with Dirichlet, Neumann, Robin or mixed boundary conditions can be reformulated in order to be used by the framework. As an example, the reformulation is presented for systems governed by Schr¨odinger equation, parabolic type, relativistic heat conduction PDE and acoustic wave equation, hyperbolic types. The second form of PDEs of interest are scalar-valued with two spatial variables. An extra spatial variable allows consideration of problems such as local stability of fluid flows in channels and dynamics of population over two dimensional domains.
The approach does not involve discretization and is based on using Sum-of-Squares (SOS) polynomials and positive semi-definite matrices to parameterize operators which are positive on function spaces. Applying the parameterization to construct Lyapunov functionals with negative derivatives allows to express stability conditions as a set of LinearMatrix Inequalities (LMIs). The MATLAB package SOSTOOLS was used to construct the LMIs. The resultant LMIs then can be solved using existent Semi-Definite Programming (SDP) solvers such as SeDuMi or MOSEK. Moreover, the proposed approach allows to calculate bounds on the rate of decay of the solution norm.
The methodology is tested using several numerical examples and compared with the results obtained from simulation using standard methods of numerical discretization and analytic solutions.
ContributorsMeyer, Evgeny (Author) / Peet, Matthew (Thesis advisor) / Berman, Spring (Committee member) / Rivera, Daniel (Committee member) / Arizona State University (Publisher)
Created2016
ContributorsProkofiev, Sergey, 1891-1953 (Composer)
ContributorsProkofiev, Sergey, 1891-1953 (Composer)
ContributorsProkofiev, Sergey, 1891-1953 (Composer)
ContributorsProkofiev, Sergey, 1891-1953 (Composer)
ContributorsProkofiev, Sergey, 1891-1953 (Composer)
ContributorsProkofiev, Sergey, 1891-1953 (Composer)