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- All Subjects: Mechanical Engineering
- Creators: Berman, Spring
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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
Description
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers - machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers.
We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.
We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.
ContributorsKamyar, Reza (Author) / Peet, Matthew (Thesis advisor) / Berman, Spring (Committee member) / Rivera, Daniel (Committee member) / Artemiadis, Panagiotis (Committee member) / Fainekos, Georgios (Committee member) / Arizona State University (Publisher)
Created2016
Description
The presented work in this report is about Real time Estimation of wind and analyzing current wind correction algorithm in commercial off the shelf Autopilot board. The open source ArduPilot Mega 2.5 (APM 2.5) board manufactured by 3D Robotics is used. Currently there is lot of development being done in the field of Unmanned Aerial Systems (UAVs), various aerial platforms and corresponding; autonomous systems for them. This technology has advanced to such a stage that UAVs can be used for specific designed missions and deployed with reliability. But in some areas like missions requiring high maneuverability with greater efficiency is still under research area. This would help in increasing reliability and augmenting range of UAVs significantly. One of the problems addressed through this thesis work is, current autopilot systems have algorithm that handles wind by attitude correction with appropriate Crab angle. But the real time wind vector (direction) and its calculated velocity is based on geometrical and algebraic transformation between ground speed and air speed vectors. This method of wind estimation and prediction, many a times leads to inaccuracy in attitude correction. The same has been proved in the following report with simulation and actual field testing. In later part, new ways to tackle while flying windy conditions have been proposed.
ContributorsBiradar, Anandrao Shesherao (Author) / Saripalli, Srikanth (Thesis advisor) / Berman, Spring (Thesis advisor) / Thanga, Jekan (Committee member) / Arizona State University (Publisher)
Created2014
Description
The environmental impact of the fossil fuels has increased tremendously in the last decade. This impact is one of the most contributing factors of global warming. This research aims to reduce the amount of fuel consumed by vehicles through optimizing the control scheme for the future route information. Taking advantage of more degrees of freedom available within PHEV, HEV, and FCHEV “energy management” allows more margin to maximize efficiency in the propulsion systems. The application focuses on reducing the energy consumption in vehicles by acquiring information about the road grade. Road elevations are obtained by use of Geographic Information System (GIS) maps to optimize the controller. The optimization is then reflected on the powertrain of the vehicle.The approach uses a Model Predictive Control (MPC) algorithm that allows the energy management strategy to leverage road grade to prepare the vehicle for minimizing energy consumption during an uphill and potential energy harvesting during a downhill. The control algorithm will predict future energy/power requirements of the vehicle and optimize the performance by instructing the power split between the internal combustion engine (ICE) and the electric-drive system. Allowing for more efficient operation and higher performance of the PHEV, and HEV. Implementation of different strategies, such as MPC and Dynamic Programming (DP), is considered for optimizing energy management systems. These strategies are utilized to have a low processing time. This approach allows the optimization to be integrated with ADAS applications, using current technology for implementable real time applications.
The Thesis presents multiple control strategies designed, implemented, and tested using real-world road elevation data from three different routes. Initial simulation based results show significant energy savings. The savings range between 11.84% and 25.5% for both Rule Based (RB) and DP strategies on the real world tested routes. Future work will take advantage of vehicle connectivity and ADAS systems to utilize Vehicle to Vehicle (V2V), Vehicle to Infrastructure (V2I), traffic information, and sensor fusion to further optimize the PHEV and HEV toward more energy efficient operation.
The Thesis presents multiple control strategies designed, implemented, and tested using real-world road elevation data from three different routes. Initial simulation based results show significant energy savings. The savings range between 11.84% and 25.5% for both Rule Based (RB) and DP strategies on the real world tested routes. Future work will take advantage of vehicle connectivity and ADAS systems to utilize Vehicle to Vehicle (V2V), Vehicle to Infrastructure (V2I), traffic information, and sensor fusion to further optimize the PHEV and HEV toward more energy efficient operation.
ContributorsAlzorgan, Mohammad (Author) / Mayyas, Abdel Ra’ouf (Thesis advisor) / Berman, Spring (Committee member) / Ren, Yi (Committee member) / Arizona State University (Publisher)
Created2016
Description
Wearable robotics is a growing sector in the robotics industry, they can increase the productivity of workers and soldiers and can restore some of the lost function to people with disabilities. Wearable robots should be comfortable, easy to use, and intuitive. Robust control methods are needed for wearable robots that assist periodic motion.
This dissertation studies a phase based oscillator constructed with a second order dynamic system and a forcing function based on the phase angle of the system. This produces a bounded control signal that can alter the damping and stiffens properties of the dynamic system. It is shown analytically and experimentally that it is stable and robust. It can handle perturbations remarkably well. The forcing function uses the states of the system to produces stable oscillations. Also, this work shows the use of the phase based oscillator in wearable robots to assist periodic human motion focusing on assisting the hip motion. One of the main problems to assist periodic motion properly is to determine the frequency of the signal. The phase oscillator eliminates this problem because the signal always has the correct frequency. The input requires the position and velocity of the system. Additionally, the simplicity of the controller allows for simple implementation.
This dissertation studies a phase based oscillator constructed with a second order dynamic system and a forcing function based on the phase angle of the system. This produces a bounded control signal that can alter the damping and stiffens properties of the dynamic system. It is shown analytically and experimentally that it is stable and robust. It can handle perturbations remarkably well. The forcing function uses the states of the system to produces stable oscillations. Also, this work shows the use of the phase based oscillator in wearable robots to assist periodic human motion focusing on assisting the hip motion. One of the main problems to assist periodic motion properly is to determine the frequency of the signal. The phase oscillator eliminates this problem because the signal always has the correct frequency. The input requires the position and velocity of the system. Additionally, the simplicity of the controller allows for simple implementation.
ContributorsDe la Fuente Valadez, Juan Oziel (Author) / Sugar, Thomas G. (Committee member) / Redkar, Sangram (Committee member) / Berman, Spring (Committee member) / Artemiadis, Panagiotis (Committee member) / Schroeder, Kyle A (Committee member) / Arizona State University (Publisher)
Created2016
Description
The advancements in the technology of MEMS fabrication has been phenomenal in recent years. In no mean measure this has been the result of continued demand from the consumer electronics market to make devices smaller and better. MEMS inertial measuring units (IMUs) have found revolutionary applications in a wide array of fields like medical instrumentation, navigation, attitude stabilization and virtual reality. It has to be noted though that for advanced applications of motion tracking, navigation and guidance the cost of the IMUs is still pretty high. This is mainly because the process of calibration and signal processing used to get highly stable results from MEMS IMU is an expensive and time-consuming process. Also to be noted is the inevitability of using external sensors like GPS or camera for aiding the IMU data due to the error propagation in IMU measurements adds to the complexity of the system.
First an efficient technique is proposed to acquire clean and stable data from unaided IMU measurements and then proceed to use that system for tracking human motion. First part of this report details the design and development of the low-cost inertial measuring system ‘yIMU’. This thesis intends to bring together seemingly independent techniques that were highly application specific into one monolithic algorithm that is computationally efficient for generating reliable orientation estimates. Second part, systematically deals with development of a tracking routine for human limb movements. The validity of the system has then been verified.
The central idea is that in most cases the use of expensive MEMS IMUs is not warranted if robust smart algorithms can be deployed to gather data at a fraction of the cost. A low-cost prototype has been developed comparable to tactical grade performance for under $15 hardware. In order to further the practicability of this device we have applied it to human motion tracking with excellent results. The commerciality of device has hence been thoroughly established.
First an efficient technique is proposed to acquire clean and stable data from unaided IMU measurements and then proceed to use that system for tracking human motion. First part of this report details the design and development of the low-cost inertial measuring system ‘yIMU’. This thesis intends to bring together seemingly independent techniques that were highly application specific into one monolithic algorithm that is computationally efficient for generating reliable orientation estimates. Second part, systematically deals with development of a tracking routine for human limb movements. The validity of the system has then been verified.
The central idea is that in most cases the use of expensive MEMS IMUs is not warranted if robust smart algorithms can be deployed to gather data at a fraction of the cost. A low-cost prototype has been developed comparable to tactical grade performance for under $15 hardware. In order to further the practicability of this device we have applied it to human motion tracking with excellent results. The commerciality of device has hence been thoroughly established.
ContributorsShetty, Yatiraj K (Author) / Redkar, Sangram (Thesis advisor) / Sugar, Thomas (Committee member) / Berman, Spring (Committee member) / Lee, Hyunglae (Committee member) / Arizona State University (Publisher)
Created2016
Description
Robotic joints can be either powered or passive. This work will discuss the creation of a passive and a powered joint system as well as the combination system being both powered and passive along with its benefits. A novel approach of analysis and control of the combination system is presented.
A passive and a powered ankle joint system is developed and fit to the field of prosthetics, specifically ankle joint replacement for able bodied gait. The general 1 DOF robotic joint designs are examined and the results from testing are discussed. Achievements in this area include the able bodied gait like behavior of passive systems for slow walking speeds. For higher walking speeds the powered ankle system is capable of adding the necessary energy to propel the user forward and remain similar to able bodied gait, effectively replacing the calf muscle. While running has not fully been achieved through past powered ankle devices the full power necessary is reached in this work for running and sprinting while achieving 4x’s power amplification through the powered ankle mechanism.
A theoretical approach to robotic joints is then analyzed in order to combine the advantages of both passive and powered systems. Energy methods are shown to provide a correct behavioral analysis of any robotic joint system. Manipulation of the energy curves and mechanism coupler curves allows real time joint behavioral adjustment. Such a powered joint can be adjusted to passively achieve desired behavior for different speeds and environmental needs. The effects on joint moment and stiffness from adjusting one type of mechanism is presented.
A passive and a powered ankle joint system is developed and fit to the field of prosthetics, specifically ankle joint replacement for able bodied gait. The general 1 DOF robotic joint designs are examined and the results from testing are discussed. Achievements in this area include the able bodied gait like behavior of passive systems for slow walking speeds. For higher walking speeds the powered ankle system is capable of adding the necessary energy to propel the user forward and remain similar to able bodied gait, effectively replacing the calf muscle. While running has not fully been achieved through past powered ankle devices the full power necessary is reached in this work for running and sprinting while achieving 4x’s power amplification through the powered ankle mechanism.
A theoretical approach to robotic joints is then analyzed in order to combine the advantages of both passive and powered systems. Energy methods are shown to provide a correct behavioral analysis of any robotic joint system. Manipulation of the energy curves and mechanism coupler curves allows real time joint behavioral adjustment. Such a powered joint can be adjusted to passively achieve desired behavior for different speeds and environmental needs. The effects on joint moment and stiffness from adjusting one type of mechanism is presented.
ContributorsHolgate, Robert (Author) / Sugar, Thomas (Thesis advisor) / Artemiades, Panagiotis (Thesis advisor) / Berman, Spring (Committee member) / Mignolet, Marc (Committee member) / Davidson, Joseph (Committee member) / Arizona State University (Publisher)
Created2017
Description
The greenhouse gases in the atmosphere have reached a highest level due to high number of vehicles. A Fuel Cell Hybrid Electric Vehicle (FCHEV) has zero greenhouse gas emissions compared to conventional ICE vehicles or Hybrid Electric Vehicles and hence is a better alternative. All Electric Vehicle (AEVs) have longer charging time which is unfavorable. A fully charged battery gives less range compared to a FCHEV with a full hydrogen tank. So FCHEV has an advantage of a quick fuel up and more mileage than AEVs. A Proton Electron Membrane Fuel Cell (PEMFC) is the commonly used kind of fuel cell vehicles but it possesses slow current dynamics and hence not suitable to be the sole power source in a vehicle. Therefore, improving the transient power capabilities of fuel cell to satisfy the road load demand is critical.
This research studies integration of Ultra-Capacitor (UC) to FCHEV. The objective is to analyze the effect of integrating UCs on the transient response of FCHEV powertrain. UCs has higher power density which can overcome slow dynamics of fuel cell. A power management strategy utilizing peak power shaving strategy is implemented. The goal is to decrease power load on batteries and operate fuel cell stack in it’s most efficient region. Complete model to simulate the physical behavior of UC-Integrated FCHEV (UC-FCHEV) is developed using Matlab/SIMULINK. The fuel cell polarization curve is utilized to devise operating points of the fuel cell to maintain its operation at most efficient region. Results show reduction of hydrogen consumption in aggressive US06 drive cycle from 0.29 kg per drive cycle to 0.12 kg. The maximum charge/discharge battery current was reduced from 286 amperes to 110 amperes in US06 drive cycle. Results for the FUDS drive cycle show a reduction in fuel consumption from 0.18 kg to 0.05 kg in one drive cycle. This reduction in current increases the life of the battery since its protected from overcurrent. The SOC profile of the battery also shows that the battery is not discharged to its minimum threshold which increasing the health of the battery based on number of charge/discharge cycles.
This research studies integration of Ultra-Capacitor (UC) to FCHEV. The objective is to analyze the effect of integrating UCs on the transient response of FCHEV powertrain. UCs has higher power density which can overcome slow dynamics of fuel cell. A power management strategy utilizing peak power shaving strategy is implemented. The goal is to decrease power load on batteries and operate fuel cell stack in it’s most efficient region. Complete model to simulate the physical behavior of UC-Integrated FCHEV (UC-FCHEV) is developed using Matlab/SIMULINK. The fuel cell polarization curve is utilized to devise operating points of the fuel cell to maintain its operation at most efficient region. Results show reduction of hydrogen consumption in aggressive US06 drive cycle from 0.29 kg per drive cycle to 0.12 kg. The maximum charge/discharge battery current was reduced from 286 amperes to 110 amperes in US06 drive cycle. Results for the FUDS drive cycle show a reduction in fuel consumption from 0.18 kg to 0.05 kg in one drive cycle. This reduction in current increases the life of the battery since its protected from overcurrent. The SOC profile of the battery also shows that the battery is not discharged to its minimum threshold which increasing the health of the battery based on number of charge/discharge cycles.
ContributorsJethani, Puneet V. (Author) / Mayyas, Abdel (Thesis advisor) / Berman, Spring (Committee member) / Ren, Yi (Committee member) / Arizona State University (Publisher)
Created2017
Description
The interaction between humans and robots has become an important area of research as the diversity of robotic applications has grown. The cooperation of a human and robot to achieve a goal is an important area within the physical human-robot interaction (pHRI) field. The expansion of this field is toward moving robotics into applications in unstructured environments. When humans cooperate with each other, often there are leader and follower roles. These roles may change during the task. This creates a need for the robotic system to be able to exchange roles with the human during a cooperative task. The unstructured nature of the new applications in the field creates a need for robotic systems to be able to interact in six degrees of freedom (DOF). Moreover, in these unstructured environments, the robotic system will have incomplete information. This means that it will sometimes perform an incorrect action and control methods need to be able to correct for this. However, the most compelling applications for robotics are where they have capabilities that the human does not, which also creates the need for robotic systems to be able to correct human action when it detects an error. Activity in the brain precedes human action. Utilizing this activity in the brain can classify the type of interaction desired by the human. For this dissertation, the cooperation between humans and robots is improved in two main areas. First, the ability for electroencephalogram (EEG) to determine the desired cooperation role with a human is demonstrated with a correct classification rate of 65%. Second, a robotic controller is developed to allow the human and robot to cooperate in six DOF with asymmetric role exchange. This system allowed human-robot cooperation to perform a cooperative task at 100% correct rate. High, medium, and low levels of robotic automation are shown to affect performance, with the human making the greatest numbers of errors when the robotic system has a medium level of automation.
ContributorsWhitsell, Bryan Douglas (Author) / Artemiadis, Panagiotis (Thesis advisor) / Santello, Marco (Committee member) / Berman, Spring (Committee member) / Lee, Hyunglae (Committee member) / Polygerinos, Panagiotis (Committee member) / Arizona State University (Publisher)
Created2017
Description
Presented in this thesis are two projects that fall under the umbrella of magnetically actuated electronics and robotics for medical applications. First, magnetically actuated tunable soft electronics are discussed in Chapter 2. Wearable and implantable soft electronics are clinically available and commonplace. However, these devices can be taken a step further to improve the lives of their users by adding remote tunability. The four electric units tested were planar inductors, axial inductors, capacitors and resistors. The devices were made of polydimethylsiloxane (PDMS) for flexibility with copper components for conductivity. The units were tuned using magnets and mobile components comprised of iron filings and ferrofluid. The characteristic properties examined for each unit are as follows: inductance and quality factor (Q-factor) for inductors, capacitance and Q-factor for capacitors, and impedance for resistors. There were two groups of tuning tests: quantity effect and position effect of the mobile component. The position of the mobile component had a larger effect on each unit, with 20-23% change in inductance for inductors (from 3.31 µH for planar and 0.44 µH for axial), 12.7% from 2.854 pF for capacitors and 185.3% from 0.353 kΩ for resistors.
Chapter 3 discusses a magnetic needle tracking device with operative assistance from a six degree-of-freedom robotic arm. Traditional needle steering faces many obstacles such as torsional effects, buckling, and small radii of curvature. To improve upon the concept, this project uses permanent magnets in parallel with a tracking system to steer and determine the position and orientation of the needle in real time. The magnet configuration is located at the end effector of the robotic arm. The trajectory of the end effector depends on the needle’s path, and vice versa. The distance the needle travels inside the workspace is tracked by a direct current (DC) motor, to which the needle is tethered. Combining this length with the pose of the end effector, the position and orientation of the needle can be calculated. Simulation of this tracking device has shown the functionality of the system. Testing has been done to confirm that a single magnet pulls the needle through the phantom tissue.
Chapter 3 discusses a magnetic needle tracking device with operative assistance from a six degree-of-freedom robotic arm. Traditional needle steering faces many obstacles such as torsional effects, buckling, and small radii of curvature. To improve upon the concept, this project uses permanent magnets in parallel with a tracking system to steer and determine the position and orientation of the needle in real time. The magnet configuration is located at the end effector of the robotic arm. The trajectory of the end effector depends on the needle’s path, and vice versa. The distance the needle travels inside the workspace is tracked by a direct current (DC) motor, to which the needle is tethered. Combining this length with the pose of the end effector, the position and orientation of the needle can be calculated. Simulation of this tracking device has shown the functionality of the system. Testing has been done to confirm that a single magnet pulls the needle through the phantom tissue.
ContributorsEdwards, Dakota (Author) / Marvi, Hamidreza (Thesis advisor) / Lee, Hyunglae (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2020