Matching Items (8)
Description
The problem of systematically designing a control system continues to remain a subject of intense research. In this thesis, a very powerful control system design environment for Linear Time-Invariant (LTI) Multiple-Input Multiple-Output (MIMO) plants is presented. The environment has been designed to address a broad set of closed loop metrics and constraints; e.g. weighted H-infinity closed loop performance subject to closed loop frequency and/or time domain constraints (e.g. peak frequency response, peak overshoot, peak controls, etc.). The general problem considered - a generalized weighted mixed-sensitivity problem subject to constraints - permits designers to directly address and tradeoff multivariable properties at distinct loop breaking points; e.g. at plant outputs and at plant inputs. As such, the environment is particularly powerful for (poorly conditioned) multivariable plants. The Youla parameterization is used to parameterize the set of all stabilizing LTI proper controllers. This is used to convexify the general problem being addressed. Several bases are used to turn the resulting infinite-dimensional problem into a finite-dimensional problem for which there exist many efficient convex optimization algorithms. A simple cutting plane algorithm is used within the environment. Academic and physical examples are presented to illustrate the utility of the environment.
ContributorsPuttannaiah, Karan (Author) / Rodriguez, Armando A (Thesis advisor) / Tsakalis, Konstantinos S (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2013
Description
Nowadays, the widespread introduction of distributed generators (DGs) brings great challenges to the design, planning, and reliable operation of the power system. Therefore, assessing the capability of a distribution network to accommodate renewable power generations is urgent and necessary. In this respect, the concept of hosting capacity (HC) is generally accepted by engineers to evaluate the reliability and sustainability of the system with high penetration of DGs. For HC calculation, existing research provides simulation-based methods which are not able to find global optimal. Others use OPF (optimal power flow) based methods where
too many constraints prevent them from obtaining the solution exactly. They also can not get global optimal solution. Due to this situation, I proposed a new methodology to overcome the shortcomings. First, I start with an optimization problem formulation and provide a flexible objective function to satisfy different requirements. Power flow equations are the basic rule and I transfer them from the commonly used polar coordinate to the rectangular coordinate. Due to the operation criteria, several constraints are
incrementally added. I aim to preserve convexity as much as possible so that I can obtain optimal solution. Second, I provide the geometric view of the convex problem model. The process to find global optimal can be visualized clearly. Then, I implement segmental optimization tool to speed up the computation. A large network is able to be divided into segments and calculated in parallel computing where the results stay the same. Finally, the robustness of my methodology is demonstrated by doing extensive simulations regarding IEEE distribution networks (e.g. 8-bus, 16-bus, 32-bus, 64-bus, 128-bus). Thus, it shows that the proposed method is verified to calculate accurate hosting capacity and ensure to get global optimal solution.
too many constraints prevent them from obtaining the solution exactly. They also can not get global optimal solution. Due to this situation, I proposed a new methodology to overcome the shortcomings. First, I start with an optimization problem formulation and provide a flexible objective function to satisfy different requirements. Power flow equations are the basic rule and I transfer them from the commonly used polar coordinate to the rectangular coordinate. Due to the operation criteria, several constraints are
incrementally added. I aim to preserve convexity as much as possible so that I can obtain optimal solution. Second, I provide the geometric view of the convex problem model. The process to find global optimal can be visualized clearly. Then, I implement segmental optimization tool to speed up the computation. A large network is able to be divided into segments and calculated in parallel computing where the results stay the same. Finally, the robustness of my methodology is demonstrated by doing extensive simulations regarding IEEE distribution networks (e.g. 8-bus, 16-bus, 32-bus, 64-bus, 128-bus). Thus, it shows that the proposed method is verified to calculate accurate hosting capacity and ensure to get global optimal solution.
ContributorsYuan, Jingyi (Author) / Weng, Yang (Thesis advisor) / Lei, Qin (Committee member) / Khorsand, Mojdeh (Committee member) / Arizona State University (Publisher)
Created2018
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
This research mainly focuses on improving the utilization of photovoltaic (PV) re-sources in distribution systems by reducing their variability and uncertainty through the integration of distributed energy storage (DES) devices, like batteries, and smart PV in-verters. The adopted theoretical tools include statistical analysis and convex optimization. Operational issues have been widely reported in distribution systems as the penetration of PV resources has increased. Decision-making processes for determining the optimal allo-cation and scheduling of DES, and the optimal placement of smart PV inverters are con-sidered. The alternating current (AC) power flow constraints are used in these optimiza-tion models. The first two optimization problems are formulated as quadratically-constrained quadratic programming (QCQP) problems while the third problem is formu-lated as a mixed-integer QCQP (MIQCQP) problem. In order to obtain a globally opti-mum solution to these non-convex optimization problems, convex relaxation techniques are introduced. Considering that the costs of the DES are still very high, a procedure for DES sizing based on OpenDSS is proposed in this research to avoid over-sizing.
Some existing convex relaxations, e.g. the second order cone programming (SOCP) relaxation and semidefinite programming (SDP) relaxation, which have been well studied for the optimal power flow (OPF) problem work unsatisfactorily for the DES and smart inverter optimization problems. Several convex constraints that can approximate the rank-1 constraint X = xxT are introduced to construct a tighter SDP relaxation which is referred to as the enhanced SDP (ESDP) relaxation using a non-iterative computing framework. Obtaining the convex hull of the AC power flow equations is beneficial for mitigating the non-convexity of the decision-making processes in power systems, since the AC power flow constraints exist in many of these problems. The quasi-convex hull of the quadratic equalities in the AC power bus injection model (BIM) and the exact convex hull of the quadratic equality in the AC power branch flow model (BFM) are proposed respectively in this thesis. Based on the convex hull of BFM, a novel convex relaxation of the DES optimizations is proposed. The proposed approaches are tested on a real world feeder in Arizona and several benchmark IEEE radial feeders.
Some existing convex relaxations, e.g. the second order cone programming (SOCP) relaxation and semidefinite programming (SDP) relaxation, which have been well studied for the optimal power flow (OPF) problem work unsatisfactorily for the DES and smart inverter optimization problems. Several convex constraints that can approximate the rank-1 constraint X = xxT are introduced to construct a tighter SDP relaxation which is referred to as the enhanced SDP (ESDP) relaxation using a non-iterative computing framework. Obtaining the convex hull of the AC power flow equations is beneficial for mitigating the non-convexity of the decision-making processes in power systems, since the AC power flow constraints exist in many of these problems. The quasi-convex hull of the quadratic equalities in the AC power bus injection model (BIM) and the exact convex hull of the quadratic equality in the AC power branch flow model (BFM) are proposed respectively in this thesis. Based on the convex hull of BFM, a novel convex relaxation of the DES optimizations is proposed. The proposed approaches are tested on a real world feeder in Arizona and several benchmark IEEE radial feeders.
ContributorsLi, Qifeng (Author) / Vittal, Vijay (Thesis advisor) / Heydt, Gerald T (Committee member) / Mittelmann, Hans D (Committee member) / Ayyanar, Raja (Committee member) / Arizona State University (Publisher)
Created2016
Description
This dissertation examines modeling, design and control challenges associatedwith two classes of power converters: a direct current-direct current (DC-DC) step-down (buck)
regulator and a 3-phase (3-ϕ) 4-wire direct current-alternating current
(DC-AC) inverter. These are widely used for power transfer in a variety of industrial
and personal applications. This motivates the precise quantification of conditions
under which existing modeling and design methods yield satisfactory designs, and
the study of alternatives when they don’t. This dissertation describes a method
utilizing Fourier components of the input square wave and the inductor-capacitor (LC)
filter transfer function, which doesn’t require the small ripple approximation. Then,
trade-offs associated with the choice of the filter order are analyzed for integrated buck
converters with a constraint on their chip area. Design specifications which would
justify using a fourth or sixth order filter instead of the widely used second order
one are examined. Next, sampled-data (SD) control of a buck converter is analyzed.
Three methods for the digital controller design are studied: analog design followed
by discretization, direct digital design of a discretized plant, and a “lifting” based
method wherein the sampling time is incorporated in the design process by lifting
the continuous-time design plant before doing the controller design. Specifically,
controller performance is quantified by studying the induced-L2 norm of the closed
loop system for a range of switching/sampling frequencies. In the final segment of
this dissertation, the inner-outer control loop, employed in inverters with an
inductor-capacitor-inductor (LCL) output filter, is studied. Closed loop sensitivities for the
loop broken at the error and the control are examined, demonstrating that traditional
methods only address these properties for one loop-breaking point. New controllers
are then provided for improving both sets of properties.
ContributorsSarkar, Aratrik (Author) / Rodriguez, Armando A (Thesis advisor) / Si, Jennie (Committee member) / Mittelmann, Hans D (Committee member) / Tsakalis, Konstantinos (Committee member) / Arizona State University (Publisher)
Created2021
Description
In this dissertation, we present a H-infinity based multivariable control design methodology that can be used to systematically address design specifications at distinct feedback loop-breaking points. It is well understood that for multivariable systems, obtaining good/acceptable closed loop properties at one loop-breaking point does not mean the same at another. This is especially true for multivariable systems that are ill-conditioned (having high condition number and/or relative gain array and/or scaled condition number). We analyze the tradeoffs involved in shaping closed loop properties at these distinct loop-breaking points and illustrate through examples the existence of pareto optimal points associated with them. Further, we study the limitations and tradeoffs associated with shaping the properties in the presence of right half plane poles/zeros, limited available bandwidth and peak time-domain constraints. To address the above tradeoffs, we present a methodology for designing multiobjective constrained H-infinity based controllers, called Generalized Mixed Sensitivity (GMS), to effectively and efficiently shape properties at distinct loop-breaking points. The methodology accommodates a broad class of convex frequency- and time-domain design specifications. This is accomplished by exploiting the Youla-Jabr-Bongiorno-Kucera parameterization that transforms the nonlinear problem in the controller to an affine one in the Youla et al. parameter. Basis parameters that result in efficient approximation (using lesser number of basis terms) of the infinite-dimensional parameter are studied. Three state-of-the-art subgradient-based non-differentiable constrained convex optimization solvers, namely Analytic Center Cutting Plane Method (ACCPM), Kelley's CPM and SolvOpt are implemented and compared.
The above approach is used to design controllers for and tradeoff between several control properties of longitudinal dynamics of 3-DOF Hypersonic vehicle model -– one that is unstable, non-minimum phase and possesses significant coupling between channels. A hierarchical inner-outer loop control architecture is used to exploit additional feedback information in order to significantly help in making reasonable tradeoffs between properties at distinct loop-breaking points. The methodology is shown to generate very good designs –- designs that would be difficult to obtain without our presented methodology. Critical control tradeoffs associated are studied and compared with other design methods (e.g., classically motivated, standard mixed sensitivity) to further illustrate its power and transparency.
The above approach is used to design controllers for and tradeoff between several control properties of longitudinal dynamics of 3-DOF Hypersonic vehicle model -– one that is unstable, non-minimum phase and possesses significant coupling between channels. A hierarchical inner-outer loop control architecture is used to exploit additional feedback information in order to significantly help in making reasonable tradeoffs between properties at distinct loop-breaking points. The methodology is shown to generate very good designs –- designs that would be difficult to obtain without our presented methodology. Critical control tradeoffs associated are studied and compared with other design methods (e.g., classically motivated, standard mixed sensitivity) to further illustrate its power and transparency.
ContributorsPuttannaiah, Karan (Author) / Rodriguez, Armando A. (Thesis advisor) / Berman, Spring M. (Committee member) / Mittelmann, Hans D. (Committee member) / Tsakalis, Konstantinos (Committee member) / Arizona State University (Publisher)
Created2018
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
Over the past few decades, there is an increase in demand for various ground robot applications such as warehouse management, surveillance, mapping, infrastructure inspection, etc. This steady increase in demand has led to a significant rise in the nonholonomic differential drive vehicles (DDV) research. Albeit extensive work has been done in developing various control laws for trajectory tracking, point stabilization, formation control, etc., there are still problems and critical questions in regards to design, modeling, and control of DDV’s - that need to be adequately addressed. In this thesis, three different dynamical models are considered that are formed by varying the input/output parameters of the DDV model. These models are analyzed to understand their stability, bandwidth, input-output coupling, and control design properties. Furthermore, a systematic approach has been presented to show the impact of design parameters such as mass, inertia, radius of the wheels, and center of gravity location on the dynamic and inner-loop (speed) control design properties. Subsequently, extensive simulation and hardware trade studies have been conductedto quantify the impact of design parameters and modeling variations on the performance of outer-loop cruise and position control (along a curve). In addition to this, detailed guidelines are provided for when a multi-input multi-output (MIMO) control strategy is advisable over a single-input single-output (SISO) control strategy; when a less stable plant is preferable over a more stable one in order to accommodate performance specifications. Additionally, a multi-robot trajectory tracking implementation based on receding horizon optimization approach is also presented. In most of the optimization-based trajectory tracking approaches found in the literature, only the constraints imposed by the kinematic model are incorporated into the problem. This thesis elaborates the fundamental problem associated with these methods and presents a systematic approach to understand and quantify when kinematic model based constraints are sufficient and when dynamic model-based constraints are necessary to obtain good tracking properties. Detailed instructions are given for designing and building the DDV based on performance specifications, and also, an open-source platform capable of handling high-speed multi-robot research is developed in C++.
ContributorsManne, Sai Sravan (Author) / Rodriguez, Armando A (Thesis advisor) / Si, Jennie (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2021