Browsing by Subject "Iterative methods (Mathematics)"

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Open Access
Development of a modular control algorithm for high precision positioning systems
(2012) Ulu, Nurcan Geçer
In the last decade, micro/nano-technology has been improved significantly. Micro/nano-technology related products started to be used in consumer market in addition to their applications in the science and technology world. These developments resulted in a growing interest for high precision positioning systems since precision positioning is crucial for micro/nano-technology related applications. With the rise of more complex and advanced applications requiring smaller parts and higher precision performance, demand for new control techniques that can meet these expectations is increased. The goal of this work is developing a new control technique that can meet increased expectations of precision positioning systems. For this purpose, control of a modular multi-axis positioning system is studied in this thesis. The multiaxis precision positioning system is constructed by assembling modular single-axis stages. Therefore, a single-axis stage can be used in several configurations. Model parameters of a single-axis stage change depending on which axis it is used for. For this purpose, an iterative learning controller is designed to improve tracking performance of a modular single-axis stage to help modular sliders adapting to repeated disturbances and nonlinearities of the axis they are used for. When modular single-axis stages are assembled to form multi-axis systems, the interaction between the axes should be considered to operate stages simultaneously. In order to compensate for these interactions, a multi input multi output (MIMO) controller can be used such as cross-coupled controller (CCC). Cross-coupled controller examines the effects between axes by controlling the contour error resulting in an improved contour tracking. In this thesis, a controller featuring cross-coupled control and iterative learning control schemes is presented to improve contour and tracking accuracy at the same time. Instead of using the standard contour estimation technique proposed with the variable gain cross-coupled control, presented control design incorporates a computationally efficient contour estimation technique. In addition to that, implemented contour estimation technique makes the presented control scheme more suitable for arbitrary nonlinear contours and multi-axis systems. Also, using the zero-phase filtering based iterative learning control results in a practical design and an increased applicability to modular systems. Stability and convergence of the proposed controller has been shown with the necessary theoretical analysis. Effectiveness of the control design is verified with simulations and experiments on two-axis and three-axis positioning systems. The resulting controller is shown to achieve nanometer level contouring and tracking performance.
Open Access
Minimizing communication through computational redundancy in parallel iterative solvers
(2011) Torun, Fahreddin Şükrü
Sparse matrix vector multiplication (SpMxV) of the form y = Ax is a kernel operation in iterative linear solvers used in scientific applications. In these solvers, the SpMxV operation is performed repeatedly with the same sparse matrix through iterations until convergence. Depending on the matrix and its decomposition, parallel SpMxV operation necessitates communication among processors in the parallel environment. The communication can be reduced by intelligent decomposition. However, we can further decrease the communication through data replication and redundant computation. The communication occurs due to the transfer of x-vector entries in row-parallel SpMxV computation. The input vector x of the next iteration is computed from the output vector of the current iteration through linear vector operations. Hence, a processor may compute a y-vector entry redundantly, which leads to a x-vector entry in the following iteration, instead of receiving that x-vector entry from another processor. Thus, redundant computation of that y-vector entry may lead to reduction in communication. In this thesis, we devise a directed-graph-based model that correctly captures the computation and communication pattern for above-mentioned iterative solvers. Moreover, we formulate the communication minimization by utilizing redundant computation of y-vector entries as a combinatorial problem on this directed graph model. We propose two heuristics to solve this combinatorial problem. Experimental results indicate that the communication reducing strategy by redundantly computing is promising.
Open Access
Utilizing query logs for data replication and placement in big data applications
(2012) Türk, Ata
The growth in the amount of data in todays computing problems and the level of parallelism dictated by the large-scale computing economics necessitates highlevel parallelism for many applications. This parallelism is generally achieved via data-parallel solutions that require effective data clustering (partitioning) or declustering schemes (depending on the application requirements). In addition to data partitioning/declustering, data replication, which is used for data availability and increased performance, has also become an inherent feature of many applications. The data partitioning/declustering and data replication problems are generally addressed separately. This thesis is centered around the idea of performing data replication and data partitioning/declustering simultenously to obtain replicated data distributions that yield better parallelism. To this end, we utilize query-logs to propose replicated data distribution solutions and extend the well known Fiduccia-Mattheyses (FM) iterative improvement algorithm so that it can be used to generate replicated partitioning/declustering of data. For the replicated declustering problem, we propose a novel replicated declustering scheme that utilizes query logs to improve the performance of a parallel database system. We also extend our replicated declustering scheme and propose a novel replicated re-declustering scheme such that in the face of drastic query pattern changes or server additions/removals from the parallel database system, new declustering solutions that require low migration overheads can be computed. For the replicated partitioning problem, we show how to utilize an effective single-phase replicated partitioning solution in two well-known applications (keyword-based search and Twitter). For these applications, we provide the algorithmic solutions we had to devise for solving the problems that replication brings, the engineering decisions we made so as to obtain the greatest benefits from the proposed data distribution, and the implementation details for realistic systems. Obtained results indicate that utilizing query-logs and performing replication and partitioning/declustering in a single phase improves parallel performance.