Constraint satisfaction modules : a methodology for analog circuit design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 119-122).This dissertation describes a methodology for solving convex constraint problems using analog circuits. It demonstrates how this methodology can be used to design circuits that solve function-fitting problems through iterated gradient descent. In particular, it shows how to build a small circuit that can model a nonlinearity by observation, and predistort to compensate for this nonlinearity. The system fits into a broader effort to investigate non-traditional approaches to circuit design. First, it breaks the traditional input-output abstraction barrier; all ports are bidirectional. Second, it uses a different methodology for proving system stability with local rather than global properties. Such stability arguments can be scaled to much more complex systems than traditional stability criteria.by Piotr Mitros.Ph.D

A mixed-signal computer architecture and its application to power system problems

Radical changes are taking place in the landscape of modern power systems. This massive shift in the way the system is designed and operated has been termed the advent of the ``smart grid''. One of its implications is a strong market pull for faster power system analysis computing. This work is concerned in particular with transient simulation, which is one of the most demanding power system analyses. This refers to the imitation of the operation of the real-world system over time, for time scales that cover the majority of slow electromechanical transient phenomena. The general mathematical formulation of the simulation problem includes a set of non-linear differential algebraic equations (DAEs). In the algebraic part of this set, heavy linear algebra computations are included, which are related to the admittance matrix of the topology. These computations are a critical factor to the overall performance of a transient simulator. This work proposes the use of analog electronic computing as a means of exceeding the performance barriers of conventional digital computers for the linear algebra operations. Analog computing is integrated in the frame of a power system transient simulator yielding significant computational performance benefits to the latter. Two hybrid, analog and digital computers are presented. The first prototype has been implemented using reconfigurable hardware. In its core, analog computing is used for linear algebra operations, while pipelined digital resources on a field programmable gate array (FPGA) handle all remaining computations. The properties of the analog hardware are thoroughly examined, with special attention to accuracy and timing. The application of the platform to the transient analysis of power system dynamics showed a speedup of two orders of magnitude against conventional software solutions. The second prototype is proposed as a future conceptual architecture that would overcome the limitations of the already implemented hardware, while retaining its virtues. The design space of this future architecture has been thoroughly explored, with the help of a software emulator. For one possible suggested implementation, speedups of four orders of magnitude against software solvers have been observed for the linear algebra operations

FAST HYBRID SOLUTION OF ALGEBRAIC SYSTEMS

We propose and analyze the error and timing of solvers consisting of both analog and digital circuitry for sparse linear systems of equations. We obtain high speed, but low precision from the analog circuits. We combine this with low speed, but high precision from the digital circuits. The hybrid circuit should be faster than digital circuits alone. As a preconditioner to standard iterative solution methods, the hybrid circuit makes the cost of the preconditioning step negligible. We also apply the hybrid circuit to a standard multilevel algorithm