The Analogue Computer As a Scientific Instrument
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Control Theory
Control theory S. Simrock DESY, Hamburg, Germany Abstract In engineering and mathematics, control theory deals with the behaviour of dynamical systems. The desired output of a system is called the reference. When one or more output variables of a system need to follow a certain ref- erence over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system. Rapid advances in digital system technology have radically altered the control design options. It has become routinely practicable to design very complicated digital controllers and to carry out the extensive calculations required for their design. These advances in im- plementation and design capability can be obtained at low cost because of the widespread availability of inexpensive and powerful digital processing plat- forms and high-speed analog IO devices. 1 Introduction The emphasis of this tutorial on control theory is on the design of digital controls to achieve good dy- namic response and small errors while using signals that are sampled in time and quantized in amplitude. Both transform (classical control) and state-space (modern control) methods are described and applied to illustrative examples. The transform methods emphasized are the root-locus method of Evans and fre- quency response. The state-space methods developed are the technique of pole assignment augmented by an estimator (observer) and optimal quadratic-loss control. The optimal control problems use the steady-state constant gain solution. Other topics covered are system identification and non-linear control. System identification is a general term to describe mathematical tools and algorithms that build dynamical models from measured data. -
'A Superb Explanatory Device': the MONIAC, an Early Hydraulic Analog Computer
‘A superb explanatory device’ The MONIAC, an early hydraulic analog computer Anna Corkhill Since 1953, the University of when it was rediscovered, partially rubber tubing and powered by a Melbourne has owned a rare restored and given a position in a mechanical pump. (In the prototype, machine: a hydraulic analog simple display case on level 1 of the the pump’s motor was recycled from computer capable of explaining the Economics and Commerce Building. a World War II Lancaster bomber, economy and performing complex The machine has recently been but the university’s MONIAC economic calculations. It is generally moved to the entrance of the new was commercially made.) It is known as the MONIAC (which Giblin Eunson Business, Economics approximately two metres high and stands for ‘MOnetary National and Education Library in the ICT one metre wide, with a metal backing Income Analog Computer’), Building, 111 Barry Street. enclosing the machine’s pump and though it has also been called Though a reasonably accurate connecting tubing. The machine has the ‘Financephalograph’, the computational device, the MONIAC’s three main water tanks, representing ‘National Income Monetary Flow key aim was to demonstrate taxes and government spending, Demonstrator’ and simply the Keynesian economic models in a savings and investment, and import– ‘Phillips Machine’, after its inventor, clear, visual way. As a pedagogical aid, export. The ‘active balances’ tank at Bill Phillips. The machine, one of it used coloured water to represent the bottom represents the total stock approximately 12 ever created, was money flowing through the economy, of currency and bank credit in the purchased by the Department of and showed the relationships between economy at any given time. -
Analog Computer on a Chip – Compiling Solutions
Analog Computer on a Chip – Compiling Solutions John Milios Nicolas Clauvelin Sendyne Corp. Sendyne Corp. New York, NY, USA New York, NY, USA [email protected] [email protected] Abstract --- The original room-sized analog computers of the sometimes if, they converge to a solution. The Columbia 1950s were programmed using paper drawings and manual cable University team, lead by Professor Yannis Tsividis, revisited the connections. The Apollo IC is the first digitally programmed analog old idea of analog computing and re-invented it using today’s computer, implemented in a 4x4 mm2 CMOS IC and capable of CMOS analog technology. The result was what we now call the solving problems with high speed and extremely low power. The Apollo IC, the first integrated, digitally programmable general high level programming language of an analog computer consists purpose analog computer (GPAC) chip [2] and associated of the differential equations describing the system to be simulated. computer board. Sendyne, through an exclusive license from The solution to each programmed model is achieved by the proper Columbia University used this technology to build the SA100, interconnection and calibration of the analog computer elements a digitally controlled analog computer that can be programmed in such a way as to implement the aforementioned differential and exchange data with a digital computer through a USB port equations. Deducing from the equations the right interconnections [3]. and implementing these in the analog computer circuitry is the role of an analog computer compiler. Such a compiler has been During the same period researchers at MIT started developed for the first time by MIT researchers for the Apollo IC investigating suitability of analog computing elements in analog computer. -
Computing Science Technical Report No. 99 a History of Computing Research* at Bell Laboratories (1937-1975)
Computing Science Technical Report No. 99 A History of Computing Research* at Bell Laboratories (1937-1975) Bernard D. Holbrook W. Stanley Brown 1. INTRODUCTION Basically there are two varieties of modern electrical computers, analog and digital, corresponding respectively to the much older slide rule and abacus. Analog computers deal with continuous information, such as real numbers and waveforms, while digital computers handle discrete information, such as letters and digits. An analog computer is limited to the approximate solution of mathematical problems for which a physical analog can be found, while a digital computer can carry out any precisely specified logical proce- dure on any symbolic information, and can, in principle, obtain numerical results to any desired accuracy. For these reasons, digital computers have become the focal point of modern computer science, although analog computing facilities remain of great importance, particularly for specialized applications. It is no accident that Bell Labs was deeply involved with the origins of both analog and digital com- puters, since it was fundamentally concerned with the principles and processes of electrical communication. Electrical analog computation is based on the classic technology of telephone transmission, and digital computation on that of telephone switching. Moreover, Bell Labs found itself, by the early 1930s, with a rapidly growing load of design calculations. These calculations were performed in part with slide rules and, mainly, with desk calculators. The magnitude of this load of very tedious routine computation and the necessity of carefully checking it indicated a need for new methods. The result of this need was a request in 1928 from a design department, heavily burdened with calculations on complex numbers, to the Mathe- matical Research Department for suggestions as to possible improvements in computational methods. -
Analog Computation and Representation
Analog Computation and Representation Corey J. Maley forthcoming in The British Journal for the Philosophy of Science Abstract Relative to digital computation, analog computation has been neglected in the philosophical literature. To the extent that attention has been paid to analog computation, it has been misunderstood. The received view—that analog computation has to do essentially with continuity—is simply wrong, as shown by careful attention to historical examples of discontinuous, discrete analog computers. Instead of the received view, I develop an account of analog computation in terms of a particular type of analog representation that allows for discontinuity. This account thus characterizes all types of analog computation, whether continuous or discrete. Furthermore, the structure of this account can be generalized to other types of computation: analog computation essentially involves analog representation, whereas digital computation essentially involves digital representation. Besides being a necessary component of a complete philosophical understanding of computation in general, understanding analog computation is important for computational explanation in contemporary neuroscience and cognitive science. Those damn digital computers! Vannevar Bush, MIT 1 Introduction 2 Analog Computers 2.1 Mechanical analog computers 2.2 Electronic analog computers 2.3 Discontinuous analog elements 3 What makes analog computation ‘analog’ and ‘computational’ 3.1 Analog as continuity 3.2 Analog as covariation 3.3 What makes it ‘analog’ 3.4 What makes it ‘computation’ 4 Questions and Objections 4.1 Aren’t these just hybrid computers? 4.2 Is this really even computation? 4.3 The Lewis-Maley account is problematic 5 Concluding thoughts 1 Introduction Like clocks and audio recordings, computation comes in both digital and analog varieties. -
Downloaded from Brill.Com10/04/2021 12:45:25PM Via Free Access 242 Revue De Synthèse : TOME 139 7E SÉRIE N° 3-4 (2018) Années 1920-1950
REVUE DE SYNTHÈSE : TOME 139 7e SÉRIE N° 3-4 (2018) 241-266 brill.com/rds ARTICLES Programming Men and Machines. Changing Organisation in the Artillery Computations at Aberdeen Proving Ground (1916-1946) Maarten Bullynck* Abstract: After the First World War mathematics and the organisation of bal- listic computations at Aberdeen Proving Ground changed considerably. This was the basis for the development of a number of computing aids that were constructed and used during the years 1920 to 1950. This article looks how the computational organisa- tion forms and changes the instruments of calculation. After the differential analyzer relay-based machines were built by Bell Labs and, finally, the ENIAC, one of the first electronic computers, was built, to satisfy the need for computational power in bal- listics during the second World War. Keywords: Computing machines – Second World War – Ballistics – Programming – Mathematics Programmer hommes et machines. Changer l’organisation des calculs d’artillerie à Aberdeen Proving ground (1916-1946) Résumé : Après la Première Guerre mondiale les mathématiques et l’organisation des calculs balistiques à Aberdeen Proving Ground changent profondément. C’est le fond du développement de plusieurs machines à calculer qui sont construites et utilisées dans les * Maarten Bullynck, né en 1977, studied mathematics, German languages and media studies in Gent and Berlin. He defended his PhD Vom Zeitalter der formalen Wissenschaften. Parallele Anleitung zur Verarbeitung von Erkenntnissen anno 1800 in 2006. From 2007 to 2008 he was a fellow of the Alexander-von-Humboldt-Stiftung with a project on J. H. Lambert, including the development of a website featuring Lambert’s collected works. -
Computer History a Look Back Contents
Computer History A look back Contents 1 Computer 1 1.1 Etymology ................................................. 1 1.2 History ................................................... 1 1.2.1 Pre-twentieth century ....................................... 1 1.2.2 First general-purpose computing device ............................. 3 1.2.3 Later analog computers ...................................... 3 1.2.4 Digital computer development .................................. 4 1.2.5 Mobile computers become dominant ............................... 7 1.3 Programs ................................................. 7 1.3.1 Stored program architecture ................................... 8 1.3.2 Machine code ........................................... 8 1.3.3 Programming language ...................................... 9 1.3.4 Fourth Generation Languages ................................... 9 1.3.5 Program design .......................................... 9 1.3.6 Bugs ................................................ 9 1.4 Components ................................................ 10 1.4.1 Control unit ............................................ 10 1.4.2 Central processing unit (CPU) .................................. 11 1.4.3 Arithmetic logic unit (ALU) ................................... 11 1.4.4 Memory .............................................. 11 1.4.5 Input/output (I/O) ......................................... 12 1.4.6 Multitasking ............................................ 12 1.4.7 Multiprocessing ......................................... -
1. Types of Computers Contents
1. Types of Computers Contents 1 Classes of computers 1 1.1 Classes by size ............................................. 1 1.1.1 Microcomputers (personal computers) ............................ 1 1.1.2 Minicomputers (midrange computers) ............................ 1 1.1.3 Mainframe computers ..................................... 1 1.1.4 Supercomputers ........................................ 1 1.2 Classes by function .......................................... 2 1.2.1 Servers ............................................ 2 1.2.2 Workstations ......................................... 2 1.2.3 Information appliances .................................... 2 1.2.4 Embedded computers ..................................... 2 1.3 See also ................................................ 2 1.4 References .............................................. 2 1.5 External links ............................................. 2 2 List of computer size categories 3 2.1 Supercomputers ............................................ 3 2.2 Mainframe computers ........................................ 3 2.3 Minicomputers ............................................ 3 2.4 Microcomputers ........................................... 3 2.5 Mobile computers ........................................... 3 2.6 Others ................................................. 4 2.7 Distinctive marks ........................................... 4 2.8 Categories ............................................... 4 2.9 See also ................................................ 4 2.10 References -
Differential Analyzer Method of Computation Introduction.—Two Fundamentally Different Approaches Have Been Developed in Using Machines As Aids to Calculating
automatic computing machinery 41 142[L].—K. Higa, Table of I u~l exp { - (\u + u~2)}du. One page type- written manuscript. Deposited in the UMT File. The table is for X = .01,.012(.004).2(.1)1(.5)10. The values are given to 3S. L. A. Aroian Hughes Aircraft Co. Culver City, California 143p/].—Y. L. Luke. Tables of an Incomplete Bessel Function. 13 pages photostat of manuscript tables. Deposited in the UMT File. The tables refer to the function jn(p,0) = exp [incos<j>\ cos n<pdt¡>. Values are given to 9D for « = 0, 1, 2 cos 0 = - .2(.1).9 = 49co/51,w = 0(.04).52. There are also auxiliary tables. The tables are intended to be applied to aerodynamic flutter calculations with Mach number .7. Y. L. Luke Midwest Research Institute Kansas City, Missouri AUTOMATIC COMPUTING MACHINERY Edited by the Staff of the Machine Development Laboratory of the National Bureau of Standards. Correspondence regarding the Section should be directed to Dr. E. W. Cannon, 415 South Building, National Bureau of Standards, Washington 25, D. C. Technical Developments Fundamental Concepts of the Digital Differential Analyzer Method of Computation Introduction.—Two fundamentally different approaches have been developed in using machines as aids to calculating. These have come to be known as analog and digital approaches. There have been many definitions given for the two systems but the most common ones differentiate between the use of physical quantities and numbers to perform the required automatic calculations. In solving problems where addition, subtraction, division and multipli- cation are clearly indicated by the numerical nature of the problem and the data, a digital machine for computation is appropriate. -
Computers and Hydraulics
I ? ::) t!E PAP 2C·6 HYDRAULICS BRANCH OFFICIAL FILE COPY tltEN BORROWli"_,D RETURN PROMPTiY COMPUTERS AND HYDRAULICS by Phillip "F." Enger Paper to be presented at ASCE Environmental Engineering Conference, Kansas City, Mo., October 18-22, 1965 ABSTRACT Experiences of a hydraulic laboratory in using computers for simple and complex hydraulic problems showed that direct application of computers to everyday problems in a small engineering office is practical and easily es tablished with reasonable effort. After about 30 hrs tTaining in a mathe matically oriented programing language, most engineers were able to program their own work for electronic digital computers, making programs for small routine problems practical. Most programs were small, but compared to manual methods, time was saved with each, adding up to a significant saving in man-days. This freed engineers for professional tasks, and more work was undertaken than would have been otherwise. Suggestions for computer applicat~on in small offices include: /(1) Use formal teaching methods to instruct engineers in a mathematically oriented programing language; (2) encourage engineers to write in a simple manner their own programs for small problems; (3) obtain the services of professional programers where large generalized problems are involved; (4) make the computer readily available to the staff; (5) obtain the cooperation of a large part of the staff./ Engineers trained in programing will attack complex problems pre viously impractical because of excessive arithmetical operations. -
A Brief History of IT
IT Computer Technical Support Newsletter A Brief History of IT May 23, 2016 Vol.2, No.29 TABLE OF CONTENTS Introduction........................1 Pre-mechanical..................2 Mechanical.........................3 Electro-mechanical............4 Electronic...........................5 Age of Information.............6 Since the dawn of modern computers, the rapid digitization and growth in the amount of data created, shared, and consumed has transformed society greatly. In a world that is interconnected, change happens at a startling pace. Have you ever wondered how this connected world of ours got connected in the first place? The IT Computer Technical Support 1 Newsletter is complements of Pejman Kamkarian nformation technology has been around for a long, long time. Basically as Ilong as people have been around! Humans have always been quick to adapt technologies for better and faster communication. There are 4 main ages that divide up the history of information technology but only the latest age (electronic) and some of the electromechanical age really affects us today. 1. Pre-Mechanical The earliest age of technology. It can be defined as the time between 3000 B.C. and 1450 A.D. When humans first started communicating, they would try to use language to make simple pictures – petroglyphs to tell a story, map their terrain, or keep accounts such as how many animals one owned, etc. Petroglyph in Utah This trend continued with the advent of formal language and better media such as rags, papyrus, and eventually paper. The first ever calculator – the abacus was invented in this period after the development of numbering systems. 2 | IT Computer Technical Support Newsletter 2. -
Some Mathematical Limitations of the General-Purpose Analog Computer LEE A
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector ADVANCES IN APPLIED MATHEhfA’ITCS 9,22-34 (1988) Some Mathematical Limitations of the General-Purpose Analog Computer LEE A. RUBEL Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801 DEDICATED TO THE MEMORY OF MARK KAc We prove that the Dirichlet problem on the disc cannot be solved by the general-purpose analog computer, by constructing, on the boundary, a function u,, that does satisfy an algebraic differential equation, but whose Poisson integral u satisfies no algebraic differential equation on some line segment inside the disc. 0 1988 Academic Press, Inc. INTRODUCTION The general-purpose analog computer (GPAC) is the mathematical ab- straction of several actual computing machines, of which the Bush differen- tial analyzer (see [KAK]) may be taken as the prototype. Although the differential analyzer and its successors were excellent machines for solving ordinary differential equations (ODES), they were not good at solving partial differential equations (PDEs). They attempted to do it by solving a large number of ODES one after the other, like scanning a square by a large number of horizontal lines, but this did not yield good results, either in the time taken or in the accuracy of the results. We discuss in this paper some of the theoretical limitations of the abstract GPAC as opposed to the practical limitations of actual machines. Our chief example will be the Dirichlet problem for the disc. We explicitly produce a function U&e”) that can be generated by a GPAC, such that if u(z)( = u(x, y) = u(re”)) is the solution of Laplace’s equation i3 2u/Jx2 + 6’ 2u/ay2 = 0 for ]z ] < 1 with boundary values U(Z) = u,,(ele) for (z] = 1, z = el’, then there does not exist any GPAC that produces u on a certain line segment inside the disc.