Komputer analog

Satu muka surat dari Bombardier's Information File (BIF) yang menjelaskan komponen dan kawalan Norden bombsight. Norden bombsight ialah sebuah komputer analog optik/mekanik digunakan oleh Tentera Udara Amerika Syarikat sewaktu Perang Dunia II, Perang Korea dan Perang Vietnam untuk membantu pengendali sebuah pesawat pengebom melepaskan bom dengan tepat.

Sebuah komputer analog adalah suatu bentuk komputer yang menggunakan aspek-aspek berterusan berubah fenomena fizikal seperti kuantiti elektrik, mekanik atau hidraulik bagi memodel masalah untuk diselesaikan. Ini berbeza dengan komputer digital, yang mewakili kuantiti berlainan secara bertambah, apabila nilai berangka mereka berubah.

Komputer analog mekanik adalah sangat penting dalam kawalan tembakan senapang pada Perang Dunia II dan Perang Korea; mereka dibina dalam bilangan yang banyak. Secara khususnya, pembangunan transistor membuat komputer analog elektronik praktikal, dan sebelum komputer digital dibangunkan secukupnya, mereka secara umum digunakan dalam sains dan industri.

Komputer analog dapat mempunyai tahap kekompleksan yang sangat luas lingkungannya. Mistar gelongsor dan nomograf adalah yang termudah, sementara komputer kawalan tembakan senjata dan komputer digital/analog kacukan besar adalah antara yang paling rumit. Komputer digital mempunyai sesetengah peringkat kekompleksan minimum (dan secara besar) yang adalah lebih besar daripada komputer analog yang lebih mudah. Kekompleksan ini diperlukan untuk melaksanakan program simpanan mereka, dan dalam banyak misal untuk mencipta hasil keluaran yang secara lanjut disesuaikan pada kegunaan manusia.

Menyediakan sebuah komputer analog memerlukan faktor skala dipilih, bersama dengan keadaan permulaan - iaitu, nilai bermula. Satu lagi keperluan ialah mencipta rangkaian saling sambung yang diperlukan di antara unsur komputer. Kadang-kadang struktur masalah perlu difikirkan semula supaya komputer akan berfungsi dengan elok. Tiada pembolehubah boleh dibenarkan melebihi batas komputer, dan pembezaan hendaklah dielak, selalunya dengan menyusun semula "rangkaian" saling sambung, menggunakan pengamir dalam erti berbeza.

Menjalankan sebuah komputer analog elektronik, dengan anggapan suatu penyediaan memuaskan, bermula dengan komputer memegang nilai pembolehubah pada nilai permulaan mereka. Menggerakkan suatu suis membebaskan pegangan dan membenarkan masalah untuk berjalan. Dalam sesetengah kes, komputer dapat, selepas suatu jarak waktu jalanan tertentu, kembali ke keadaan awal untuk set semula masalah, dan menjalankannya lagi.

Garis masa komputer analog

• Mekanisme Antikythera dipercayai komputer analog mekanik terkenal awal. Ia direkabentuk untuk mengira kedudukan astronomi. Ia ditemukan pada 1901 di Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to circa 100 BC. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later.

• The astrolabe was invented in the Hellenistic world in either the first or second centuries BC and is often attributed to Hipparchus. A combination of the planisphere and dioptra, the astrolabe was effectively an analog computer capable of working out several different kinds of problems in spherical astronomy. An astrolabe incorporating a mechanical calendar computer and gear-wheels was invented by Abi Bakr of Isfahan in 1235.

• Medieval Muslim astronomers produced many different types of astrolabes and used them for over a thousand different problems related to astronomy, astrology, horoscopes, navigation, surveying, timekeeping, Qibla (direction of Mecca), Salah (prayer), etc. In the 11th century, Abū Ishāq Ibrāhīm al-Zarqālī invented the universal latitude-independent astrolabe.

• Abu Raihan Al-Biruni reka cipta astrolab mekanikal invented the first mechanical geared lunisolar calendar astrolabe, an early fixed-wired knowledge processing machine with a gear train and gear-wheels, circa 1000 AD.

• The Planisphere was a star chart astrolabe also invented by Abu Rayhan al-Biruni in the early 11th century.

• The Equatorium was an astrometic calculating instrument invented by Abū Ishāq Ibrāhīm al-Zarqālī (Arzachel) in Islamic Spain circa 1015.

• The castle clock, an astronomical clock invented by Al-Jazari in 1206, is considered to be the first programmable analog computer. It displayed the zodiac, the solar and lunar orbits, a crescent moon-shaped pointer travelling across a gateway causing automatic doors to open every hour, and five robotic musicians who play music when struck by levers operated by a camshaft attached to a water wheel. The length of day and night could be re-programmed every day in order to account for the changing lengths of day and night throughout the year.

• Rare Asian mechanical clocks of past centuries had a steadily-descending hours pointer, and a set of scales that were periodically changed according to the length of daylight.^{[petikan diperlukan]}

A slide rule

• The slide rule is a hand-operated analog computer for doing (at least) multiplication and division, invented around 1620–1630, shortly after the publication of the concept of the logarithm. As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometric functions et cetera.

• The differential analyser, a mechanical analog computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. Invented in 1876 by James Thomson, they were first built in the 1920s and 1930s.^{[petikan diperlukan]} Extensions and enhancements were the basis of some parts of mechanical analog gun fire control computers.

• By 1912 Arthur Pollen had developed an electrically driven mechanical analog computer for fire-control systems, based on the differential analyser. It was used by the Imperial Russian Navy in World War I.^{[petikan diperlukan]}

• World War II era gun Directors, Gun Data Computers, and bomb sights used mechanical analog computers.^{[petikan diperlukan]}

• The FERMIAC was an analog computer invented by physicist Enrico Fermi in 1947 to aid in his studies of neutron transport.

• The MONIAC Computer was a hydraulic model of a national economy first unveiled in 1949.^{[petikan diperlukan]}

• Computer Engineering Associates was spun out of Caltech in 1950 to provide commercial services using the "Direct Analogy Electric Analog Computer" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems") developed there by Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi.

• Heathkit EC-1, an educational analog computer made by the Heath Company, USA c. 1960.^{[petikan diperlukan]}

• General Electric also marketed an "educational" analog computer kit of a simple design in the early 1960s consisting of a two transistor tone generator and three potentiometers wired such that the frequency of the oscillator was nulled when the potentiometer dials were positioned by hand to satisfy an equation. The relative resistance of the potentiometer was then equivalent to the formula of the equation being solved. Multiplication or division could be performed depending on which dials were considered inputs and which was the output. Accuracy and resolution was, of course, extremely limited and a simple slide rule was more accurate, however, the unit did demonstrate the basic principle.

Electronic analog computers

Polish analog computer AKAT-1.

The similarity between linear mechanical components, such as springs and dashpots (viscous-fluid dampers), and electrical components, such as capacitors, inductors, and resistors is striking in terms of mathematics. They can be modeled using equations that are of essentially the same form.

However, the difference between these systems is what makes analog computing useful. If one considers a simple mass-spring system, constructing the physical system would require making or modifying the springs and masses. This would be followed by attaching them to each other and an appropriate anchor, collecting test equipment with the appropriate input range, and finally, taking measurements. In more complicated cases, such as suspensions for racing cars, experimental construction, modification, and testing is not so simple nor inexpensive.

The electrical equivalent can be constructed with a few operational amplifiers (Op amps) and some passive linear components; all measurements can be taken directly with an oscilloscope. In the circuit, the (simulated) 'stiffness of the spring', for instance, can be changed by adjusting a potentiometer. The electrical system is an analogy to the physical system, hence the name, but it is less expensive to construct, generally safer, and typically much easier to modify.

As well, an electronic circuit can typically operate at higher frequencies than the system being simulated. This allows the simulation to run faster than real time (which could, in some instances, be hours, weeks, or longer). Experienced users of electronic analog computers said that they offered a comparatively intimate control and understanding of the problem, relative to digital simulations.

The drawback of the mechanical-electrical analogy is that electronics are limited by the range over which the variables may vary. This is called dynamic range. They are also limited by noise levels. Floating-point digital calculations have comparatively-huge dynamic range (Good modern handheld scientific/engineering calculators have exponents of 500.)

These electric circuits can also easily perform a wide variety of simulations. For example, voltage can simulate water pressure and electric current can simulate rate of flow in terms of cubic metres per second. (In fact, given the proper scale factors, all that is required would be a stable resistor, in that case.) Given flow rate and accumulated volume of liquid, a simple integrator provides the latter; both variables are voltages. In practice, current was rarely used in electronic analog computers, because voltage is much easier to work with.

Analog computers are especially well-suited to representing situations described by differential equations. Occasionally, they were used when a differential equation proved very difficult to solve by traditional means.

An electronic digital system uses two voltage levels to represent binary numbers. In many cases, the binary numbers are simply codes that correspond, for instance, to brightness of primary colors, or letters of the alphabet (or other symbols). The manipulation of these binary numbers is how digital computers work. The electronic analog computer, however, manipulates electrical voltages that are proportional to the magnitudes of quantities in the problem being solved.

Accuracy of an analog computer is limited by its computing elements as well as quality of the internal power and electrical interconnections. The precision of the analog computer readout was limited chiefly by the precision of the readout equipment used, generally three or four significant figures. Precision of a digital computer is limited by the word size; arbitrary-precision arithmetic, while relatively slow, provides any practical degree of precision that might be needed.

Analog-digital hybrid computers

There is an intermediate device, a 'hybrid' computer, in which an analog output is converted into digits. The information then can be sent into a standard digital computer for further computation. Because of their ease of use and because of technological breakthroughs in digital computers in the early 70s, the analog-digital hybrids were replacing the analog-only systems.

Hybrid computers are used to obtain a very accurate but not very mathematically precise 'seed' value, using an analog computer front-end, which value is then fed into a digital computer, using an iterative process to achieve the final desired degree of precision. With a three or four digit precision, highly-accurate numerical seed, the total computation time necessary to reach the desired precision is dramatically reduced, since many fewer digital iterations are required (and the analog computer reaches its result almost instantaneously). Or, for example, the analog computer might be used to solve a non-analytic differential equation problem for use at some stage of an overall computation (where precision is not very important). In any case, the hybrid computer is usually substantially faster than a digital computer, but can supply a far more precise computation than an analog computer. It is useful for real-time applications requiring such a combination (e.g., a high frequency phased-array radar or a weather system computation).

Polish Analog computer ELWAT.

Batasan

In general, analog computers are limited by non-ideal effects. An analog signal is composed of four basic components: DC and AC magnitudes, frequency, and phase. The real limits of range on these characteristics limit analog computers. Some of these limits include the operational amplifier offset, finite gain, and frequency response, noise floor, non-linearities, temperature coefficient, and parasitic effects within semiconductor devices. For commercially available electronic components, ranges of these aspects of input and output signals are always figures of merit.

Current research

Although digital computation is extremely popular, some research in analog computation is still being done. A few universities still use analog computers to teach control system theory. Comdyna manufactured small analog computers until roughly the end of the 20th century. At Indiana University Bloomington, Jonathan Mills has developed the Extended Analog Computer based on sampling voltages in a foam sheet. At the Harvard Robotics Laboratory, analog computation is a research topic.

Although digital computer simulation of electronic circuits is very successful and routinely used in design and development, there is one category of analog circuit that cannot be simulated digitally, and that is an (analog) circuit made to exhibit chaotic behavior. Because everything in the analog circuit is essentially simultaneous, but a digital simulation is sequential, simulation of a chaotic circuit fails.^{[petikan diperlukan]}.

Practical examples

These are examples of analog computers that have been constructed or practically used:

• Antikythera mechanism
• astrolabe
• differential analyzer
• Deltar
• Kerrison Predictor
• mechanical integrators, fo example, the planimeter
• MONIAC Computer (hydraulic model of UK economy)
• nomogram
• Norden bombsight
• planimeter
• Rangekeeper and related fire control computers
• slide rule
• tide-predicting machine
• Torpedo Data Computer
• Torquetum
• Water integrator
• Mechanical computer

Analog (music) synthesizers can also be viewed as a form of analog computer, and their technology was originally based in part on electronic analog computer technology. The ARP 2600's Ring Modulator was actually an moderate-accuracy analog multiplier.

Real computers

Computer theorists often refer to idealized analog computers as real computers (because they operate on the set of real numbers). Digital computers, by contrast, must first quantize the signal into a finite number of values, and so can only work with the rational number set (or, with an approximation of irrational numbers).

These idealized analog computers may in theory solve problems that are intractable on digital computers; however as mentioned, in reality, analog computers are far from attaining this ideal, largely because of noise minimization problems. In theory, ambient noise is limited by quantum noise (caused by the quantum movements of ions). Ambient noise may be severely reduced— but never to zero— by using cryogenically cooled parametric amplifiers. Moreover, given unlimited time and memory, the (ideal) digital computer may also solve real number problems. ^{[petikan diperlukan]}

Lihat juga

• Signal (electrical engineering)
• Signal (computing)
• Differential equation
• Dynamical system
• Chaos theory
• Slide rule
• Analogical models
• Antikythera mechanism

Other types of computers:

• DNA computer
• Molecular computer
• Quantum computer
• Wetware computer
• Digital computer

People associated with analog computer development:

• George A. Philbrick

Rujukan

• A.K. Dewdney. "On the Spaghetti Computer and Other Analog Gadgets for Problem Solving", Scientific American, 250(6):19-26, June 1984. Reprinted in The Armchair Universe, by A.K. Dewdney, published by W.H. Freeman & Company (1988), ISBN 0-7167-1939-8.

• Universiteit van Amsterdam Computer Museum. (2007). Analog Computers.

• Jackson, Albert S., "Analog Computation". London & New York: McGraw-Hill, 1960. OCLC 230146450

Pautan luar

• Large collection of electronic analog computers with lots of pictures and documentation
• Simulation of a car suspension system with an electronic analog computer
• Introduction to Analog-/Hybrid-Computing (pdf)
• Example programs for Analog Computers (pdf)
• Large collection of old analog and digital computers at Old Computer Museum
• A great disappearing act: the electronic analogue computer Chris Bissell, The Open University, Milton Keynes, UK Accessed February 2007
• German computer museum with still runnable analog computers
• Analog computer basics
• Lecture 20: Analog vs Digital (in a series of lectures on "History of computing and information technology")
• Analog computer trumps Turing model
• Jonathan W. Mills's Analog Notebook
• Indiana University Extended Analog Computer
• Harvard Robotics Laboratory Analog Computation
• Comdyna - a current manufacturer of analog computing hardware
• The Enns Power Network Computer - an analog computer for the analysis of electric power systems (advertisement from 1955)