ANALOG COMPUTERS

Analog Computers and Digital computers are the two kinds of computers, the combination of which is responsible for the invention of the modern Hybrid computers. The analog systems carry out arithmetic and logical operations by manipulating and processing data which you input such as the weight, temperature, voltage, power density, etc. But unlike the digital computer that changes all inputs to binary digits of “1” and “0”, the analog computer does not change inputted data to any such sign language.

The analog computer has become obsolete type of computer these days. It is different from a digital computer as it can perform numerous mathematical operations simultaneously. The digital computers, however could not operate the more complex operations. The Analog System is also unique in terms of operation as it utilizes continuous variables for the purpose of mathematical computation. It utilizes mechanical, hydraulic, or electrical energy or operation.
Analog computers are based on principles completely different from digital computers. Problem variables are represented by electrical voltages which can vary continuously within a certain range, usually -10 to +10 volts for a transistor-based machine. Electronic circuit modules allow the variables to be added, integrated (with respect to time) and multiplied by a constant. This makes it is possible to solve a system of ordinary linear differential equations by properly combining a number of adders, integrators, amplifiers and potentiometers using flexible chords and a patch panel (see the examples).

Analog computer programming

The figure shows the set-up for the solution of a very simple second-order linear differential equation, representing the dynamics of a body moving (in one dimension) under the influence of gravity. Before the computation can be started, initial conditions (IC) must be specified. This is accomplished by charging the capacitors in both integrators to the voltages representing the zero-time velocity and position, respectively. On the patch panel a special IC input is provided for every integrator. By simply turning a console switch controlling the value of the integrating capacitors, the problem's time scale can be scaled up or down, making it suitable for plotting on a pen recorder, or for viewing on an oscilloscope. In the latter case the solution can be repeated quickly completely automatically.

The next, more complicated example is a program for solving a pair of coupled second-order linear differential equations. Finally I'll show an example of a sequential optimization program , running on a hybrid configuration (a combination of an analog and a digital computer). Note that the digital part is used only for storing intermediate results.

References

MacKay and Fisher: Analogue Computing at Ultra-high Speed. Chapman & Hall (London) 1962
Korn and Korn: Electronic Analog and Hybrid Computers. MacGraw-Hill (New-York) 1964
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Large machines like the EAI 680 also support non-linear operations: square-rooting, arbitrary (piecewise linear) function generation, multiplication of two variables, and comparing the values of two variables. The last mentioned operation results in a boolean quantity which, perhaps combined with other boolean results (using the machine's patchable logic circuitry) can be used to change the 'program' dynamically. For instance, the simulation of a bouncing ball requires the solution of one differential equation when the ball is in free fall, while another equation (describing the forces occurring during elastic deformation) is applicable when the ball is in ground contact. The results of the computation can be shown graphically graphically, in real time, on an oscilloscope or plotter, or be digitized for being stored or further processed by a digital computer in a hybrid system. Also the results can be used directly for the control of some physical process.
The analog computer which is a complex machine is an integration of various mechanical parts which has pipes, valves, levers, gears and several key parts which can be named as follows :-

• Fixed function generators
  







• Operational amplifiers
  







• Potentiometers
  







• Integrators
  







• Advantages and Disadvantages of Analog Computers
  

The advantage of an analog computer is that it can simultaneously find solutions to several mathematical problems and that too while being precise unlike the digital computer. But it is not free of drawbacks. Unlike the digital computer it lacks speed of calculation. There are other functional problems which mar the efficiency of analog systems. Of these, the problems of non-linearities, temperature co-efficient, parasitic effects and noise floor are the main problems so to say. The core mathematical operations used in an electric analog computer are :-

• Summation
  







• inversion
  







• exponentiation
  







• logarithm
  







• integration with respect to time
  







• differentiation with respect to time
  







• multiplication and division
  

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