Hybrid computer

The emergence of hybrid computing systems was associated with the fact that for a number of problems arising in the technique of modeling complex systems, neither analog nor digital methods were enough.

These tasks were:

• Automatic control of fast moving objects;
• Optimization of control systems;
• Flight simulators, especially military equipment.

Digital cars of the era ^{[ when? ]} did not have sufficient speed for processing arising data arrays in real time, and analog machines did not allow to achieve the full possible variety of simulated situations.

Therefore, a solution was found to divide the computing process into several classes of operations, and then assign the most complex functional signal processing to the analog modules of the system, and decision-making algorithms, scenarios and setting the initial and final conditions to digital modules.

All this made it possible to reduce the computing power of the used digital computers and increase the speed of the resulting hybrid systems.

In a hybrid computing system, many of the drawbacks inherent in each type of computing machine are eliminated, and such advantages as ^{[1] [2]} are combined:

• high accuracy and speed;
• the variety of management and programming capabilities inherent in digital systems;
• direct interaction with controlled and controlled equipment inherent in analog systems.
• the absence in critical nodes of additional transformations of physical quantities and the resulting time delays and sampling errors.
• a relatively small number of simple elements that implement complex functional dependencies inherent in analog systems.

For the interaction of analog and digital computer components , special conversion devices are used, in particular, an analog-to-digital converter (ADC) and a digital-to-analog converter (DAC), controlled amplifiers, switches, etc. ^[2]

Hybrid computing systems are built from the following elements:

• AVM and digital computer blocks
• Converters of Representation of Values
• Intrasystem Communication Devices
• Periphery equipment

An effective hybrid complex can be created only as a result of a thorough study of the subject area, clarification of all the features of the application and a detailed analysis of typical tasks. Therefore, talking about some unified architecture of hybrid computing systems is fundamentally wrong.

Hybrid computers, like analog ones, can be divided into two main groups:

• Specialized - hybrid systems designed to solve only one class of problems, but allowing to do this with maximum efficiency.
• Universal - hybrid systems aimed at solving a wide class of problems. The construction of such systems means writing specialized programs for the appropriate equipment and special programs that service the communication of machines in a single complex, as well as automating the process of preparing and setting tasks in a single programming language of the complex.

Also distinguish analog-oriented, digital-oriented and balanced hybrid computing systems.

• In analog-oriented systems, the digital block (s) is used as an additional external device to the main AVM . Using a digital computer as a peripheral unit for preparing and converting data significantly increases the power and functionality of the analog part of the hybrid system.
• Digital-oriented systems are AVMs with digital control and logic, they are built on analog computing and discrete logical networks so that the analog network implements the conditions of the problem, and a discrete search for solutions. AVM models elements of real equipment (including those involving real parts of it), and also serves to repeatedly execute functionally complex subprograms and tasks (solving partial differential equations, inverting matrices, generating continuous functions), thereby significantly saving the computing power of digital module.
• Balanced systems are the most powerful. They typically consist of universal digital and universal analog computers. Moreover, each of the parts of the system can function autonomously.

Types

• Pulse Time Computer ^[3]
• Pulse frequency computer ^[4]

The following main groups of tasks are effectively solved by hybrid systems:

• Real-time simulation of automatic control systems containing both analog and digital devices;
• Real-time playback of processes containing high-frequency components and variables that vary in a wide amplitude and frequency range;
• Statistical modeling;
• Modeling of biological systems;
• Solving partial differential equations;
• Optimization of control systems.

Real-time Simulation

One of the typical tasks of the first group is the simulation of a rolling mill control system. In this case, the analog computer reproduces the dynamics of the processes in the camp itself, and the control machine is modeled by a general-purpose computer with a special program. The short duration of transients in the drives of the mills and the interconnection of a large number of quantities when trying to simulate them entirely on a digital computer in real time would require the use of ultra-fast digital computers, while the accuracy of modeling the most critical, fast processes would be determined primarily by sampling errors.

This class of tasks is typical for controlling military installations, for example, air defense systems or military formations.

Moving Object Management

The second group includes two subgroups of tasks:

Homing Tasks

They are characterized by the fact that the trajectory of movement is formed in the process of movement itself as a result of control and external influences. As the object approaches the target, the rate of change of some parameters becomes so great that the use of purely digital solutions requires ultra-high speed, and a purely analogue solution is not able to cover a large dynamic range of measured values ​​with acceptable accuracy. In addition, an analog machine can correctly handle not every “borderline” situation.

In this case, the hybrid system allows you to compensate for the shortcomings of both technologies and "get out" of abnormal conditions.

Integrated simulators

The construction of the computational part of complex simulators showed that the greatest modeling accuracy is achieved if the equations of motion around the center of gravity are assigned to the analog part, and the digital machine is engaged in the motion of the center of gravity in space and all kinematic relationships.

Stochastic Processes

This group usually includes tasks solved by processing the results of multiple implementation of a random process.

Examples:

• Monte Carlo solution of multidimensional partial differential equations
• Solving stochastic programming problems
• Finding singular points, extrema of functions of many variables.

The implementation of a random process by an analog machine, firstly, does not require a proportional increase in energy costs with increasing speed, and secondly, it allows (in contrast to digital algorithms ) to reduce the repeatability of the generated sequences, especially with a very long length.

In this case, a high-speed AVM operates in the mode of repeated repetition of a solution, and processing of the results obtained at its outputs, processing of boundary conditions , calculation of functionals is entrusted to a digital computer. In addition, it is the digital computer that sets the criteria and determines the end of the calculation.

Hybrid solutions can reduce the time it takes to solve problems of this type by several orders of magnitude compared to purely digital algorithms, and also, in some cases, without significant costs to increase the reliability of the results.

Biological systems

Close results are achieved when hybrid systems investigate the processes of excitation propagation in biological systems. The specificity of this type of problem, even in its simplest version, modeling of such a medium consists in constructing a complex nonlinear system of partial differential equations.

Management Optimization

The solution of optimal control problems when applied to objects above the third order encounters fundamental difficulties.

The complexity of modeling and obtaining solutions especially increases if optimal control is required to be sought on a working system.

It is hybrid computing systems that can eliminate or at least minimize these difficulties. For this, with the help of a computer, methods such as the Pontryagin maximum principle , which are extremely computationally complex, are implemented.

Private derivatives

GVMs are also effectively used in problems where the main thing is the construction and solution of nonlinear partial differential equations.

These can be both analysis tasks and optimization and identification tasks.

Examples of optimization tasks:

• Selection of a heat-conducting material for a given temperature distribution according to the nonlinearity of its characteristics;
• The choice of aircraft geometry to obtain the required aerodynamic characteristics;
• Calculation of the necessary distribution of the thickness of the evaporating layer, which protects the spacecraft from overheating when entering the dense layers of the atmosphere;
• Optimization of the aircraft’s heating system, which prevents icing with minimal heating costs;
• Calculation of the irrigation network and the establishment of optimal costs in the channels thereof.

When solving these problems, a digital computer is connected to a grid model that is repeatedly used in the solution process.

The increase in the computing power of microprocessors by several orders of magnitude, the miniaturization of digital equipment has reduced the need to build hybrid systems for most of the tasks described, and at present hybrid solutions can retain their application:

• in solving highly specialized scientific problems
• in control systems of miniature aircraft
• in communication systems for robots. ^[five]

Extrema is a family of desktop hybrid computing systems. In terms of speed and a set of conditions, machines of this family are close to analog computers . The latest models were built on the basis of an analog processor with additional systems for setting the initial values ​​of variables. To control the computational process, a visual display device and a device for measuring and monitoring the conditions of the problem, the formation of time and clock signals were used. Used to solve systems of nonlinear algebraic and transcendental equations, systems of finite inequalities, systems of ordinary and nonlinear differential equations with given initial conditions, finding the coordinates of the maximum and minimum functions of many variables with various constraints, nonlinear programming problems, etc. ^[1] Main characteristics of the latest models :

• number of functional converters - 128
• number of variables sought - 16
• the number of equations and inequalities considered is 20
• maximum order of systems of differential equations - 16

Besides the advantages of the “division of labor”, hybrid computing systems have their own design difficulties, which are absent in both digital and analog equipment.

The main problem is sampling errors:

• time delay of the analog-to-digital converter, digital computer and digital-to-analog converter;
• rounding error in analog-to-digital and digital-to-analog converters;
• error of simultaneous sampling of analog signals to an analog-to-digital converter
• error of the simultaneous issuance of digital signals to a digital-to-analog converter
• errors associated with the discrete nature of the output of the output from the computer.

Since in hybrid systems there is a multiple two-way data exchange between the analog and digital parts, a variable value of the time delay introduced by software processing can lead to non-linear feedback occurring by the model that is not intended. When working with digital computers with ADC and DAC converters, this does not cause such significant problems, and in a hybrid computing system this can lead to loss of stability and disrupt the performance of the entire system.

To evaluate the errors of a particular complex, an extremely complex analysis of the primary errors of the equipment and the secondary errors introduced by the transformations is required. Without this, the development of accurate computing systems is impossible.

Despite the fact that the primary errors of the AVM and the digital computer from which the hybrid systems are built are well understood, the problem of estimating the error in solving nonlinear problems using a hybrid complex has not yet been solved.

In the literature, there are cases of erroneous assignment to hybrid computing systems of analog computing machines having separate elements of discrete logic:

• Parallel logic AVM
• Digitally Controlled AVM
• AVM with reuse of critical elements, equipped with a storage device.

It should be noted that such computers retain the analog representation as the main one, and digital elements have exclusively auxiliary functions.

• Dictionary of Cybernetics / Edited by Academician V. S. Mikhalevich . - 2nd. - Kiev: The main edition of the Ukrainian Soviet Encyclopedia named after M.P. Bazhan, 1989. - 751 p. - (C48). - 50,000 copies. - ISBN 5-88500-008-5 .
• Hybrid Computing System - article from the Great Soviet Encyclopedia . B. Ya. Kogan.