On the Selection of the Type of Analog Multiplication-Division Device for Use in Chemical Production Control

B. P. Batyshev, V. M. Razin, I. G. Smyshlyaeva, N. V. Trikhanova

A characteristic feature of the development of the modern chemical industry is the widespread use of electronic computers for solving a variety of problems associated with the study and control of the technological production process.

At present, digital computers are the most common as control computers. This is explained by the fact that, in the mode of long-term continuous operation, digital computers considerably surpass analog computers in computational accuracy and in the ability to process a larger amount of information arriving from numerous sensors. However, analog computers have a number of advantages: high reliability of operation of the computing elements, simplicity of technical servicing and programming. Coupling analog computers with production processes is carried out without converting signals into the discrete form required when digital computers are used [1].

Comparing the capabilities of analog and digital computers used as control computers, one may conclude that digital computers are preferable for controlling large-scale production; control of individual production units can successfully be entrusted to analog computers.

In the near future, widespread introduction of analog computers is expected, which are 5–10 times cheaper than digital ones [2].

Requirements for Analog Computing Devices Used in Chemical Production Control Systems

Analog computing devices used in control systems must operate for a long time without adjustment, in direct connection with production facilities. Therefore the following requirements are imposed on them:

1. The gain in the direct channel may be equal to 1000, which is considerably less than the gain of an amplifier used in typical analog computers.

2. The output voltages of amplifiers, when performing control operations, must not exceed certain values; integrating amplifiers, whose output voltage may exceed—

…reach limiting values, must be protected by diode limiters.

1. Zero drift must be reduced to a minimum; for this purpose an MDU channel is usually used, which also eliminates the need for frequent adjustment of the output voltage.

2. Design and arrangement. Convenient placement of elements, good ventilation, and the introduction of semiconductor elements and integrated circuits increase operational reliability. The availability of replaceable units simplifies maintenance. Small general-purpose analog computers are often used as temporary units in control systems.

3. Stability of operation in the temperature range from 0–5 to 30–50°C.

4. High operating accuracy is often not necessary and on average amounts to 0.5% [3].

Classification of analog multiplier-divider devices

Analog MDUs are understood to mean devices that perform the mathematical operation of simultaneous multiplication and division of input continuous physical quantities, with multiplication being the principal operation. At present a large number of physical and mathematical principles for multiplying analog quantities are known [4]. In this connection, multiplying devices are divided into two classes: 1) direct-action MUs; 2) indirect-action MUs.

Indirect-action MUs are based on mathematical dependences of the form

\[ xy = \int x \cdot dy + \int y \cdot dx . \tag{1} \]

MUs implementing expression (1) are built on mathematical integrators (friction devices). The accuracy of such devices is determined by the accuracy with which the mechanical system is made and varies within the range \((0.2 \pm 0.1)\%\). Their use is limited by their bulkiness and low speed.

\[ xy = \frac{1}{2}[\cos(a+b)-\cos(a-b)], \tag{2} \]

where

\[ x=\sin a,\qquad y=\sin b . \]

To implement expression (2), a large number of blocks is required, four of which are nonlinear. Therefore the accuracy of this scheme is low and amounts to \((5–12)\%\).

\[ xy = a^{\log_a x + \log_a y}. \tag{3} \]

The disadvantages of such a scheme are its bulkiness and the presence of several nonlinearity blocks. Its advantage is that it is possible to obtain at once the product of three or more factors, as well as simultaneous extraction of the square root. The accuracy is 1–5%.

\[ xy = \frac{1}{4}\left[(x+y)^2-(x-y)^2\right]. \tag{4} \]

Circuits based on implementation of dependence (4) are currently widely used in general-purpose analog computers. They have relatively high accuracy, 0.5–1%, and a wide bandwidth of the operational amplifiers used in the circuit. However, all indirect-action MUs are bulky,

include functional converters that require constant adjustment during operation; therefore it is undesirable to use them in control systems [5, 6, 7].

The construction of direct-action multiplication devices is based on known physical laws. These are devices based on the use of the Hall effect [5, 8], and devices based on the use of various types of voltage modulation. Thus, to perform multiplication, double amplitude modulation, a combination of amplitude and phase modulation, amplitude and pulse modulation, etc., may be used [3, 9].

Direct-action MDs may be built according to closed-loop and open-loop schemes.

In designing open-loop schemes, strict requirements are imposed on the elements of the MD with respect to their linearity, the accuracy of the pulse shape, etc. All conditions must not only be fulfilled, but also maintained unchanged with great accuracy under different operating modes of the circuit.

Such requirements are not imposed if the same elements are used to construct an open-loop MD. Closed-loop MDs are more complex and bulky, but they have much higher accuracy and stability compared with open-loop MDs. In addition, closed-loop MDs usually also perform the division operation simultaneously; i.e., it becomes possible to obtain a multiplication–division circuit at once [10].

The most frequently used circuits are those employing pulse modulation, since the operation of these circuits depends less on the characteristics of the elements used in them. Among the latter, an important place is occupied by circuits in which amplitude and width modulation are combined. They have been named time-pulse division–multiplication circuits [10].

Time-pulse MDDs belong to electronic analog devices, since both electrical voltages and time intervals are, by their nature, continuous quantities. A time interval is easily converted into a digital quantity by counting the number of pulses of constant repetition frequency that fit into the converted time interval; therefore a transition to a digital form of representation of variables is possible, which makes the precise device digital-analog.

Another reason for the popularity of time-pulse MDDs is the relative simplicity of their construction in comparison with circuits using other types of modulation and other principles of construction.

Time-pulse MDDs have high accuracy in comparison with other types of MDDs—0.5–0.1%—owing to the accuracy with which width and pulse modulation can be carried out. They contain a small number of elements and have high reliability because of the wide use of switching modes of the elements.

Their principal shortcoming is the narrow frequency passband; therefore they should expediently be used in production-process control systems where high speed is not required.

An interesting feature of time-pulse-type circuits is the possibility of building adders and functional converters on them, thereby opening up the possibility of constructing specialized analog computing machines of the time-pulse type.

Time-pulse closed-loop MDU belong to the class of precise devices, whose reduced relative error amounts to from tenths to hundredths of a percent. Their accuracy is determined by the accuracy of operation of the elements and depends on the correctness and thoroughness of their design. Time-pulse MDU circuits are implemented with tubes and semiconductors. With the advent of integrated circuits, it is expedient, in particular in order to ensure accuracy over a temperature range, operating stability, etc., to develop time-pulse MDU on integrated circuits.

Conclusions

For the use of MDU in chemical production control systems, it is expedient to employ time-pulse closed-loop MDU circuits implemented on semiconductors or integrated circuits.

1. Time-pulse MDU circuits ensure an accuracy from tenths to hundredths of a percent.

2. They consist of simple units, in which the switching modes of semiconductors are used, and possess high stability.

3. They can operate satisfactorily in the range from \(0^\circ\) to \(60^\circ\mathrm{C}\), and when integrated circuits are used, from \(-60^\circ\) to \(+60^\circ\mathrm{C}\).

4. Time-pulse-type circuits can also be used for constructing adders, functional converters, and other units of analog computers.

LITERATURE

1. A. L. Leonov, F. Ya. Revzin. Automation of Chemical Processes and Ways of Its Development. Moscow, “Khimiya,” 1967.

2. V. A. Lutsenko, L. N. Finyakin. Analog Computers in Chemistry and Chemical Technology. Moscow, “Khimiya,” 1967.

3. Computer Engineering. Reference Book, vol. 1, Analog Computing Devices. Edited by G. D. Khaskin and G. A. Korn. Moscow, “Energiya,” 1964.

4. B. Ya. Kogan. Electronic Modeling Devices and Their Application for the Study of Automatic Control Systems. Moscow, Fizmatgiz, 1966.

5. V. B. Smolov, A. N. Lebedev et al. Continuous-Action Computing Machines. Moscow, “Vysshaya shkola,” 1964.

6. I. M. Vitenberg, V. D. Chalyi. Circuits for Multiplication and Division of Variables. Moscow, “Energiya,” 1964.

7. Encyclopedia of Modern Technology, Multiplying Devices, vol. 2. Moscow, “Energiya,” 1964.

8. B. A. Kazakov. Computing Devices of Continuous-Action Machines. Moscow, “Mashinostroenie,” 1965.

9. I. V. Latenko. Analog Multiplying Devices. GITL, Ukrainian SSR, Kiev, 1963.

10. V. B. Smolov, E. P. Ugryumov. Time-Pulse Computing Devices. Moscow, “Energiya,” 1968.