Fuzzy system of automatic tuning of electromagnetic excitation system of vibration-frequency liquid density meter

A fuzzy system for setting the location of electromagnetic exciter of vibration-frequency density meter is presented, taking into account the possible nonlinearities of the object. This paper proposes a system and algorithm for tuning the location of electromagnetic exciter of vibration-frequency density meter using fuzzy set theory. The use of fuzzy control methods allowed us to obtain a system for tuning the location of the electromagnetic exciter of the vibration-frequency density meter without the use of cumbersome computational procedures characteristic of the classical control method.


Introduction
Nowadays, vibration-frequency liquid density meters are mainly used in accounting and calculation operations and monitoring of technological processes in various industries [1].The principle of operation of these devices is based on the dependence of the frequency of auto-oscillations of the tube rigidly fixed at the ends, through which the flow of the measured liquid is organized.The system of auto oscillations, as a rule, is created by electromagnetic receiver and exciter of oscillations, connected respectively to the input and output of the electronic amplifier.In the conditions of serial production there is a need to adjust the system of auto oscillations [2] , the essence of which is as follows.At the stationary position of the electromagnetic receiver of oscillations carry out the movement to the left or right of the electromagnetic exciter of oscillations until the output of the receiver of oscillations does not appear the maximum possible signal.In this case, the exciter is initially located in the place of the expected beam of the first harmonic of the tube oscillations.This operation is usually done manually, which is not acceptable for mass production.
Vibration-frequency liquid density meters are innovative instruments that play a crucial role in various industries, offering accurate and efficient measurement of liquid densities.This technology relies on the principle that the resonant frequency of a vibrating element is influenced by the density of the surrounding liquid.Here are some key aspects that make vibration-frequency liquid density meters noteworthy: • These density meters are renowned for their exceptional precision and accuracy in measuring liquid densities.The use of vibration frequencies allows for highly sensitive and reliable readings, making them suitable for applications where precise density measurements are critical.• Vibration-frequency density meters are versatile and can be employed across diverse industries, including but not limited to pharmaceuticals, petrochemicals, food and beverage, and research laboratories.Their adaptability makes them an ideal choice for various liquids with different properties.• The dynamic nature of vibration-frequency measurements enables real-time monitoring of changes in liquid density.This capability is particularly valuable in processes where immediate adjustments are necessary based on fluctuations in the composition or concentration of liquids.• These meters often boast a design that minimizes moving parts and requires little maintenance.The simplicity of their construction enhances reliability and reduces the need for frequent calibration, contributing to cost-effectiveness and operational efficiency.• Vibration-frequency density meters are designed to accommodate a wide range of liquid types, including corrosive and abrasive substances.This makes them suitable for demanding industrial environments where the properties of liquids can vary significantly.• The non-intrusive nature of vibration-frequency density measurement is advantageous, especially when dealing with sensitive or valuable liquids.This method avoids contamination and disruption of the liquid being measured, preserving the integrity of the sample.• Many vibration-frequency density meters can be seamlessly integrated into process control systems.This integration facilitates automation and enables industries to maintain precise control over their processes based on real-time density data.• The efficient operation of these density meters often results in reduced waste and energy consumption, aligning with sustainability goals.Their reliable performance contributes to more efficient industrial processes with fewer resource requirements.Thus, vibration-frequency liquid density meters are cutting-edge instruments that combine precision, versatility, and real-time monitoring capabilities.Their application in diverse industries highlights their significance in ensuring quality control, process efficiency, and adherence to strict standards.As technology continues to advance, these density meters are likely to play an increasingly integral role in optimizing various liquid-related processes.
In connection with the above-mentioned, the solution of the problem of automating the tuning of the electromagnetic excitation system of the resonator excitation of the vibration-frequency liquid density meter using the provisions of the theory of fuzzy control is relevant.

Problem statement
The purpose of the paper is to evaluate the possibility of applying fuzzy control methods to automatically adjust the amplitude level of oscillation of a density meter.

Results and discussion
On the basis of the accumulated information and qualitative reasoning on the adjustment of the exciter location and density meter tube, the transition to a qualitative description of the object was carried out, the basis of which is a rule of the form: "If the value in amplitude of voltage oscillations is "very low" and the dynamics of voltage change (voltage derivative) is "positive" then the controlling influence on the exciter is "the duration is very long" and "the direction is downward", etc." [3].
The movement of the receiver of the oscillation exciter is considered as the controlled quantity.Figure 1 shows a simplified structural diagram of the system of automatic adjustment of the level of amplitude of oscillations of the resonator.
The input of the system receives voltage U from the block -1 through analog digital converter -4.The obtained value comes to one of the inputs of the fuzzy controller.The second input receives the derivative dU/dt from the computing unit -5.The fuzzy controller includes: fuzzifier -6, designed to transform crisp signals into fuzzy sets; linguistic rule tables (LRT) -7, i.e. a set of fuzzy rules describing fuzzy relations between input and output parameters of the controller; defuzzifier -8, where the obtained fuzzy value after defuzzification in the form of a crisp control action comes to the input of the motor control unit -9 and the motor -10.For the automatic tuning system, the Mamdani algorithm was chosen as a fuzzy algorithm [3][4][5].This algorithm is the most frequently used in practice, because it has proved itself very well in a number of real-time control tasks.
At work of the controller according to Mamdani's algorithm in the system of automatic adjustment (setting the voltage of the level of amplitude of oscillations in the normalized limits) to the input of the fuzzy controller were given: the calculated value of the voltage of the level of amplitude of oscillations and the direction of voltage change.From the output, the switching direction (up, down or no change in position) and the duration of motor on-off were taken.
All input and output values are clear values, because they are taken from real automation devices, which give clear values of the measured parameters.Further, in the controller itself, these values are already converted to fuzzy values.After triggering of fuzzy rules, the obtained output variables are again converted to clear (normal) form.
The following linguistic variables were used to operate the fuzzy controller: 1.At the input of the controller (input variables): Voltage.Voltage is the voltage of the oscillation amplitude level.The odd values of this linguistic variable are as follows (figure 2):  In the process, different variants of the controller were tested.According to the above variables, 15 fuzzy inference rules for this system have been made.The linguistic table of the rules is given on the table.The symbols in the term labels mean:

Conclusions
As a result of the research, it was obtained that the fuzzy controller performs fewer switching operations in most of the cases as compared to the manual controller.This results in less time for tuning the oscillation amplitude level of the density meter.Devices based on fuzzy logic have another important property -relatively easy extensibility.Adding new properties, new functionalities for such devices is easy and uncomplicated.I.e. when there is a need for additional functions, it is possible to add them to the operation of the fuzzy device.
It can be argued that devices based on fuzzy logic are more preferable for automatic adjustment of vibration-frequency density meter vibration amplitude level than devices based on conventional logic The automatic adjustment of the oscillation amplitude level of the density meter itself is of higher quality, and the number of switching operations is reduced.

Figure 1 .
Figure 1.Structural scheme of the system of automatic adjustment of electromagnetic exciter location of vibration-frequency liquid density meter.

Figure 6 .
Figure 6.Surface dependences of output parameters on input variables.

Table 1 .
Table of linguistic rules.