Fuzzy Regulator for Two-Phase Gas–Liquid Pipe Flows Control
Abstract
:1. Introduction
2. The Two-Phase Gas–Liquid Mixtures Flow
2.1. Characteristics of the Flow Types
2.2. Flow Type Recognition
2.3. Control Techniques for Flow Processes
3. Two-Phase Flow Experimental Rig: Facility and Control Methodology
4. Fuzzy Regulator Principles
if (SG = t1SG) or (SG = t2SG) and (SL = t1SL) then (Fc = t3Fc)
- V—variable name, e.g., gas stream,
- T—set of variable terms, e.g., small, medium, or big
- D—crisp domain of a linguistic variable, e.g., ,
- G—the syntactic rule, whose grammar generates the derivative terms—the T labels, e.g., T(gas stream) = {…, “medium small”, “medium”, …}
- M—the semantic rule that sets the meaning M(l) to each linguistic value l.
- d—is the domain of the measurement,
- —is the mean measurement value for the measurement data collected in time t,
- —is the standard abbreviation for the measurement data collected in time t,
- —is the i-th term of input signal S.
then (NSG = t2SG) and (NSL = t2SL),
- SC, SL—the signals of the first class: the fuzzified value of the gas stream and the fuzzified values of the liquid stream,
- fC, fG—the signals of the second class: the current flow type and the required (given) flow type,
- tij—the i-th value (term) of the j-th input signal.
- —the membership functions describing the first class linguistic variables (fuzzy sets—µSG(x), µSC(x)),
- —the membership functions describing the second class linguistic variables (fuzzy relations—µfC(x,y), µfG(x,y)).
5. Implementation
- The module for input signal fuzzification (1) that contains the first class (measurement data) (2) and second class (flow type) (3) signals fuzzification modules,
- The diagnostic signals (Z1, Z2, Z3) retrieved from the measurement instruments,
- The flow type reference signal set by the user (Z4),
- The inference rules module (4),
- The inference module based on the modified fuzzified Mamdani implication,
- The defuzzification module that implements the center of sums defuzzification method (5) and which processes the fuzzified control signals (Z′1 and Z′2),
- The module of the crisp sets (n1 and n2) (6).
- For the linguistic variable—fuzzified gas stream:
- For the linguistic variable—fuzzified liquid stream:
- x—is the gas stream value,
- y—is the liquid stream value,
- —is the membership level of the flow type achieved for the gas stream x and liquid stream y,
- —is the membership level determined for i-th term of the fuzzified gas stream for the measured value x of the gas stream,
- —is the membership level determined for i-th term of the fuzzified liquid stream for the measured value y of the liquid stream.
andflow type is plugandrequired flow type is slug
thenfuzzy gas stream is largeandfuzzy liquid stream is large
- Area #2 represents the current flow type,
- Area #3 represents the required flow type,
- Area #2 corresponds with the fuzzified values of gas and liquid streams that determine for current flow type.
6. Results
- Establishing the initial state,
- Selecting the required flow type by the expert,
- Validation of the stabilized flow type by the expert and the feedback from the diagnostic module [30].
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Test Run | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Human expert evaluation | Plug → Transitional | Transitional → Plug | Plug → Slug | Slug → Plug | Plug → Transitional | Transitional → Slug | Slug → Transitional | Transitional → Slug | Slug → Plug | Plug → Slug | Slug → Transitional | Transitional → Stratified | Stratified → Slug | Slug → Dispersed | Dispersed → Stratified |
Presented system evaluation | Plug → Transitional | Transitional → Plug | Plug → Slug | Slug → Plug | Plug → Transitional | Transitional → Slug | Slug → Transitional | Transitional → Slug | Slug → Plug | Plug → Slug | Slug → Transitional | Transitional → Stratified | Stratified → Slug | Slug → Dispersed | Dispersed → Stratified |
Test Run | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
Human expert evaluation | Stratified → Waved | Waved → Stratified | Stratified → Slug | Slug → Dispersed | Dispersed → Transitional | Transitional → Dispersed | Dispersed → Plug | Plug → Waved | Waved → Plug | Plug → Dispersed | Dispersed → Stratified | Stratified → Dispersed | Dispersed → Waved | Waved → Dispersed | Dispersed → Slug |
Presented system evaluation | Stratified → Waved | Waved → Stratified | Stratified → Slug | Slug → Dispersed | Dispersed → Transitional | Transitional → Dispersed | Dispersed → Plug | Plug → Waved | Waved → Plug | Plug → Dispersed | Dispersed → Stratified | Stratified → Dispersed | Dispersed → Waved | Waved → Dispersed | Dispersed → Slug |
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Fiderek, P.; Kucharski, J.; Wajman, R. Fuzzy Regulator for Two-Phase Gas–Liquid Pipe Flows Control. Appl. Sci. 2022, 12, 399. https://doi.org/10.3390/app12010399
Fiderek P, Kucharski J, Wajman R. Fuzzy Regulator for Two-Phase Gas–Liquid Pipe Flows Control. Applied Sciences. 2022; 12(1):399. https://doi.org/10.3390/app12010399
Chicago/Turabian StyleFiderek, Paweł, Jacek Kucharski, and Radosław Wajman. 2022. "Fuzzy Regulator for Two-Phase Gas–Liquid Pipe Flows Control" Applied Sciences 12, no. 1: 399. https://doi.org/10.3390/app12010399
APA StyleFiderek, P., Kucharski, J., & Wajman, R. (2022). Fuzzy Regulator for Two-Phase Gas–Liquid Pipe Flows Control. Applied Sciences, 12(1), 399. https://doi.org/10.3390/app12010399