# Fuzzy Regulator for Two-Phase Gas-Liquid Pipe Flows Control
## 2 The Two-Phase Gas-Liquid Mixtures Flow
### Control Techniques for Flow Processes  
The task of flow control is of substantial meaning in any branch of industry where these processes are used for production, transport, etc. Because of the applications' variety in each case, the needs and demands are different. Nevertheless, the important thing is to keep the flow regime on the given level or avoid slugs' occurrences. In the case of such dynamic, stochastic, and nonlinear processes as flows, one must remember that holding the same level of phases' streams supply does not guarantee the flow regime stability [33]. Therefore, it is necessary to process continuous monitoring and to react in case of any abnormalities. In the world literature, many research works may be found that use various modelling techniques to provide the tools for control process simulation or even for threats estimation. The example showing the control task's complexity is the mathematical flow control scheme introduced in [34] to minimize the turbulences based on four different models. Next, in [35] the readers may find out the discussion on the interdisciplinarity of the algorithms development process for flow control purposes. The authors issued requirements and limitations for optimizing process control tasks in the context of various applications. Furthermore, some problems in the flow modelling and control based on the flow pattern and flow map using the specified Eotvos number classification have been demonstrated in [36]. The authors of [37] deal with the results from simulations with the feedback flow control. They show how to avoid slugs and hold on to the stable conditions at the pipeline inlet and outlet. In contrast, without control, severe slug flow was experienced. In [38], in turn, the authors made an exhaustive analysis of control models commonly used by industrial control engineers. A discussion about the advantages and limitations of the single-input single-output (SISO) system in contrast to the multi-input multi-output (MIMO) feedback control system may be found. The case study on the controllabilityproperties of a typical pipeline-riser system of two fluid flow with the PDE-based (partial differential equations) model was described in [39]. Besides the theoretical achievements, some works have been performed to design the feedback control solutions based on PID [40] or PI [41] controllers to demonstrate that this strategy can guarantee the stability of the flows, whereas manual choking appeared to be insufficient. In [42], the auto-tuned PI controller algorithm was introduced, which was developed and implemented for severe slugging control focusing on achieving stable operation and maximizing production. On the other hand, the example of the linear quadratic Gaussian feedback control applied to the separated boundary layer to reduce its separation bubble size has been developed in [43]. Moreover, the feedback linearization based on the riser-base and topside pressure was used in [44] for the control design of the production choke valve to prevent severe slugging flow conditions. Nevertheless, the authors of [45] analyzed the disadvantages of the production choke control system based on feedback PI-controller in the context of their new approach to the nonlinear state-feedback control law based on a first-principles model of the slugging phenomenon. In this case, only one parameter (the gas pressure) was adjusted. Elsewhere, the detailed analysis and discussion about some problems and optimization of the linear controllers were performed in [46] and especially in the case of slug attenuation in [47] or in [48]. Generally, after studying the referred works, one conclusion may be drawn. Due to the complexity of the flow processes, the design of the robust control system based on an active feedback control makes a significant challenge to achieve the desired performance and optimal efficiency. Some solutions for flow control were developed to increase the system stability and optimize production.