# Design of an IMCPID Optimized Neural Network for Stepless Flow Control of Reciprocating Machinery
## 1 Introduction  
Reciprocating compressors are widely used in some industrial fields such as petroleum, chemical, natural gas transportation and so on. It is the main power-consuming equipment in industrial factories and it is usually run at factory setting. However, in some conditions, the outlet flow of compressors needs to be regulated with the real-time demand of the downstream production process. Therefore, it is necessary and meaningful to control the outlet flow of compressors. Many approaches have been proposed, and the by-pass regulation is the simplest and most reliable method [1]. However, this method will cause a huge waste of electricity because the reflux gas will be sent back to the inlet of the compressor to be compressed again. In comparison with the by-pass regulation, the stepless flow control method has a better energy-saving performance because excess gas will be expelled from the compression cylinder prior to the compression process. Thus, this part of the gas will not be compressed, and some power consumption can be reduced. After equipping with the stepless flow control system, the effective power of the compressor will be greatly improved, and a lot of electricity will be saved. The stepless flow control system for the reciprocating compressor should meet the following requirements [2, 3]:  
* The control system should be capable of continuous stepless flow regulation within 0-100% working load. * The control system should require low investment and low energy consumption. * The control system should be reliable, safe and convenient to operate. * The control system should have a wide range of applications. From the point of view of control science, the stepless flow control system has multiple controlled variables and multiple manipulated variables [4]. The inlet flow of each stageis the manipulated variable, and the outlet gas pressure of each stage is the controlled variable. Thus, this is a multiple-input and multiple-output (MIMO) system. The primary feature of MIMO system is the strong coupling, where each manipulated variable can affect the other controlled variables. It is harder to design the controller than the single-input and single-output (SISO) system due to the interaction process between controlled variables and manipulated variables. Thus, one of the main control objectives for a MIMO system is reducing the coupling. Many approaches have been proposed to solve this control problem in state space and transfer function matrix representations. Some frequency-based frameworks have been researched in this study including the relative gain array (RGA) measure, feed-forward decoupling method, IMCPID and neural network [5]. The Proportional Integral Derivative (PID) control has been widely used in the industrial fields due to its simple structure and stable characteristics. However, for some dynamic processes such as time-delay, nonlinearity and coupling, the PID controller does not always represent high efficiency. In the past decades, the question of how to find simpler PID tuning methods has caught a mass of interest [6]. In both academic research and engineering applications, many PID-type controller designs have been developed, such as the famous Ziegler-Nichols (ZN) tuning rules [7], the well-know \(\mathrm{H_{2}/H_{\infty}}\) robust optimal design method [8], the internal model control principle [9] and neural network PID [10]. In the above methods, IMC is considered as the simplest tuning rule of PID controller. This because all the three controller parameters of PID can be obtained from the only user-defined tuning parameter of IMC called \(\lambda\) (\(\lambda>0\)). It is easy to control the linear or nonlinear, time-delay and coupling systems for the IMC scheme due to its simple and robust performance characteristics [11]. Many studies have been conducted to obtain PID tuning methods using IMC schemes which are achieved by complex mathematical manipulations or require a filter algorithm.