# Design of an IMCPID Optimized Neural Network for Stepless Flow Control of Reciprocating Machinery
## 1 Introduction
For the stable linear and separable nonlinear system, an IMC-based PID (IMCPID) tuning scheme employing first-order in place of second or higher-order filter is presented [12]. Some heuristic methods have also been developed to get PID parameters [13; 14; 15]. A IMCPID controller has been slightly modified in [16] to demonstrate the importance of mid-frequency and high-frequency robustness for tuning parameters. As some processes having model uncertainty, [17] proposed an IMC tuning method based on gain margin and maximum peak criterion. In order to eliminate the effects of uncertainty of system parameters, some adaptive control methods have been used in industrial processes [18; 19]. The model-reference adaptive control and self-tuning regulator control can effectively solve the disturbance problem in linear system [20]. The method in [21] combines IMC and adaptive PSD control. The result of applying it to the main steam temperature system shows that the method is effective. However, the parametric uncertainties and external disturbances of nonlinear systems are more sophisticated than those of linear systems. To solve this problem, some intelligent techniques [11] have been applied to adaptive controller, including neural network and fuzzy logic control, etc. Paper [22] presents an IMCPID control method to modified the weight of the set-point online with fuzzy logic, which can improve the set-point tracking performance and robustness of the system. In paper [23], the technique of the self-tuning neural network PID control for the stabilizer fin to reduce ship rolling motion is successfully developed. Because the neural network can approximate any continuous function, the adaptive controller based on neural networks has excellent online estimation characteristics [22]. In this paper, a neural network based on IMCPID control strategy is proposed to improve the performance of the stepless flow controller. A feedforward decoupling method is designed which can eliminate the coupling and transform the multiloop system into several independent single-input and single-output loops [24]. In the feedback loop, an adaptive IMCPID control method is proposed which uses the system error as the input signal of the neural network and regulates the IMCPID parameter \(\lambda\) by its self-learning in real time [23]. The main purpose of this paper is to solve the problem of PID parameter setting in the actual industrial field operation process, which is usually a complex job. Therefore, we proposed a more concise neural network combined with an IMCPID control method, which reduces the number of system parameters and the difficulty of parameter setting. Some researchers found out that after applying neural networks to these nonlinear systems, not only will the parameter tuning process become simpler, but also the control performance will present more excellently [25]. PID neural network will automatically adjust the control parameters due to its self-organizing, self-learning and self-adaptation characteristics [26]. The simulation experiments show that the IMCPID controller based on neural network for a stepless flow control system has better performances in set-point tracking, stability and robustness than those of the other considered controllers. The rest of this paper is organized as follows. Section 2 gives the mathematical model for a stepless flow control system of a reciprocating compressor. In Section 3, The IMCPID-based neural network (IMCPIDNN) control scheme is presented. The simulation results of a multivariable nonlinear control system are compared and discussed in Section 4. Finally, the conclusion and some open problems are given in Section 5.