# Research Progress of Related Technologies of Electric-Pneumatic Pressure Proportional Valves
## 3 Related Technology Research Progresses  
### Numerical Simulation Researches  
Pneumatic pressure proportional valve is composed of more complex pneumatic components, including a variety of gas, pneumatic actuators, controllers, and electrical mechanical converters. When analyzing the relationships among various components of the valve, the numerical analysis method is often used, which can predict the performance of the valve, optimize the structure design of the valve, and improve the design efficiency. Electric mechanical converter will be the proportion of the input current or voltage converted into force or displacement output through the armature of special design. To establish the mathematical model is the key for modeling proportional solenoid valve. [PERSON], [PERSON] [20] proposed a kind of nonlinear dynamic model of high speed solenoid valve that comprises of a proportional solenoid and the spool, and the model can accurately predict for a given input voltage steady state and dynamic response. The dynamic analysis of the proportional pressure valve is carried out by [PERSON] and [PERSON] [21; 22]. The dynamic mathematical model of the valve is established, and the flow characteristics of the valve pressure are taken into account to improve the dynamic response characteristics of the pressure valve. Excepting the direct relationship between the input signal and the output force, the magnetic circuit analysis is a common method thatcan clearly identify each physical quantity and can be used to analyze the static performance of electromagnet. However, the magnetic circuit analysis method cannot describe the dynamic of the electromagnet. In the current study, the researchers tend to limit the method to establish the mathematical model of the electromagnet [23]. For example, [PERSON] and [PERSON] [24] analyzed various characteristics of electromagnets by using the finite element method, including resistivity, response speed, and material properties. The finite element model has the advantages of high precision, but it is difficult to use it to find out effective results because there is a large amount of calculation and complex algorithm. Furthermore, except for the mathematical models, there are semi-empirical modeling methods in which the experimental data are used to fit the nonlinear part of the system [9; 20; 25; 26; 27]. In the research of proportional electromagnet circuit, there is the nonlinear induced voltage of the electromagnet motion and in the modeling of a proportional electromagnet, it is hard to find the reasonable approximation of induced voltage. Many scholars estimated the induced voltage indirectly, that is to say, that they obtained the relationship between the induced voltages by fitting the experimental data. The semi-empirical model is used to study the approximate the induced voltage in XU [25], which is based on the relationship between the output force of the electromagnet and the armature. The linear least square method is used to fit the static experimental results of electromagnetic force, and further obtain the approximate nonlinear induction voltage. [PERSON] [20] used a semi-empirical modeling method to estimate the electromagnet as a pure combination of resistance and nonlinear inductance. The coil current and magnetic flux are calculated by experiment. In [PERSON]'s Research [26], which is based on the linear relationship between the reciprocal of the equivalent inductance of the coil and the coil current, the linear coefficients are fitted by the experimental data but are less effective. The reason is the ignorance of the influence of the armature displacement on the output force of the proportional electromagnet. A pneumatic pressure proportional valve for ankle foot orthopedic instruments was studied by [PERSON], [PERSON] [28].