DYNAMICS OF PNEUMATIC DRIVE. LECTURE CYCLE.MATHEMATICAL MODEL OF THE SERVO PNEUMATIC ACTUATOR

Abstract

The paper considers the basic concepts of a mathematical model. The connection between the model and reality and its place and relevance in the modern world is shown. The developed mathematical model of a servo pneumatic device, which includes an actuator and a proportional or discrete pneumatic valve, is presented. The basic equations describing the dynamics of the servo pneumatic device, boundary and initial conditions are given, which make it possible to analyze the stability of the drive. A non-linear object-oriented computer model of a pneumatic servo device is presented. The model is built in the form of block diagrams of equations that describe the relationship between the original physical quantities. The influence of the nature of the inductance of the electromagnet coil on the dynamic properties of the system is shown. The developed method for identifying the transfer function of pneumatic devices and its application in the preparation of mathematical models is presented. A technique for studying the stability of pneumatic systems has been created, based on establishing an unambiguous relationship between the experimentally obtained frequency characteristics of the pneumatic apparatus included in the system and the type of its transfer function. The form of transfer functions for the pneumatic devices under consideration is obtained. For the proportional pneumatic valves presented in the work, the quality indicators of transient processes in the time domain are formulated and determined, and the phase and amplitude margins are found. The criteria for the performance of pneumatic systems are formulated. The ratios for determining the described criteria are given. The boundaries of the operability of systems with a pneumatic drive have been established. The scientific novelty of the results presented in the work is that a non-linear object-oriented computer model of a servo pneumatic device has been created, unlike the existing ones, it is built in the form of block diagrams of equations that describe the relationship between the initial physical quantities, and has the principle of modularity. The model includes the transfer function of the control devices obtained using the developed method for identifying the parameters of the transfer function. This work is based and is implemented as a course of lectures of the course “Dynamics of Pneumatic drive”, is red by the author at the Bauman Moscow State Technical University at the Department of “Hydromechanics, Hydraulic Machines and Hydropneumoautomatics” (E10), as part of the preparation of masters in the specialty 05.04.13 – Hydraulic machines and hydropneumatic drives.