Mathematical Modelling and Simulation of Pneumatic Systems

Abstract

Program support, simulation and the animation of dual action pneumatic actuators controlled with proportional spool valves are developed. Various factors are involved, such as time delay in the pneumatic lines, leakage between chambers, and air compressibility in cylinder chambers as well as non-linear flow through the valve. Taking into account the complexity of the model, and the fact that it is described by partial different equations, it is important to develop the program support based on numerical methods for solving this kind of problems. Simulation and program support in Maple and Matlab programming languages are conducted, and it is shown the efficiency of the results, from engineering view of point. These pneumatic systems have a lot of advantages if we compare them with the same hydraulic types; they are suitable for clean environments, and much safer. In accordance with project and space conditions, valves are positioned at relatively large distance from pneumatic cylinder. Considering real pneumatic systems, it is crucial to describe them with time delay, nonlinearities, with attempt of not creating only academic model. Despite of these problems, development of fast algorithms and using the numerical methods for solving partial different equations, as well as enhanced simulation and animation techniques become the necessity. Various practical stability approaches, for solving complex partial equations, used similar algorithms, (Dihovicni, 2006). In the third part it is described special group of distributed parameter systems, with distributed control, where control depends of one space and one time coordinate. It has been presented mathematical model of pneumatic cylinder system. The stability on finite space interval is analyzed and efficient program support is developed. Solving problem of constructing knowledge database of a decision making in process safety is shown in fourth part. It is provided analyses of the requirements as well the analyses of the system incidents caused by specification, design and the implementation of the project. Main focus of this part is highlighted on practical stability problem and conditions for optimal performance of pneumatic systems. Algorithm of decision making in safety of pneumatic systems is developed, and the system has been realized taking into account C# approach in Windows environment.