Modeling of dynamic objects of pipeline transport

Abstract

The paper investigates the construction of a discrete model of pipeline transport, using the results passive or active experimentation. Urgency of the problem stems from the fact that in modern management systems are widely used in conjunction digital and discrete devices and integrated approach is required to describe such systems. Traditionally, many dynamical systems and objects are described by ordinary differential equations, which are derived from the laws of physics. In order to implement the model analog computer facilities, this model undergoes further sampling procedure. Another approach involves the simulation in the form of discrete functions. Discrete dynamical model of the object in this case is the source and directly on the basis of this model is calculated transfer function. As a theoretical framework we use Theorem Kalman, the essence of which is that the output of the system at any given time is determined by the input signal, its background and the prehistory of the state of the system. The more discrete variables recorded in the recording pattern, the higher the accuracy. The results of calculations - the coefficient values and view of the difference equation modeling. An example of the construction of the discrete model using linear differential equations and the method of least squares approximation as an instrument of the difference equation to the experimental data. Construction of a discrete model of the object may not be sufficient for the synthesis of the regulatory system. In some cases there is a need for an analog model for future use well-developed methods of continuous systems. However, the correspondence between the Laplace transform and Z - transformation will allow to calculate a continuous function which coincides with a discrete function, only moments quantization. Values of a continuous function between the sample times cannot be determined unambiguously. A discrete function may correspond to a plurality of analog functions. Effective method to overcome this difficulty and obtain adequate continuous model is the use of Tustin transformation . We consider a transition to a continuous model using a modified conversion A. Tustin .