The Models of Non-Stationary End Position Control Systems With Digital Corrective Circuits

The article discusses approaches to modeling the end position control systems of the AUV with a containing, in addition to a non-stationary connection, discrete corrective links. We will use the name of such systems
$-\tau{-}$
systems. The use of a digital computer in the final position control system leads to the need to use differential-difference equations. A simple replacement of discrete systems by continuous ones can lead to an error in the estimation of the system behavior, and in some cases, to system instability. The control system is considered as a non-stationary continuous-discrete system. A general scheme, a simplified scheme and a continuous analogue of the control system are considered. The choice of describing mathematical models using operational calculus is justified by the fact that the solution of differential and finite-difference equations are transcendental functions that are not expressed in terms of elementary functions. As a result, we are talking about revealing the properties of these functions. The exact solution of the end position equations presented in the form of inversion integrals can be obtained as a result of applying the transformations of the operational calculus. The mathematical model of the system is represented in the form of transfer functions.