SYNTHESIS AND SIMULATION OF THE OPTIMUM ACCORDING TO THE SPEED OF THE TRACKING SYSTEM.

A method of construction and calculation of the structural scheme of the facility management system is proposed, which is constructively formed by the serial connection of the first-order aperiodic link and the integrator, and is formally described by a mathematical model in the form of a product of the corresponding transfer functions. An electric motor with an input voltage source can serve as a common typical implementation of the specified control object. The proposed method makes it possible to build a control system that is close to optimal in terms of speed. Moreover, optimality, in this case, is determined by the fact that the object in the process of functioning is turned on in relay mode. The transient process for a defined control object, under the conditions of the optimal mode, is two stages: acceleration and braking, which are carried out at the maximum values of the input influence - that is, the input voltage. To determine the switching moments of the input influence (signal), the phase plane method is used, and the phase coordinates are: on the abscissa axis, the output value (for the given example, the frequency of rotation of the motor shaft), and on the ordinate axis, the rate of change of the output value (or derivative from the rotation frequency of the motor shaft, i.e. the corresponding acceleration). A structural diagram of the control system was developed, which ensures acceleration and braking of the object at the maximum values of the input signal. The optimality of the transition process is ensured by the fact that the control error is compared with the signal coming from the link of the configured switching line. Formulas for calculating the switching line on the phase plane are presented, as well as the program for calculating the switching line, written in the MATLAB environment in m-file format. The system was modeled in the MATLAB-Simulink package, which confirms the optimality of the control process. [ABSTRACT FROM AUTHOR]