Abstract
An important part of modern methods of synthesizing automatic control systems is selection of a characteristic polynomial that can provide the desired dynamics. However, standard polynomials allow only rough setting of the desired dynamic properties of a system. A more convenient and clear alternative of imparting desired properties to the system in static and dynamic modes is to use not the standard characteristic polynomials but the desired transfer function that is not selected from a list of standard forms but is set solely on the basis of technological requirements and technical implementation capacity of a particular type of equipment. The study suggests presenting the desired transition function of the automatic control system in a quantized form, i.e. as a set of operated coordinate values that change during a certain period that is relatively small in comparison with the duration of the transition process itself. A possibility of using quantized transition functions is represented as the sum of time-shifted Heaviside functions for the synthesis of regulators in open-loop control systems. A method has been developed to determine analytically the operator images of the desired quantized transition functions of finite duration by relying only on the values of the signal levels in the quantization time and the value of the quantization period.
Highlights
An important part of modern methods for automated control systems synthesis is selection of the desired characteristic polynomial
The roots locations of characteristic equations for closed-loop systems by standard polynomials have semi-empirical nature: they cannot be considered optimal according to some optimization criterion
The Butterworth polynomial puts the roots on the half-circle with a radius ω0 at equal angular distances (Fig. 1)
Summary
An important part of modern methods for automated control systems synthesis is selection of the desired characteristic polynomial. The coefficients of Graham and Lathrop polynomials are defined by mathematical modelling. In this way, standard polynomials allow us to specify the necessary dynamic properties of the system only roughly. The existing problematic issues in using standard characteristic polynomials for the regulators’ synthesis require finding innovative approaches to solving the problem of assigning desired dynamics to the automatic control systems. A mathematical apparatus should be suggested and be devoid of the disadvantages of standard characteristic polynomials. This determines the direction and relevance of the research that is presented in the study
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