Evaluation of dynamic characteristics of a linear time-varying system
Keywords:
time-varying control system, transfer function, equivalence criterion, Levenberg-Marquardt algorithmAbstract
Purpose. The development of methodological support for the construction of an algorithm for calculating the coefficients of the transfer function of the second order link, which is equivalent to a time-varying system in the selected time interval from the point of view of the smallest average value of the modulus of the difference of dimensionless state vectors. Design / Method / Approach. Mathematical models of a time-varying system and a second-order link are used, along with a criterion that determines the transfer function coefficients. The Levenberg-Marquardt algorithm finds the minimum, and the Runge-Kutta algorithm solves differential equations. The output of the time-varying system is obtained numerically, while the second-order link’s output is an analytical solution. Findings. Based on the calculations carried out for the selected data example, the possibility of determining the transfer function coefficients of the second-order link is shown, which, from the point of view of the smallest average value of the modulus of the difference of dimensionless state vectors on the selected time interval, is equivalent to time-varying system. Theoretical Implications. It is possible to have an estimate of the margin of stability, type and duration of the transient process during the selected time interval of the system operation by using the mathematical apparatus of linear stationary systems. Practical Implications. It leads to the expansion of the methodological base of analysis and synthesis of linear time-varying systems. Originality / Value. It lies in the using the Levenberg-Marquardt method to determine the coefficients of the transfer function which is equivalent to the equations of a time-varying system at a certain time interval from the point of view of the selected criterion. Research Limitations / Future Research. The algorithm was developed for the rocket rotational control system in one plane. The transfer function coefficients depend on constraints and the test signal within 15%. Further research includes an equivalent stationary approximation considering actuator inertia and center of mass disturbances. Article Type. Conceptual.
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