Transfer Function of a Time-Varying Control System Considering Actuator Inertia

Purpose. Methodological support for building an algorithm for determining the transfer function (TF) of a link, which, considering the actuator dynamics and the disturbed motion of the mass center, is equivalent on a selected trajectory section to a time-varying control system (TCS) for the rocket movement in one plane. Design / Method / Approach. TCS is modeled using differential equations with changing coefficients. To define the type of TF, the Laplace transformation of the equations is performed, while its coefficients are determined by finding the equivalence criterion extreme of the output signals of the TCS and the link under the action of the test signal. Findings. The example of the TCS for the rocket movement in the yaw plane shows the possibility of an algorithm constructing for studying its dynamic characteristics by using the mathematical apparatus of linear stationary systems. Theoretical Implications. Finding the extreme of the equivalence criterion of the TCS and the link using the Levenberg-Marquardt method, with the coordinates of the extreme point being the arguments of the TF coefficients. Practical Implications. Using the TF of equivalent link, it is possible to obtain for the selected trajectory section a quantitative estimate of the stability margin, the duration of the transient process, the accuracy of disturbance compensation, and the transmission coefficient depending on the signal frequency input. The obtained results contribute to the methodological base expansion for linear time-varying systems research. Originality / Value. Analytical solution of the link differential equation for a test signal in the form of a sequence of rectangular and parabolic pulses using the Laplace transform. This will make it possible to obtain estimates of individual indicators of systems with time-varying parameters by using the mathematical apparatus of stationary systems. Research Limitations / Future Research. The algorithm is for the case of TCS of a rocket motion in one plane developed. The next stage of the study is to assess the algorithm complexity level as the order of the TCS mathematical model increases. Article Type. Methodological.