Studying effects of time quantization on frequency response of a digital relay-operated electromechanical system for controlling thrust vector of a liquid-propellant rocket engine

The paper contains results from a study of effects of time quantization on frequency response of a digital relay-operated electromechanical system for controlling thrust vector of a liquid-propellant rocket engine for a crew transportation spacecraft. The paper presents results from a development effort on a math model for time quantization of signals in a thrust vector control system, as well as from an evaluation of the math model of time quantization effects through calculations of frequency response for the steering channel of the system. The study is based on: a math model of a magnetoelectric motor, a math model of a dual-drive electromechanical actuator, non-linear math model for dynamics of the digital relay-operated electromechanical system for controlling liquid engine thrust vector, multi-channel monoharmonic autointegration method for calculating amplitude-phase-frequency characteristics of the digital relay-operated electromechanical system for controlling liquid engine thrust vector and a method for numerical solution of systems of Runge-Kutta fourth-order non-linear differential equations. The study found that time quantization has a significant effect on frequency response of steering channels in the control system for liquid engine thrust vector. While discrepancies in phase frequency characteristics start virtually immediately after the first frequency in the frequency array of the input monoharmonic signal, discrepancies in amplitude-frequency and logarithmic amplitude-frequency characteristics start around 3 Hz, which follows from the Nyquist-Shannon-Kotelnikov theorem stating that it is possible to perfectly reconstruct a signal represented by a series of digital samples, if the sampling rate is more than twice as high as the frequency in the signal spectrum.