pulse-width pulse-frequency modulator

In this article, the problem of controlling the attitude of a spacecraft with integral pulse width and frequency integrator is investigated and the said integrator is developed as a fractional order. The spacecraft is controlled by a two-state on-off thruster actuator with a combination of proportional-derivative law and integrator. In order to focus more on studying the behavior of the proposed integrator, the operator model is ideally considered, although it is due to the use of a nonlinear control system integrator. Average fuel consumption and operator activity are included as two main evaluation indicators, and on the other hand, the absolute average value of the sign error on spacecraft status is also included as another important indicator in the study of the behavior of the proposed integrator. In order to compare the results fairly, the situation control problem has been done for the same assumed conditions and for the integrator of integer order and fractional order. The comparative results for changing the fractional power of the fractional order integrator filter and checking the three performance criteria have been done. Also, the influence of the uncertainty of the moment of inertia of the spacecraft, the uncertainty of the reference entry angle and the range of external disturbances have also been studied. The obtained results indicate the change of the performance criterion for changing the order of the fractional combiner filter and show the more appropriate performance of the proposed combiner for a range of fractional powers.

This paper presents a modification to a type of Pulse-width Pulse-Frequency (PWPF) Modulator utilized an integrator block. In this modulator that called here as "Integral Pulse-Width Pulse-Frequency (IPWPF)," an integrator is used instead of the first-order low-pass filter. To improve the performance of the control system, the modulator is modified by using a logical circuit in order to reset the output of the integrator. In this logical circuit, if the error signal becomes less than a specified small value, the integrator will be reset, that is, "Small Error-Reset Integrator (SE-RI)." The modification is applied to the stabilization and pointing modes. In stabilization mode, the control gain is obtained analytically such that the angular rate of the satellite becomes zero or less than a specific percentage of its initial value by a single pulse. Simulation results show that the performance of the modified IPWPF is comparable with that of PWPF in pointing mode.

In this study, the preferred regions of Pulse-Width Pulse-Frequency Modulator (PWPFM) are obtained analytically for the static analysis. For this purpose, a comprehensive parametric study is carried out based on the two performance indices of fuel consumption and the number of thruster firings. The preferred regions are presented by normalized relations and curves. Moreover, the exact analytical solutions of the two performance indices are obtained for a class of modulators with the assumption of constant inputs. The advantages of the present study are non dimensional analysis and obtaining the preferred regions in terms of each others, resulting in more accurate regions as opposed to inequality relations using constant values for a specified input signal. In addition, in the case of specified minimum pulse width (having the update frequency and thruster time constant), determining the preferred regions becomes more limited. In this regard, useful relations and curves based on the maximum possible value for the number of the thruster firings are derived and presented.