Spacecraft vibration reduction using pulse-width pulse-frequency modulated input shaper

Abstract

Minimizing vibrations of a flexible spacecraft actuated by on-off thrusters is a challenging task. This paper presents the first study of Pulse-Width PulseFrequency (PWPF) modulated thruster control using command input shaping. Input shaping is a technique which uses shaped command to ensure zero residual vibration of a flexible structure. PWPF modulation is a control method which provides pseudo-linear operation for an on-off thruster. The proposed method takes full advantage of the pseudo-linear property of a PWPF modulator and integrates it with a command shaper to minimize the vibration of a flexible spacecraft induced by on-off thruster firing. Compared to other methods, this new approach has numerous advantages: 1) effectiveness in vibration suppression, 2) dependence only on modal frequency and damping, 3) robustness to variations in modal frequency and damping, 4) easy computation and 5) simple implementation. Numerical simulations performed on an eight-mode model of the Flexible Spacecraft Simulator (FSS) in the Spacecraft Research and Design Center (SRDC) at US Naval Postgraduate School (NPS) demonstrate the efficacy and robustness of the method.

Fractional Describing Function Analysis of PWPF Modulator

“…There are various kinds of pulse modulators, such as pulse-width modulator, pulse-frequency modulator, pseudo-rate modulator, and pulse-width pulse-frequency (PWPF) modulator [14,15]. PWPF modulator is preferred for its operation has almost linear input/output relationship [16,17]. A PWPF modulator mainly comprises two components: a first-order lag filter and a Schmitt trigger inside a feedback loop, as shown in Figure 1.…”

Vibration Suppression of Flexible Spacecraft During Attitude Maneuvers

“…For system modeling, several assumptions are made: 1) the beam is assumed to be an Euler-Bernoulli beam and flexible only in a direction transverse to its length in the plane of motion; 2) the piezoelectric layer is homogeneous and is uniaxially polarized; 3) the piezoelectric material is perfectly bonded to the beam; and 4) the gravitational effect, hub dynamics, and internal/external disturbances are neglected for simplicity. Now, applying the extended Hamilton's principle, the equations of motion for the flexible spacecraft with surface-bonded piezoceramics are 7,8 Jθ γ e = B T q…”

“…The CSVS method is used to modify the exist-ing command so that less vibration will be caused by the command itself. In addition, to extend the CSVS method to the system with on-off thrusters, a scheme of combining CSVS method with the pulse-width pulse-frequency (PWPF) modulation 6,8 is first given, which do not require the complicated nonlinear optimizations to design the constant amplitude commands for the system and can suppress the relatively large-amplitude vibrations excited by rapid maneuvers. With the presence of this command shaping control, an additional independent flexible control system, the PPF control technique using piezoelectric materials, acting on the flexible parts can be designed for further vibration suppression during and after the maneuver.…”

A linear programming approach for designing multilevel PWM waveforms

“…It is also desirable to design a switching signal with the lowest harmonic distortion so that effect of PWM signal on the intended operation of mechanical system is minimal. Refer to Gürleyük (2011) and Song, Buck, and Agrawal (1999) for examples on vibration damping using multilevel PWM signals. Another application of multilevel PWMs is in switch-mode power amplifiers which are crucial components of modern day Radio Frequency (RF) transmitters used in wireless communication systems.…”