Modeling of piezoelectric actuator's hysteresis and its effect on the control accuracy of a LEO-to-GEO laser-communication for a small satellite

Compared to conventional large satellites in the past, small satellite classes (less than 150 kg) show their advantages for mass production, such as short time and low cost for development and launch, to cope with the demand for emerging missions that require a sufficient number of satellites in orbit. However, the traditional communication method, in which a low earth orbit (LEO) small satellite sends data to a ground station using radio frequency, has several disadvantages. Firstly, the limitation of radio-frequency bandwidth leads to a low data rate and difficulty in getting a frequency license. Secondly, there is a significant delay during which data cannot be sent to the ground due to lacking a line of sight between the LEO satellite and the ground station. Additionally, the duration time for the small satellite to communicate with the ground station is just less than 10 minutes approximately. To resolve the above issues, we investigate the case that a less-than-150-kg satellite carries out a laser communication link from LEO to a satellite in geostationary orbit (GEO). Due to the constraints of size, weight, and power (SWaP), traditional bulky LEO-GEO relay systems cannot be applied for the small satellite. However, using the combination of the satellite body pointing and a piezo Fast-Steering Mirror (FSM), which reduces the SWaP considerably, makes it feasible that the LEO-to-GEO communication can be implemented in a small satellite for the first time. While utilizing laser communication can increase the data rate, the relay communication via the GEO satellite helps the small satellite to extend the communication duration significantly. Moreover, since there is a line of sight between the two terminals in any of about 15 orbits per day of the LEO satellite, data taken by the small satellite can be downloaded to the ground via the GEO one in almost real time. This research aims at investigating and proving the feasibility of a small satellite to transmit a laser communication link to its GEO counterpart. In this paper, we describe the LEO-to-GEO laser communication of the small satellite with a study of pointing-budget and link-budget analysis. Furthermore, a hardware-based simulation of the fine control mechanism is conducted. The hysteresis that affects severely to the piezo mechanism, and hence, the final control accuracy, is modeled accurately and its effect is shown.