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The amount of satellite energy acquired has a direct impact on operational capacities of the satellite. As for practical high functional density microsatellites, solar tracking guidance design of solar panels plays an extremely important role. Targeted at stationary tracking problems incurred in a new system that utilizes panels mounted in the two-dimensional turntable to acquire energies to the greatest extent, a two-dimensional solar tracking stationary guidance method based on feature-based time series was proposed under the constraint of limited satellite attitude coupling control capability. By analyzing solar vector variation characteristics within an orbit period and solar vector changes within the whole life cycle, such a method could be adopted to establish a two-dimensional solar tracking guidance model based on the feature-based time series to realize automatic switching of feature-based time series and stationary guidance under the circumstance of different ^{∘} and below under the integrated constraints, which meet engineering application requirements.

As microsatellites are featured with being light, small, smart, and cheap, they not only have become the research hotspot of satellite technology development and application, but are growing towards a direction of high functional density and practical applications. In order to adapt to multitype tasks and diversified applications, the requirement for higher payload power appropriate for high functional density microsatellites has been increasingly intense for the consideration of higher cost performance, rapid deployment, and extensive applicability. However, energy maximization must be taken into account with an aim to make microsatellites applied in high-power loads. Specific to application characteristics of microsatellites cluster or network, the scheme of energy maximization should be universal. Especially for the typical nonsolar synchronous inclined orbits such as Globalstar system, the solar panels adopting a solar tracking revolving mechanism is the only approach to solving energy acquisition issues provided that the platform itself remains an earth-oriented demand.

In order to maximize the output power improving the efficiency, many methods and devices of sun tracking and maximum power point tracking were proposed, which belong to the special issue of solar energy application in ground photovoltaic systems. There are some fuzzy techniques that were proposed in photovoltaic systems [

For satellite, the maximum energy acquisition purpose is the same that is achieved generally by solar array drive assembly (SADA). As the microsatellites pursue a high performance-price ratio strictly limiting development costs, it is impossible to select expensive SADA with slip ring. The light-small two-dimensional turntable could be used to carry the solar panels to realize solar tracking. For the convenience of open-loop control, stepping motor was utilized as a drive element. Nevertheless, the stepping motor still has some shortcomings such as poor dynamic behavior, high pulse step overshoot, and great rate ripple, and it is a nonnegligible interference source as far as satellites with a high requirement for attitude stabilization, such as earth observation satellites. Now, satellite rotating mechanism has been extensively investigated at home and abroad, covering mechanism models, ground-based validation, controller design, and attitude control coupling [

Solving the problem related to rotating mechanism motion stability of solar panels is a key to guaranteeing high pointing accuracy and high attitude stabilization of satellites. Factors that affect rotating mechanism motion stability can be elaborated from the following two aspects. Firstly, cogging torque of the stepping motor leads to instability of control, which can be resolved by means of compensation, and research on this issue has been relatively mature. SPOT satellite of France adopts a great subdivision sine/cosine driving strategy and an accelerometer to measure perturbed moment and implement compensation [

A solar tracking stationary guidance method based on feature-based time series was proposed under the background of microsatellite solar panels loaded with two-dimensional turntable. Through phase division for time within an orbit period, the target velocity was divided into several segments of steady speeds, so as to solve guidance input instability problems and substantially reduce variable speed control. The high-stability and small-disturbance control of the two-dimensional turntable can be fulfilled.

Concerning a microsatellite that adopts orbital inclination of 55^{∘}, ^{∘} and

Specific to the microsatellite characteristics, when ^{∘} inclined orbit, such a phenomenon exists within a period long enough to incur unbalanced satellite energy supply making the entire satellite unable to run normally. Resultantly, two-dimensional rotation must be conducted to realize solar tracking orientation of the panels under the circumstance that earth-oriented status of the satellite is maintained, which is able to maximize energy acquired. As the two-dimensional turntable is employed, 360-degree continuous rotation cannot be completed; thus an appropriate two-dimensional solar tracking stationary guidance strategy should be formed to guarantee that the satellite can acquire enough energies for operation in a condition of different

The two-dimensional turntable mechanism makes use of a stepping motor. Without loss of generality, friction moment, fluctuating moment, cogging torque, and mechanism dynamics were taken into account, while mutual induction winding, high-order harmonic torque, and external disturbance torque of the motor were ignored. Based on a cogging moment compensation method, velocity stability of the turntable could be improved. In addition, it has been assumed that the angular velocity of the turntable can be matched with the guidance input.

With regard to the microsatellite, area of its solar panels unfolded is very large so that it is able to occlude payload or sensor field of view of its planes ^{∘} dependent on physical design outcomes.

Due to the influence of the capacity possessed by an actuator selected for the microsatellite, the maximum angular velocity and the maximum angular acceleration of the turntable should be no more than 0.2^{∘}/s and 0.01^{∘}/

Within the range of limited maximum rotation angle denoted as ^{∘}

Not only can solar vector be acquired by an on-board sun sensor or obtained through calculations based on sun ephemeris, but its expression in an orbital coordinate system is obtained in line with an attitude transformation relation.

In conformity with input and constraint conditions, feature-based time series and angle/angular velocity series required by turntable control can be autonomously calculated to form target angles and angular velocities controlling the turntable in diverse time points. These series consist of pitching direction control time series

Time series is a set of variables ordered chronically and the solar tracking angular relation can be described by multiple time series in one orbit. Therefore, characteristic time points should be selected to form time series for guidance implementation. Then, guidance requirement of the specified accuracy is fulfilled through density control over the series.

Design purpose of the two-dimensional solar tracking stationary guidance law is to guarantee maximization of energies acquired by the solar panels under constraints.

Under constraint described in Section

A schematic diagram of solar panels optimal pointing under constraints.

When the satellite is in a light region, solar tracking guidance strategy of the panels can be illustrated as follows. On one hand, while the solar vector is within a constrained conical plane formed by the maximum rotation angle of the solar panels principal axis, the panel can track the sun, which is referred to as sun-oriented; on the other hand, if the solar vector is outside the constrained conical plane described above, solar panels can track projection of the solar vector on the conical plane, which is known as quasi-sun-oriented.

When the satellite is in a shadow region, solar tracking of panels principal axis has no significance. Considering this, only a guidance strategy of “rotating to the symmetric position in constant speed via the shortest path” is proposed. In other words, when the satellite is in a shadow region, rotating mechanism of the solar panels rotates its principal axis to the pointing at the moment of moving out of the shadow region from that when it moves into the shadow region along the shortest path. As azimuth pointing of the solar panels entering or exiting the shadow region is the complementary opposite number and the pointing and their pitch angle are identical, they are called symmetric positions.

By analyzing different temporal intervals, the included angle between sun pointing and zenith direction is the target attitude angle

Point 1 to 2, the light region,

Point 2 to 3, the light region,

Point 3 to 4, the shadow region,

Point 4 to 1, the light region,

To sum up, solar tracking guidance strategy of panels can be concluded as follows.

If

If

If

Subjected to synthetic constraint conditions described in Section

According to the constraint of angle tracking error should be no more than

To meet relevant synthetic constraint conditions, autonomous switching of feature-based time series was implemented for solar tracking of panels according to large and small

The difficulty of the two-dimensional rotation mode lies in constraints over angular velocity and angular acceleration. Besides, it is less likely for azimuth angular velocity across the zenith to meet demands if

Expression of solar vector in the orbital coordinate system is used to figure out the next time point when the sun moves across zenith of the satellite and the number of characteristic time points within an orbit period. Regarding the latter, it incorporates the maximum angular velocity equilibrium point, the maximum limited angle time point, and the light and shadow region demarcation time point. Then, time of one orbit is divided into several time slots according to characteristic time points to calculate the mean angular velocity under the circumstance that two points on both ends of each time slot remain consistent with the target attitude, to update the time series dependent on the calculated maximum angular acceleration, and to finally output time series and angular velocity series needed by the turntable. Moreover, time slots in the time series can be further segmented by means of dichotomy to increase the number of series subsections, so that angular accuracy in the entire guidance process can be improved.

As regards characteristic time points in the minimum feature-based time series, they can be computed in the following ways.

(1) Time point

(2) Maximum angular velocity equilibrium time point

(3) Maximum limited angle time point

(4) Light and shadow region demarcation time point

(5) Other time points are calculated by a symmetric method as follows:

Solar panels guidance procedure in a condition of large angle has been shown in Figure

Solar tracking of panels guidance process in the case of large angle.

Due to time point calculation error accumulation and that of angular deviation in a condition of angular velocity control, time points in the time series and angular velocities in angular velocity series should be corrected during execution of guidance strategy. While correction of time points was realized by updating covering time, angular velocities were corrected by actual turntable feedback angle recalculations of switching time points.

Under the circumstance of small

Solar tracking of panels guidance process in a condition of small angle.

Under the circumstance of one-dimensional rotation, the solar vector rotates within the orbital plane at a uniform velocity. Therefore, the sun-oriented pitch angular velocity can be calculated by the following equation.

Angular velocity of the shadow region means going back to the symmetric position within the time slot of this region. In the one-dimensional condition, pitch angle of such a position is the limited angle. For pitch angular velocity of the shadow region, it can be figured out by the following equation.

Under constraint described in Section

Two-dimensional pointing situations under limited angle constraint based on a pattern partition strategy.

If

In terms of the guidance strategy design based on feature-based time series, time of an orbit period was divided into seven segments according to seven characteristic time points under the circumstance that switching point of two modes was

Comparison between guidance based on feature-based time series and sun-oriented guidance.

Figure

Additionally, matching between angles at both ends of each sequence can ensure that angle errors of the entire orbit cannot accumulate. Meanwhile, error precision of the angle can be improved along with the increase in density of the time series.

Based on joint debugging of MATLAB/Simulink and STK, joint simulation was conducted for guidance law design. While a guidance law calculation generation model, a turntable control model, and a turntable output model were all constructed by Simulink, STK played a role in analog input and solar tracking situation visualization when utilized to output real-time orbit and on-board time. Through calculations of real-time data, real-time tracking conditions were observed to obtain angle errors of solar tracking subjected to a guidance strategy, as shown in Figures

Guidance error in a condition of small

Guidance error in a condition of large

A one-dimensional solar tracking pattern was utilized under the circumstance of small

A two-dimensional solar tracking pattern was utilized under the circumstance of large angle. Errors are incurred in the actual velocity and averaged velocity between tracking points of diverse segments. Moreover, such errors arrive at their maximum values as the azimuth angle crosses zero. In the case that

Solar panels fail to reach their target angle physically because of limited angle constraints, which produces the maximum value of angle error denoted as

In order to verify the validity of the proposed method, physical system verification was carried on, which was composed of the on-board computer, power supply, and two-dimensional turntable. The sun vector was taken by recursive calculation, and the guidance data was calculated by the on-board computer according to former method. The rotation of the turntable was controlled to achieve the sun-oriented mode. The turntable was designed for a certain type of microsatellite, and its physical picture has been shown in Figure

Two-dimensional turntable physical picture.

The main performance of the turntable has been shown in Table

Main performance of the turntable.

Item | Value |
---|---|

Range of rotation angle | Azimuth angle: |

Range of stationary tracking angular velocity | |

Maximum tracking angular acceleration | No less than |

Minimum tracking angular acceleration | No more than |

Stabilization of dynamic tracking rotation angular velocity | Better than |

Based on the microsatellite orbital characteristics, two modes of large and small

Comparison between turntable output attitude and solar tracking attitude under the circumstance of large

Under the circumstance of large and small

Comparison between turntable output attitude and solar tracking attitude under the circumstance of large

There was a small deviation between the turntable two-dimensional angle and sun-oriented direction during execution of guidance strategy, which could guarantee the acquisition of satellite energy. The composition angular deviation of sun-oriented direction has been shown in Figure

Angular deviation between turntable output attitude and the solar tracking attitude under the circumstance of large

The temporal interval between 2000 s and 4000 s in Figure

A stationary low disturbance solar tracking guidance method applicable to two-dimensional solar panels was proposed to realize enough energy acquisition based on the microsatellite platform. Moreover, it supports payload power consumption demands required by multitype tasks performed by the microsatellite, such as space-based space surveillance, earth observation, navigation enhancement, and low-orbit communication, which fills in the gap of solutions to engineering applications of the microsatellite in two-dimensional solar panels and provides new ideas for replacement of the traditional SADA with two-dimensional turntable. Simulation results demonstrate that such a method has the potential to effectively improve guidance stability of the turntable. Therefore, it is a valid solution to solar tracking stationary guidance problems of microsatellite panels.

Segmental and autonomous switching modes were utilized to extract time series within the satellite orbit period according to feature points for the purpose of guidance planning. Moreover, patterns and time series lengths can be autonomously switched in line with the current positional relations with the sun so as to form two-dimensional solar tracking guidance laws in the period.

The guidance method proposed is not only applicable to diverse near-earth orbits of different orbital inclination, but able to guarantee the solar tracking accuracy of the panels to be below

The authors declare that they have no conflicts of interest.