Spacecraft Angular Rates Estimation with Gyrowheel Based on Extended High Gain Observer
Abstract
:1. Introduction
2. Descriptions of Gyrowheel
Gyrowheel Physical Structure
3. Gyrowheel Mathematical Modeling
3.1. Gyrowheel Coordinates and Frames
3.2. Gyrowheel Kinematic Equations
3.3. Gyrowheel Dynamic Equations
3.4. Relationship between the Unmeasurable Variables and the Measurable Variables
3.5. Description of Angular Rates Estimation Problem Using Gyrowheel State Equation
- (1)
- The errors caused by the linearization of nonlinear equations of GW in large tilt angles can be avoided.
- (2)
- The problem of dynamic drift error compensation existing both traditional mechanic gyroscopes [14] and GW can be solved by the above derivation and the following application of full dynamical model in angular rates estimation.
- (3)
- The initial iteration error accumulation of the calculated angular rates of the spacecraft, caused by the angular acceleration () in the term , is eliminated by the real-time estimation of the term.
- (4)
- The amplification of measurement noise by the multi-difference of measured tilt angles with measurement noise can be weakened by appropriately choosing the design parameters of HGO [15].
4. Gyrowheel High Gain Observer for Angular Rates Estimation
4.1. Gyrowheel High Gain Observer Design
4.2. EHGO Error Convergence Proof
4.3. Influence Analysis of Measurement Noise
5. Simulation
6. Conclusions
- (1)
- A complete dynamical model of GW is built with chosen generalized coordinates () by Lagrange’s Method, and since the generalized coordinates () and its derivatives in the GW dynamical model are unmeasurable, the relationships between the unmeasurable generalized coordinates and the measurable variables () by sensors are derived to construct the nonlinear state equation expressed by measurable variables for the spacecraft rate estimations with the GW.
- (2)
- The affine nonlinear state equation of GW and measurement equation are built based on the contribution (1). Combining the affine nonlinear state equation with measurement equation and extending the relevant terms of spacecraft angular rates as states, a high gain observer is designed to estimate the relevant terms of the spacecraft angular rates. Through solving the known differential equation, the spacecraft angular rates can be calculated.
- (3)
- The stability of the designed EHGO in contribution (2) is proved by Lyapunov’s stability theory, and the effects of the design parameter ε and measurement noise on the estimation accuracy are also analyzed.
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
GW7 | Gyrowheel |
ACS | Attitude control system |
HGO | High gain observer |
EHGO | Extended high gain observer |
CMG | Control moment gyroscope |
MSDGCMG | Magnetically suspended double-gimbal control moment gyroscope |
AMBs | Active magnetic bearings |
DOF | Degrees of freedom |
SINS | Strapdown inertial navigation system |
DTG | Dynamically tuned gyroscope |
VSDGCMG | Variable speed control moment gyroscope |
Appendix A
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Parameter Name | Value |
---|---|
Rotor transverse-axis inertia | kg · m2 |
Rotor spin-axis inertia | kg · m2 |
Gimbal transverse-axis inertia | kg · m2 |
Gimbal spin-axis inertia | kg · m2 |
Torsion Spring Stiffness | |
Torsion Spring damping | 0 Nm/(rad/s) |
Spacecraft Inertia | kg · m2 |
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Liu, X.; Yao, Y.; Ma, K.; Zhao, H.; He, F. Spacecraft Angular Rates Estimation with Gyrowheel Based on Extended High Gain Observer. Sensors 2016, 16, 537. https://doi.org/10.3390/s16040537
Liu X, Yao Y, Ma K, Zhao H, He F. Spacecraft Angular Rates Estimation with Gyrowheel Based on Extended High Gain Observer. Sensors. 2016; 16(4):537. https://doi.org/10.3390/s16040537
Chicago/Turabian StyleLiu, Xiaokun, Yu Yao, Kemao Ma, Hui Zhao, and Fenghua He. 2016. "Spacecraft Angular Rates Estimation with Gyrowheel Based on Extended High Gain Observer" Sensors 16, no. 4: 537. https://doi.org/10.3390/s16040537
APA StyleLiu, X., Yao, Y., Ma, K., Zhao, H., & He, F. (2016). Spacecraft Angular Rates Estimation with Gyrowheel Based on Extended High Gain Observer. Sensors, 16(4), 537. https://doi.org/10.3390/s16040537