Indirect Measurement of Rotor Dynamic Imbalance for Control Moment Gyroscopes via Gimbal Disturbance Observer
<p>Schematics of SGCMG and rotor imbalance. (<b>a</b>) SGCMG; (<b>b</b>) Rotor imbalance.</p> "> Figure 2
<p>Design procedure of gimbal disturbance observer. (<b>a</b>) Observer design in theory; (<b>b</b>) observer with virtual measurement; (<b>c</b>) practical observer without the calculation of the differential <math display="inline"> <semantics> <mover accent="true"> <mi>ω</mi> <mo>˙</mo> </mover> </semantics> </math>.</p> "> Figure 2 Cont.
<p>Design procedure of gimbal disturbance observer. (<b>a</b>) Observer design in theory; (<b>b</b>) observer with virtual measurement; (<b>c</b>) practical observer without the calculation of the differential <math display="inline"> <semantics> <mover accent="true"> <mi>ω</mi> <mo>˙</mo> </mover> </semantics> </math>.</p> "> Figure 3
<p>Amplitude–frequency characteristics of <span class="html-italic">G</span>(<span class="html-italic">s</span>).</p> "> Figure 4
<p>Frequency characteristics of <span class="html-italic">G</span><sub>1</sub>(<span class="html-italic">s</span>).</p> "> Figure 5
<p>Frequency characteristics of <span class="html-italic">G</span><sub>3</sub>(s).</p> "> Figure 6
<p>Block diagram of disturbance observer and gimbal servo system.</p> "> Figure 7
<p>Structure of semi-physical experiment platform.</p> "> Figure 8
<p>Experimental curves when <span class="html-italic">Ω</span> = 3000 r/min. (<b>a</b>) gimbal speed <span class="html-italic">ω</span>; (<b>b</b>) electromagnetic torque <span class="html-italic">T<sub>e</sub>;</span> (<b>c</b>) estimate of <span class="html-italic">T<sub>dz</sub></span>; (<b>d</b>) estimate of <span class="html-italic">u<sub>d</sub></span>; (<b>e</b>) estimate of <span class="html-italic">x</span><sub>3</sub>; (<b>f</b>) estimate of <span class="html-italic">d</span>.</p> "> Figure 8 Cont.
<p>Experimental curves when <span class="html-italic">Ω</span> = 3000 r/min. (<b>a</b>) gimbal speed <span class="html-italic">ω</span>; (<b>b</b>) electromagnetic torque <span class="html-italic">T<sub>e</sub>;</span> (<b>c</b>) estimate of <span class="html-italic">T<sub>dz</sub></span>; (<b>d</b>) estimate of <span class="html-italic">u<sub>d</sub></span>; (<b>e</b>) estimate of <span class="html-italic">x</span><sub>3</sub>; (<b>f</b>) estimate of <span class="html-italic">d</span>.</p> "> Figure 9
<p>Experimental curves when <span class="html-italic">Ω</span> = 6000 r/min. (<b>a</b>) gimbal speed <span class="html-italic">ω</span>; (<b>b</b>) electromagnetic torque <span class="html-italic">T<sub>e</sub>;</span> (<b>c</b>) estimate of <span class="html-italic">T<sub>dz</sub></span>; (<b>d</b>) estimate of <span class="html-italic">u<sub>d</sub></span>; (<b>e</b>) estimate of <span class="html-italic">x</span><sub>3</sub>; (<b>f</b>) estimate of <span class="html-italic">d</span>.</p> "> Figure 9 Cont.
<p>Experimental curves when <span class="html-italic">Ω</span> = 6000 r/min. (<b>a</b>) gimbal speed <span class="html-italic">ω</span>; (<b>b</b>) electromagnetic torque <span class="html-italic">T<sub>e</sub>;</span> (<b>c</b>) estimate of <span class="html-italic">T<sub>dz</sub></span>; (<b>d</b>) estimate of <span class="html-italic">u<sub>d</sub></span>; (<b>e</b>) estimate of <span class="html-italic">x</span><sub>3</sub>; (<b>f</b>) estimate of <span class="html-italic">d</span>.</p> "> Figure 10
<p>Experimental curves when <span class="html-italic">Ω</span> = 9000 r/min. (<b>a</b>) gimbal speed <span class="html-italic">ω</span>; (<b>b</b>) electromagnetic torque <span class="html-italic">T<sub>e</sub>;</span> (<b>c</b>) estimate of <span class="html-italic">T<sub>dz</sub></span>; (<b>d</b>) estimate of <span class="html-italic">u<sub>d</sub></span>; (<b>e</b>) estimate of <span class="html-italic">x</span><sub>3</sub>; (<b>f</b>) estimate of <span class="html-italic">d</span>.</p> "> Figure 10 Cont.
<p>Experimental curves when <span class="html-italic">Ω</span> = 9000 r/min. (<b>a</b>) gimbal speed <span class="html-italic">ω</span>; (<b>b</b>) electromagnetic torque <span class="html-italic">T<sub>e</sub>;</span> (<b>c</b>) estimate of <span class="html-italic">T<sub>dz</sub></span>; (<b>d</b>) estimate of <span class="html-italic">u<sub>d</sub></span>; (<b>e</b>) estimate of <span class="html-italic">x</span><sub>3</sub>; (<b>f</b>) estimate of <span class="html-italic">d</span>.</p> ">
Abstract
:1. Introduction
2. Mathematical Model and Problem Formulation
2.1. Rotor Mass Imbalance
2.2. Gimbal Servo System with Dynamic Imbalance Torque
2.3. Problem Formulation
3. Indirect Measurement of Rotor Dynamic Imbalance
3.1. Disturbance Model
3.2. Gimbal Disturbance Observer Design
3.3. Observer Convergence Analysis
3.4. Gain Tuning Guidelines
3.5. Discussions
4. Experimental Results
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Xu, X.B.; Chen, S.; Liu, J.H. Elimination of harmonic force and torque in active magnetic bearing systems with repetitive control and notch filters. Sensors 2017, 17, 763. [Google Scholar] [CrossRef] [PubMed]
- Cui, P.L.; Zhang, H.J.; Yan, N.; Fang, J.C. Performance testing of a magnetically suspended double gimbal control moment Gyro based on the single axis air bearing table. Sensors 2012, 12, 9129–9145. [Google Scholar] [CrossRef] [PubMed]
- Mackunis, W.; Leve, F.; Patre, P.M.; Fitz-Coy, N.; Dixon, W.E. Adaptive neural network-based satellite attitude control in the presence of CMG uncertainty. Aerosp. Sci. Technol. 2016, 54, 218–228. [Google Scholar] [CrossRef]
- Bhat, S.P.; Tiwari, P.K. Controllability of spacecraft attitude using control moment Gyroscopes. IEEE Trans. Autom. Control 2009, 54, 585–590. [Google Scholar] [CrossRef]
- Heiberg, C.J. A practical approach to modeling single-gimbal control momentum Gyroscopes in agile spacecraft. In Proceedings of the AIAA Guidance, Navigation, and Control Conference, Denver, CO, USA, 14–17 August 2000. [Google Scholar]
- Kusuda, Y.; Takahashi, M. Feedback control with nominal inputs for satellites using control moment Gyros. J. Guid. Control Dyn. 2011, 34, 1209–1218. [Google Scholar] [CrossRef]
- Heiherg, C.J.; Bailey, D.; Wie, B. Precision pointing control of agile spacecraft using single gimbal control Gyroscopes. In Proceedings of the AIAA Guidance, Navigation, and Control Conference, New Orleans, LA, USA, 11–13 August 1997. [Google Scholar]
- Zhang, Y.; Xu, S.J. Vibration isolation platform for control moment Gyroscopes on satellites. J. Aerosp. Eng. 2012, 25, 641–652. [Google Scholar] [CrossRef]
- Li, S.S.; Zhong, M.Y. High precision disturbance compensation for a three-axis Gyro-stabilized camera mount. IEEE/ASME Trans. Mechatron. 2015, 20, 3135–3147. [Google Scholar] [CrossRef]
- Lu, M.; Hu, Y.W.; Wang, Y.G.; Li, G.; Wu, D.Y.; Zhang, J.Y. High precision control design for SGCMG gimbal servo system. In Proceedings of the IEEE International Conference on Advanced Intelligent Mechatronics (AIM), Busan, Korea, 7–11 July 2015. [Google Scholar]
- Peng, C.; Fan, Y.H.; Huang, Z.Y.; Fang, J.C. Frequency-varying synchronous micro-vibration suppression for a MSFW with application of small-gain theorem. Mech. Syst. Signal Process. 2017, 82, 432–447. [Google Scholar] [CrossRef]
- Wei, Z.J.; Li, D.X.; Luo, Q.; Jiang, J.P. Performance analysis of a flywheel microvibration isolation platform for spacecraft. J. Spacecr. Rockets 2015, 52, 1263–1268. [Google Scholar] [CrossRef]
- Luo, Q.; Li, D.X.; Jiang, J.P. Analysis and optimization of microvibration isolation for multiple flywheel systems of spacecraft. AIAA J. 2016, 54, 1719–1731. [Google Scholar] [CrossRef]
- Zhang, Y.; Li, M.; Song, Z.Y.; Shan, J.J.; Guan, X.; Tang, L. Design and analysis of a moment control unit for agile satellite with high attitude stability requirement. Acta Astronaut. 2016, 122, 90–105. [Google Scholar] [CrossRef]
- Zhang, Y.; Zhang, J.R. Disturbance characteristics analysis of CMG due to imbalance and installation Errors. IEEE Trans. Aerosp. Electron. Syst. 2014, 50, 1017–1026. [Google Scholar] [CrossRef]
- Zheng, S.Q.; Feng, R. Feedforward compensation control of rotor imbalance for high-speed magnetically suspended centrifugal compressors using a novel adaptive notch filter. J. Sound Vib. 2016, 366, 1–44. [Google Scholar] [CrossRef]
- Luo, Q.; Li, D.X.; Zhou, W.Y.; Jiang, J.P.; Yang, G.; Wei, X.S. Dynamic modeling and observation of micro-vibrations generated by a Single Gimbal Control Moment Gyro. J. Sound Vib. 2013, 332, 4496–4516. [Google Scholar] [CrossRef]
- Luo, Q.; Li, D.X.; Zhou, W.Y. Studies on vibration isolation for a multiple flywheel system in variable configurations. J. Vib.Control 2013, 21, 105–123. [Google Scholar] [CrossRef]
- Zhang, Y.; Li, M.; Zhang, J.R. Vibration control for rapid attitude stabilization of spacecraft. IEEE Trans. Aerosp. Electron. Syst. 2017, 53, 1308–1320. [Google Scholar] [CrossRef]
- Zhou, W.Y.; Li, D.X.; Luo, Q.; Liu, K. Analysis and testing of microvibration produced by momentum wheel assemblies. Chin. J. Aeronaut. 2012, 25, 640–649. [Google Scholar] [CrossRef]
- Lee, J. Theoretical and experimental motion analysis of self-compensating dynamic balancer. KSME J. 1995, 9, 167–176. [Google Scholar] [CrossRef]
- Wang, Q.X.; Wang, F. A new vibration mechanism of balancing machine for satellite-borne spinning rotors. Chin. J. Aeronaut. 2014, 27, 1318–1326. [Google Scholar] [CrossRef]
- Liu, C.; Liu, G. Field dynamic balancing for rigid rotor-AMB system in a magnetically suspended flywheel. IEEE/ASME Trans. Mechatron. 2016, 21, 1140–1150. [Google Scholar] [CrossRef]
- Fang, J.C.; Wang, Y.G.; Han, B.C.; Zheng, S.Q. Field balancing of magnetically levitated rotors without trial weights. Sensors 2013, 13, 16000–16022. [Google Scholar] [CrossRef]
- Xu, X.B.; Chen, S. Field balancing and harmonic vibration suppression in rigid AMB-rotor system with rotor imbalances and sensor runout. Sensors 2015, 15, 21876–21897. [Google Scholar] [CrossRef] [PubMed]
- Xu, X.B.; Chen, S.; Zhang, Y.N. Automatic balancing of AMB systems using plural notch filter and adaptive synchronous compensation. J. Sound Vib. 2016, 374, 29–42. [Google Scholar] [CrossRef]
- Peng, C.; Fang, J.C.; Xu, X.B. Mismatched disturbance rejection control for voltage-controlled active magnetic bearing via state-space disturbance observer. IEEE Trans. Power Electron. 2015, 30, 2753–2762. [Google Scholar] [CrossRef]
- Noshadi, A.; Shi, J.; Lee, W.S.; Shi, P.; Kalam, A. Repetitive disturbance observer-based control for an active magnetic bearing system. In Proceedings of the 2015 5th Australian Control Conference (AUCC), Gold Coast, Australia, 5–6 November 2015. [Google Scholar]
- Inoue, T.; Liu, J.; Ishida, Y.; Yoshimura, Y. Vibration control and unbalance estimation of a nonlinear rotor system using disturbance observer. J. Vib. Acoust. 2009, 131, 031010. [Google Scholar] [CrossRef]
- Wu, Z.; Lyu, H.T.; Shi, Y.L.; Shi, D. On stability of open-loop operation without rotor information for brushless DC motors. Math. Probl. Eng. 2014, 2014, 740498. [Google Scholar] [CrossRef]
Gimbal | Rotor | ||
---|---|---|---|
Pole pairs | 6 | Pole pairs | 8 |
Rated voltage | 45 V (DC) | Rated voltage | 45 V (DC) |
Maximal speed | 21 r/min | Maximal speed | 10,000 r/min |
Speed set point for test | 1°/s | Speed set point for test | 3000/6000/9000 r/min |
Torque constant | 1.435 Nm/A | Torque constant | 0.035 Nm/A |
Phase resistance | 1.3 Ω | Phase resistance | 0.5 Ω |
Phase inductance | 6.5 mH | Phase inductance | 0.1 mH |
Inertia | 0.082 kg·m2 | Inertia | 0.039 kg·m2 |
Friction coefficient | 0.001 Nm | Dynamic imbalance | 1.2 g·cm2 |
Rotor Speed | Mean Value | Standard Deviation |
---|---|---|
3000 rpm | 1.1984 g·cm2 | 0.0023 g·cm2 |
6000 rpm | 1.2003 g·cm2 | 0.0007 g·cm2 |
9000 rpm | 1.1991 g·cm2 | 0.0006 g·cm2 |
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Huang, L.; Wu, Z.; Wang, K. Indirect Measurement of Rotor Dynamic Imbalance for Control Moment Gyroscopes via Gimbal Disturbance Observer. Sensors 2018, 18, 1873. https://doi.org/10.3390/s18061873
Huang L, Wu Z, Wang K. Indirect Measurement of Rotor Dynamic Imbalance for Control Moment Gyroscopes via Gimbal Disturbance Observer. Sensors. 2018; 18(6):1873. https://doi.org/10.3390/s18061873
Chicago/Turabian StyleHuang, Liya, Zhong Wu, and Kan Wang. 2018. "Indirect Measurement of Rotor Dynamic Imbalance for Control Moment Gyroscopes via Gimbal Disturbance Observer" Sensors 18, no. 6: 1873. https://doi.org/10.3390/s18061873
APA StyleHuang, L., Wu, Z., & Wang, K. (2018). Indirect Measurement of Rotor Dynamic Imbalance for Control Moment Gyroscopes via Gimbal Disturbance Observer. Sensors, 18(6), 1873. https://doi.org/10.3390/s18061873