0
Research Papers

Switching Antiwindup Design on Enlarging the Domain of Attraction for a Supercavitating Vehicle Subject to Actuator Saturation

[+] Author and Article Information
Baochen Qiang

32nd Institute of China Electronics Technology
Group Corporation,
Shanghai 200233, China
e-mail: nxb000@sina.com

Zhang Le

Equipment Engineering Department,
Shenyang Ligong University,
Shenyang 110168, China
e-mail: zhanglesylu@sina.com

1B. Qiang and L. Zhang contributed equally to this work.

2Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 3, 2016; final manuscript received February 12, 2017; published online June 5, 2017. Assoc. Editor: Tesheng Hsiao.

J. Dyn. Sys., Meas., Control 139(9), 091010 (Jun 05, 2017) (12 pages) Paper No: DS-16-1284; doi: 10.1115/1.4036230 History: Received June 03, 2016; Revised February 12, 2017

This paper presents a new switching antiwindup compensation design to maximize the domain of attraction for a supercavitating vehicle subject to actuator saturation. The dive-plane dynamics of the vehicle are considered. By applying the linear differential inclusion expression of saturated feedbacks, conditions under which the compensator locally stabilizes the closed-loop system are then derived. The design of antiwindup gains on maximizing the system's domain of attraction is finally formulated and solved as an iterative optimization problem with linear matrix inequality constraints. Simulations are conducted for systems with magnitude and rate limits to evaluate the effectiveness of the proposed method.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Dzielski, J. , and Kurdila, A. , 2003, “ A Benchmark Control Problem for Supercavitating Vehicles and an Initial Investigation of Solutions,” J. Vib. Control, 9(7), pp. 791–804. [CrossRef]
Kulkarni, S. S. , and Pratap, R. , 2000, “ Studies on the Dynamics of a Supercavitating Projectile,” Appl. Math. Modell., 24(2), pp. 113–129. [CrossRef]
Kirschner, I. N. , Kring, D. C. , Stokes, A. W. , Fine, N. E. , and Uhlman, J. S. , 2002, “ Control Strategies for Supercavitating Vehicles,” J. Vib. Control, 8(2), pp. 219–242. [CrossRef]
Lin, G. , Balachandran, B. , and Abed, E. H. , 2007, “ Nonlinear Dynamics and Bifurcations of a Supercavitating Vehicle,” IEEE J. Oceanic Eng., 32(4), pp. 753–761. [CrossRef]
Nguyen, V. , 2011, “ Dynamics and Control of Non-Smooth Systems With Applications to Supercavitating Vehicles,” Ph.D. thesis, University of Maryland, College Park, MD.
Saranjam, B. , 2013, “ Experimental and Numerical Investigation of an Unsteady Supercavitating Moving Body,” Ocean Eng., 59, pp. 9–14. [CrossRef]
Mao, X. , and Wang, Q. , 2009, “ Nonlinear Control Design for a Supercavitating Vehicle,” IEEE Trans. Control Syst. Technol., 17(4), pp. 816–832. [CrossRef]
Vanek, B. , Bokor, J. , Balas, G. J. , and Arndt, R. E. , 2007, “ Longitudinal Motion Control of a High-Speed Supercavitation Vehicle,” J. Vib. Control, 13(2), pp. 159–184. [CrossRef]
Balas, G. J. , Bokor, J. , Vanek, B. , and Arndt, R. E. , 2006, “ Control of High-Speed Underwater Vehicles,” Control of Uncertain Systems: Modelling, Approximation, and Design, Springer, Berlin, pp. 25–44.
Lin, G. , Balachandran, B. , and Abed, E. H. , 2006, “ Nonlinear Dynamics and Control of Supercavitating Bodies,” AIAA Paper No. 2006-6445.
Lin, G. , Balachandran, B. , and Abed, E. H. , 2008, “ Dynamics and Control of Supercavitating Vehicles,” ASME J. Dyn. Syst. Meas. Control, 130(2), p. 021003. [CrossRef]
Qiang, B. , Han, Y. , Sun, Y. , and Bai, T. , 2014, “ Absolute Stability Control of Supercavitating Vehicles Based on Backstepping,” IEEE International Conference on Mechatronics and Automation (ICMA), Tianjin, China, Aug. 3–6, pp. 1918–1923.
Lin, G. , Balachandran, B. , and Abed, E. H. , 2010, “ Absolute Stability of Second-Order Systems With Asymmetric Sector Boundaries,” IEEE Trans. Autom. Control, 55(2), pp. 458–463. [CrossRef]
Mao, X. , and Wang, Q. , 2006, “ Nonlinear Robust Control Design for a Supercavitating Vehicle,” ASME Paper No. IMECE2006-14519.
Mao, X. , and Wang, Q. , 2013, “ Adaptive Control Design for a Supercavitating Vehicle Model Based on Fin Force Parameter Estimation,” J. Vib. Control, 21(6), pp. 1220–1233. [CrossRef]
Mao, X. , and Wang, Q. , 2011, “ Delay-Dependent Control Design for a Time-Delay Supercavitating Vehicle Model,” J. Vib. Control, 17(3), pp. 431–448. [CrossRef]
Hassouneh, M. A. , Nguyen, V. , Balachandran, B. , and Abed, E. H. , 2013, “ Stability Analysis and Control of Supercavitating Vehicles With Advection Delay,” ASME J. Comput. Nonlinear Dyn., 8(2), p. 021003. [CrossRef]
Mirzaei, M. , Eghtesad, M. , and Alishahi, M. M. , 2015, “ Planing Force Identification in High-Speed Underwater Vehicles,” J. Vib. Control, 22(20), pp. 4176–4191. [CrossRef]
Xinhua, Z. , Yao, S. , Zengkun, Q. , and Minyan, H. , 2016, “ Catastrophe Characteristics and Control of Pitching Supercavitating Vehicles at Fixed Depths,” Ocean Eng., 112, pp. 185–194. [CrossRef]
Kothare, M. V. , Campo, P. J. , Morari, M. , and Nett, C. N. , 1994, “ A Unified Framework for the Study of Anti-Windup Designs,” Automatica, 30(12), pp. 1869–1883. [CrossRef]
Hu, T. , and Lin, Z. , 2001, Control Systems With Actuator Saturation: Analysis and Design, Birkhäuser, Boston, MA.
Sanabria, D. E. , Balas, G. , and Arndt, R. , 2015, “ Modeling, Control, and Experimental Validation of a High-Speed Supercavitating Vehicle,” IEEE J. Oceanic Eng., 40(2), pp. 362–373. [CrossRef]
Kuklinski, R. , Castano, J. , and Henoch, C. , 2001, “ Experimental Study of Ventilated Cavities on Dynamic Test Model,” 4th International Symposium on Cavitation (CAV2001), Pasadena, CA, June 20–23.
Kuklinski, R. , Fredette, A. , Henoch, C. , and Castano, J. , 2006, “ Experimental Studies in the Control of Cavitating Bodies,” AIAA Paper No. 2006-6443.
Vanek, B. , Balas, G. J. , and Arndt, R. E. , 2010, “ Linear, Parameter-Varying Control of a Supercavitating Vehicle,” Control Eng. Practice, 18(9), pp. 1003–1012. [CrossRef]
Zhao, X.-H. , Sun, Y. , Zhao, G.-L. , and Fan, J.-L. , 2014, “ μ-Synthesis Robust Controller Design for the Supercavitating Vehicle Based on the BTT Strategy,” Ocean Eng., 88, pp. 280–288. [CrossRef]
Mao, X. , and Wang, Q. , 2011, “ Robust Adaptive Backstepping Control Design for a Supercavitating Vehicle Model,” ASME Paper No. DSCC2011-5906.
Zhang, L. , and Qiang, B. , 2015, “ Stability Analysis and Control Design of a Supercavitating Vehicle Subject to Actuator Saturation,” J. Mar. Sci. Technol. (in press).
Qiang, B. , and Zhang, L. , 2016, “ Output Feedback Control Design on Enlarging the Domain of Attraction for a Supercavitating Vehicle Subject to Actuator Saturation,” Inst. Meas. Control, Trans. (in press).
Cao, Y.-Y. , Zongli, L. , and Ward, D. G. , 2002, “ An Antiwindup Approach to Enlarging Domain of Attraction for Linear Systems Subject to Actuator Saturation,” IEEE Trans. Autom. Control, 47(1), pp. 140–145. [CrossRef]
Grimm, G. , Hatfield, J. , Postlethwaite, I. , Teel, A. R. , Turner, M. C. , and Zaccarian, L. , 2003, “ Antiwindup for Stable Linear Systems With Input Saturation: An LMI-Based Synthesis,” IEEE Trans. Autom. Control, 48(9), pp. 1509–1525. [CrossRef]
Hencey, B. , and Alleyne, A. , 2009, “ An Anti-Windup Technique for LMI Regions,” Automatica, 45(10), pp. 2344–2349. [CrossRef]
Mulder, E. F. , Kothare, M. V. , and Morari, M. , 2001, “ Multivariable Anti-Windup Controller Synthesis Using Linear Matrix Inequalities,” Automatica, 37(9), pp. 1407–1416. [CrossRef]
Sawada, K. , Kiyama, T. , and Iwasaki, T. , 2009, “ Generalized Sector Synthesis of Output Feedback Control With Anti-Windup Structure,” Syst. Control Lett., 58(6), pp. 421–428. [CrossRef]
Wu, F. , and Soto, M. , 2004, “ Extended Anti-Windup Control Schemes for LTI and LFT Systems With Actuator Saturations,” Int. J. Robust Nonlinear Control, 14(15), pp. 1255–1281. [CrossRef]
Lu, L. , and Lin, Z. , 2010, “ A Switching Anti-Windup Design Using Multiple Lyapunov Functions,” IEEE Trans. Autom. Control, 55(1), pp. 142–148. [CrossRef]
Li, Y. , and Lin, Z. , 2013, “ Design of Saturation-Based Switching Anti-Windup Gains for the Enlargement of the Domain of Attraction,” IEEE Trans. Autom. Control, 58(7), pp. 1810–1816. [CrossRef]
Logvinovich, G. V. , 1969, Hydrodynamics of Free-Boundary Flows, U.S. Naukova Dumka Publishing House, Kiev, Ukraine (in Russian).
Hassan, S. , 1999, “ Analysis of Hydrodynamic Planing Forces Associated With Cavity Riding Vehicles,” Naval Undersea Warfare Center Technical Memorandum, Newport, RI, Memo No. 990085.
Paryshev, E. V. , 2003, “ Mathematical Modeling of Unsteady Cavity Flows,” Fifth International Symposium on Cavitation (CAV), Osaka, Japan, Nov. 1–4, pp. 1–18.
Dzielski, J. E. , 2011, “ Longitudinal Stability of a Supercavitating Vehicle,” IEEE J. Oceanic Eng., 36(4), pp. 562–570. [CrossRef]
Nguyen, V. , and Balachandran, B. , 2011, “ Supercavitating Vehicles With Noncylindrical, Nonsymmetric Cavities: Dynamics and Instabilities,” ASME J. Comput. Nonlinear Dyn., 6(4), p. 041001. [CrossRef]
Boyd, S. , Ghaoui, L. E. , Feron, E. , and Balakrishnan, V. , 1994, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.
Qiang, B. , and Zhang, L. , 2016, “ Robust Dynamic Output Feedback Control for a Supercavitating Vehicle,” J. Syst.Control. Eng., (in press).

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of a supercavitating vehicle

Grahic Jump Location
Fig. 2

Relationship between the vertical speed and the planing force

Grahic Jump Location
Fig. 3

Saturation characteristics of satG(•)

Grahic Jump Location
Fig. 4

Convex polyhedron representations of a 2D saturated actuator

Grahic Jump Location
Fig. 5

Cross sections of E(PuncompensatedUOC) and E(PcompensatedUOC) at xc = 0

Grahic Jump Location
Fig. 6

Initial responses of the saturated system with and without the UOC based antiwindup compensator

Grahic Jump Location
Fig. 7

Cross sections of E(Psaturation) at xc = 0

Grahic Jump Location
Fig. 8

Initial responses of the system with and without the antiwindup compensator resulting from the saturation-oriented controller

Grahic Jump Location
Fig. 9

System state trajectories starting from the boundary of the estimated domain of attraction

Grahic Jump Location
Fig. 10

Initial responses of the system with and without the antiwindup compensator in the presence of magnitude limits only

Grahic Jump Location
Fig. 11

Initial responses of the system with and without the antiwindup compensator in the presence of magnitude and rate limits

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In