Design and experimental realization of a backstepping nonlinear H ∞ control for an autonomous underwater vehicle using a nonlinear matrix inequality approach
Restricted accessResearch articleFirst published online July, 2018
Design and experimental realization of a backstepping nonlinear H ∞ control for an autonomous underwater vehicle using a nonlinear matrix inequality approach
This paper focuses on the development of a nonlinear control (NHC) algorithm for an autonomous underwater vehicle (AUV) in the vertical plane. A three-degree-of-freedom AUV depth model is developed in terms of a nonlinear affine form which is used to design the control algorithm. The depth is controlled using a backstepping technique which generates a desired pitch angle for the NHC algorithm. The nonlinear control is designed using the -gain analysis which is transformed into a Hamilton–Jacobi–Isaacs (HJI) inequality. Further, the HJI inequality is presented in terms of a nonlinear matrix inequality structure in order to find a solution for the NHC problem using the concept of convex optimization. Hence, we desire to test the convex property of the nonlinear system before the realization of the control algorithm. The robust behaviour of the NHC algorithm is realized by ensuring the performance of the proposed control algorithm in the face of model and parameter uncertainties. A comparison between the NHC algorithm and the state-dependent Riccati equation is made in order to show the efficacy of the developed control algorithm. Furthermore, an experimental study of the proposed control scheme has been pursued to analyse the effectiveness of the developed control algorithm.
BallJAHeltonJWWalkerML (1993) H∞ control for nonlinear systems with output feedback. IEEE Transactions on Automatic Control38(4): 546–559.
2.
CaoJSuYZhaoJ (2011) Design of an adaptive controller for dive-plane control of a torpedo-shaped AUV. Journal of Marine Science and Application10(3): 333–339.
3.
CollinsEGSadhukhanDWatsonLT (1999) Robust controller synthesis via non-linear matrix inequalities. International Journal of Control72(11): 971–980.
4.
CristiRPapouliasFAHealeyAJ (1990) Adaptive sliding mode control of autonomous underwater vehicles in the dive plane. IEEE Journal of Oceanic Engineering15(3): 152–160.
5.
DantasJLda CruzJJde BarrosEA (2014) Study of autonomous underwater vehicle wave disturbance rejection in the diving plane. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment228(2): 122–135.
6.
DoyleJCGloverKKhargonekarPPet al. (1989) State-space solutions to standard H2 and H∞ control problems. IEEE Transactions on Automatic Control34(8): 831–847.
7.
FossenTI (1994) Guidance and Control of Ocean Vehicles. New York, NY: Wiley.
8.
HongEYSoonHGChitreM (2010) Depth control of an autonomous underwater vehicle, STARFISH. In: IEEE OCEANS 2010, 24–27May2010, Sydney, Australia: IEEE, pp. 1–6.
9.
HuangYLuWM (1996) Nonlinear optimal control: Alternatives to Hamilton-Jacobi equation. In: Proceedings of the 35th IEEE conference on decision and control, Kobe, Japan, 13 December 1996, pp. 3942–3947. New York: IEEE.
10.
IsidoriAAstolfiA (1992) Disturbance attenuation and H∞-control via measurement feedback in nonlinear systems. IEEE Transactions on Automatic Control37(9): 1283–1293.
11.
IsidoriAKangW (1995) H∞ control via measurement feedback for general nonlinear systems. IEEE Transactions on Automatic Control40(3): 466–472.
12.
JoeHKimMYuS (2014) Second-order sliding-mode controller for autonomous underwater vehicle in the presence of unknown disturbances. Nonlinear Dynamics78(1): 183–196.
13.
KatayamaHAokiH (2014) Straight-line trajectory tracking control for sampled-data underactuated ships. IEEE Transactions on Control Systems Technology22(4): 1638–1645.
14.
LapierreL (2009) Robust diving control of an AUV. Ocean Engineering36(1): 92–104.
15.
Liceaga-CastroEvan der MolenGM (1995) Submarine H∞ depth control under wave disturbances. IEEE Transactions on Control Systems Technology3(3): 338–346.
16.
LiJHLeePM (2005) A neural network adaptive controller design for free-pitch-angle diving behavior of an autonomous underwater vehicle. Robotics and Autonomous Systems52(2–3): 132–147.
17.
LuWMDoyleJC (1995) H∞ control of nonlinear systems: A convex characterization. IEEE Transactions on Automatic Control40: 1668–1674.
18.
LuWMDoyleJC (1997) Robustness analysis and synthesis for nonlinear uncertain systems. IEEE Transactions on Automatic Control42(12): 1654–1662.
19.
MahapatraSSubudhiBRoutRet al. (2016) Nonlinear H∞ control for an autonomous underwater vehicle in the vertical plane. In: Proceedings of the 4th IFAC conference on advances in control and optimization of dynamical systems (ACODS-2016), Tiruchirappalli, India, 1–5 February 2016, pp. 391–395. IFAC.
20.
MoreiraLSoaresCG (2008) H2 and H∞ designs for diving and course control of an autonomous underwater vehicle in presence of waves. IEEE Journal of Oceanic Engineering33(2): 69–88.
21.
NaikMSSinghSN (2007) State-dependent Riccati equation-based robust dive plane control of AUV with control constraints. Ocean Engineering34(11–12): 1711–1723.
22.
PanHXinM (2012) Depth control of autonomous underwater vehicles using indirect robust control method. International Journal of Control85(1): 98–113.
23.
PresteroTJ (2001) Verification of a six-degree of freedom simulation model for the REMUS autonomous underwater vehicle. Master’s Thesis, Department of Ocean and Mechanical Engineering, Massachusetts Institute of Technology, MA.
24.
QuigleyMConleyKGerkeyBPet al. (2009) ROS: An open-source robot operating system. In: ICRA workshop on open source software, Kobe, Japan, January 2009.
25.
RepouliasFPapadopoulosE (2007) Planar trajectory planning and tracking control design for underactuated AUVs. Ocean Engineering34(11–12): 1650–1667.
26.
RoutRSubudhiB (2016) NARMAX self-tuning controller for line-of-sight-based waypoint tracking for an autonomous underwater vehicle. IEEE Transactions on Control Systems Technology1–8 (in press).
27.
SilvestreC (2000) Multi-objective optimization theory with applications to the integrated design of controllers/plants for autonomous vehicles. PhD Thesis, Instituto Superior Technico (IST), Lisbon, Portugal.
28.
SilvestreCPascoalA (2007) Depth control of the INFANTE AUV using gain-scheduled reduced order output feedback. Control Engineering Practice15(7): 883–895.
29.
SinhaPPechevA (2004) Nonlinear H∞ controllers for electromagnetic suspension systems. IEEE Transactions on Automatic Control49(4): 563–568.
30.
SohnSIOhJHLeeYSet al. (2015) Design of a fuel-cell-powered catamaran-type unmanned surface vehicle. IEEE Journal of Oceanic Engineering40(2): 388–396.
31.
SyahroniNSeoYBChoiJW (2008) Depth control of autonomous underwater vehicle based on open control platform. 6–11 July 2008, Seoul, IFAC. IFAC Proceedings Volumes41(2): 3707–3712.
32.
TsiotrasPCorlessMRoteaMA (1998) An L2 disturbance attenuation solution to the nonlinear benchmark problem. International Journal of Robust and Nonlinear Control8: 311–330.
33.
Van der SchaftAJ (1991) On a state space approach to nonlinear H∞ control. Systems & Control Letters16(1): 1–8.
34.
Van der SchaftAJ (1992) L2-gain analysis of nonlinear systems and nonlinear state-feedback H∞ control. IEEE Transactions on Automatic Control37(6): 770–784.
35.
WangYLHanQL (2016a) Network-based fault detection filter and controller coordinated design for unmanned surface vehicles in network environments. IEEE Transactions on Industrial Informatics12(5): 1753–1765.
36.
WangYLHanQL (2016b) Network-based heading control and rudder oscillation reduction for unmanned surface vehicles. IEEE Transactions on Control Systems Technology1–12 (in press).
37.
WillemsJC (1972) Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis45(5): 321–351.
38.
YanZpYuHmHouS (2016) Diving control of underactuated unmanned undersea vehicle using integral-fast terminal sliding mode control. Journal of Central South University23(5): 1085–1094.
39.
YeonJSYimJParkJH (2011) Robust control using recursive design method for flexible joint robot manipulators. Journal of Mechanical Science and Technology25(12): 3205–3213.
40.
YimJParkJH (1999) Nonlinear H∞ control of robotic manipulator. In: IEEE international conference on systems, man, and cybernetics, Tokyo, 12–15 October 1999, pp. 866–871. IEEE.
41.
YousfiSDjennouneSBettayebM (2008) Comparison of linear and nonlinear H∞ control for a permanent magnet synchronous motor. In: 5th international multi-conference on systems, signals and devices, Amman, Jordan, 20–22 July 2008, pp. 1–6. IEEE.
42.
ZhouHLiuKLiYet al. (2015) Dynamic sliding mode control based on multi-model switching laws for the depth control of an autonomous underwater vehicle. International Journal of Advanced Robotic Systems12(7): 1–10.
