In this paper, the problem of vehicle sideslip angle estimation is studied based on a single-track model, and an approach to robust ℋ∞ filter design with sampled-data measurements is proposed. Considering the changes of the vehicle mass, the moment of inertia about the yaw axis and the nonlinear relationships between the road surface and tyres, the vehicle lateral dynamics are characterized by a system with parameter uncertainties, which belong to a given convex polytope. By utilizing an input delay approach, the filtering error system is transformed into a continuous-time system with time delay in the state. By introducing a Lyapunov–Krasovskii functional and a free weighting matrix technique, LMI-based conditions have been formulated for the stability analysis of the filtering error system and the existence of admissible filters, which ensure the filtering error system is asymptotically stable with a prescribed ℋ∞ disturbance attenuation level. Finally, some simulation results are provided to illustrate the effectiveness of the proposed method.
ArndtCKaridasJ (2006) Estimation of tire-road contact for integrated control applications in current vehicles. In: Proceedings of IEEE conference of control applications, Munich, Germany, 4–6 October 2006, pp.2784–2789. IEEE Press.
2.
BaffetGChararaADherbomezG (2007) An observer of tire-road forces and friction for active security vehicle systems. IEEE Transactions on Mechatronics12(6): 651–551.
3.
BamiehBPearsonJ (1992) A general framework for linear periodic systems with applications to ℋ∞ sampled-data control. IEEE Transaction on Automatic Control37(4): 418–435.
Canudas-De-WitCTsiotrasPVelenisE. (2003) Dynamic friction model for road/tire longitudinal interaction. Vehicle Systems Dynamics3(39): 189–226.
6.
CheliFSabbioniEPesceM. (2007) A methodology for vehicle sideslip angle identification: Comparison with experimental data. Vehicle System Dynamics5(6): 549–563.
7.
ChenBCHsiehFC (2008) Sideslip angle estimation using extended Kalman filter. Vehicle Systems Dynamics46: 353–364.
8.
DoumiatiMVictorinoACChararaA. (2011) Onboard real-time estimation of vehicle lateral tire-road forces and sideslip angle. IEEE/ASME Transactions on Mechatronics16(4): 601–614.
9.
DuHZhangNDongG (2010) Stabilizing vehicle lateral dynamics with considerations of parameter uncertainties and control saturation through robust yaw control. IEEE Transactions on Vehicular Technology59(5): 2593–2597.
10.
DugoffJFanchesPSegelL (1970) An analysis of tire properties and their influence on vehicle dynamic performance, SAE technical paper no. 700377. DOI: 10.4271/700377.
11.
ElsayedAGrimbleMJ (1989) A new approach to the ℋ∞ design of optimal digital linear filters. IMA Journal of Mathematical Control and Information6(2): 233–251.
12.
EsmailzadehEGoodarziAVossoughiGR (2013) Optimal yaw moment control law for improved vehicle handling. Mechatronics13(7): 659–675.
13.
FridmanE (2008) A refined input delay approach to sampled-data control. Automatica46(2): 421–427.
14.
GaoHChenT (2007) Stabilization of nonlinear systems under variable sampling: A fuzzy control approach. IEEE Transactions on Fuzzy Systems15(5): 972–983.
15.
GaoHSunWShiP (2010) Robust sampled-data ℋ∞ control for vehicle active suspension systems. IEEE Transactions on Control Systems Technology18(1): 238–245.
16.
GaoXYuZNeubeckJ. (2010) Sideslip angle estimation based on input-output linearisation with tire-road friction adaptation. Vehicle System Dynamics48(2): 217–234.
17.
GripHFImslandLJohansenTA. (2009) Vehicle sideslip estimation. IEEE Control Systems Magazine29(5): 36–52.
18.
KimJ (2009) Identification of lateral tyre force dynamics using an extended Kalman filter from experimental road test data. Control Engineering Practice17(3): 357–367.
19.
LiBSongXZhaoJ (2014) Sampled-data ℋ∞ for a class of Markovian jump systems with input saturation via stochastic sampling design. Transactions of the Institute of Measurement and Control36(3): 291–299.
20.
LiuKFridmanE (2012) Networked-based stabilization via discontinuous Lyapunov functionals. International Journal of Robust and Nonlinear Control22(4): 420–436.
21.
NamKOhSFuiimotH. (2013) Estimation of sideslip and roll angles of electric vehicles using lateral tire force sensors through RLS and Kalman filter approaches. IEEE Transactions on Industrial Electronics60(3): 988–1000.
22.
NguangSKShiP (1999) ℋ∞ filtering of nonlinear sampled-data systems with parameter uncertainties. In: Proceedings of American control conference, California, USA, 2–4 June 1999, pp.1274–1278. IEEE Press.
23.
PacejkaHBBakkerE (1991) The magic formula tyre model. International Journal of Vehicle Mechanics and Mobility2: 1–18.
24.
PhanomchoengGRajamaniRPiyabongkarnD (2011) Nonlinear observer for bounded Jacobian systems with application to automotive slip angle estimation. IEEE Transactions on Automatic Control56(5): 1163–1170.
25.
PiyabongkarnDRajamaniRGroggJA. (2009) Development and experimental evaluation of a slip angle estimator for vehicle stability control. IEEE Transactions on Control Systems Technology17(1): 78–88.
26.
QiuJDingSXGaoH. (2015a) Fuzzy-model-based reliable static output feedback ℋ∞ control of nonlinear hyperbolic PDE systems. IEEE Transactions on Fuzzy Systems (99): 1. DOI: 10.1109/TFUZZ.2015.2457934.
27.
QiuJFengGYangJ (2009) A new design of delay-dependent robust H∞ filtering for discrete-time T-S fuzzy systems with time-varying delay. IEEE Transactions on Fuzzy Systems17(5): 1044–1058.
28.
QiuJGaoHDingSX (2016) Recent advances on fuzzy-model-based nonlinear networked control systems: A survey. IEEE Transactions on Industrial Electronics63(2): 1207–1217.
29.
QiuJWeiYKarimiHR (2015b) New approach to delay-dependent ℋ∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions. Journal of The Franklin Institute352(1): 189–215.
30.
SegelM (1956) Theoretical prediction and experimental substantiation of the response of the automobile to steering control. Proceedings of Automobile Division of the Institute of Mechanical Engineers7: 310–330.
31.
ShenBWangZLiuX (2012) A stochastic sampled-data approach to distributed ℋ∞ filtering in sensor networks.IEEE Transactions on Circuit and Systems I58(9): 2237–2246.
32.
SolmazSBaşlamişliSÇ (2012) Simultaneous estimation of road friction and sideslip angle based on switched multiple non-linear observers. IET Control Theory and Applications6(14): 2235–2247.
33.
StéphantJChararaAMeizelD (2007) Evaluation of a sliding mode observer for vehicle sideslip angle. Control Engineering Practice15(7): 803–812.
34.
TsengHEMadauDAshrafiB. (1999) Technical challenges in the development of vehicle stability control system. Proceedings of IEEE international conference of control applications, Hawaii, USA, 21–22 August 2007, pp.1660–1666. IEEE Press.
35.
VenhovensPJTNaabK (1999) Vehicle dynamics estimation using Kalman filters. Vehicle System Dynamics32(2): 171–184.
36.
VietinghoffAHiemerMKienckeU (2005) Nonlinear observer design for lateral vehicle dynamics. Proceedings of 16th IFAC world congress, Prague, Czech Republic, 4–8 July 2005, pp.988–993. IFAC Press.
37.
WangTGaoHQiuJ (2016) A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Transactions on Neural Networks and Learning Systems27(2): 416–425.
38.
WangZHuangB (2000) Robust ℋ2/ℋ∞ for linear systems with error variance constraints. IEEE Transactions on Signal Processing48(8): 2463–2467.
39.
WangZHoDWCLiuX (2002) Variance-constrained filtering for uncertain stochastic systems with miss measurements. IEEE Transactions on Automatic Control48(7): 1254–1258.
40.
WangZHuangBHuoP (2001) Sampled-data filtering with error covariance assignment. IEEE Transactions on Signal Processing49(3): 666–670.
41.
WenzelTABurnhamKJBlundellMV. (2007) Kalman filter as a virtual sensor: Applied to automotive stability systems. Transactions of the Institute of Measurements and Control29(2): 95–115.
42.
YouSHHahnJOLeeH (2009) New adaptive approaches to real-time estimation of vehicle sideslip angle. Control Engineering Practice17(12): 1367–1379.
43.
ZhangCFengGGaoH. (2011) ℋ∞ filtering for nonlinear discrete-time systems subject to quantization and packet dropouts. IEEE Transactions on Fuzzy Systems19(2): 353–365.
