In order to isolate the propagation of unwanted vibrations to passengers and improve vehicle maneuverability, it is common practice to predict road profile roughness in the scope of active suspension design. An algebraic estimator designed for the estimation of the road profile excitation has been investigated in this study based on vehicle dynamics responses. An approximation of road profile excitation by a piecewise constant function has been proposed using the operational calculus method and the differential algebraic theory. The proposed technique allows for the usage of cheap instrumentation with a small number of sensors and employs a straightforward calibration process. Accurate approximation of the road profile was obtained from the measurement of sprung mass and unsprung mass vertical displacements. The performance and robustness of the proposed algebraic predictor is compared with an augmented Kalman estimator. Numerical results are provided to analyze the effectiveness and the limitations of the proposed algorithm for road profile reconstruction. Furthermore, a comparison with real profile was studied.
HarrisNKGonzálezAOBrienEJet al.Characterisation of pavement profile heights using accelerometer readings and a combinatorial optimisation technique. J Sound Vib2010; 329: 497–508.
2.
HeynsTHeynsPSDe VilliersJP. A method for real-time condition monitoring of haul roads based on Bayesian parameter estimation. J Terramech2012; 49: 103–113.
3.
Douangphachanh V and Hiroyuki O. Estimation of road roughness condition from smartphones under realistic settings. In: 2013 13th international conference on ITS telecommunications (ITST), 2013, pp.433–439. New York: IEEE.
4.
GonzálezAO’brienEJLiYYet al.The use of vehicle acceleration measurements to estimate road roughness. Veh Syst Dyn2008; 46: 483–499.
5.
Johnsson R and Odelius J. Methods for road texture estimation using vehicle measurements. In: International conference on noise and vibration engineering, 17–19 September 2012, pp.1573–1582. Belgium: KU Leuven.
6.
SayersMW. The little book of profiling: Basic information about measuring and interpreting road profiles, Ann Arbor, MI: UMTRI, 1998.
7.
Eriksson J, et al. The pothole patrol: Using a mobile sensor network for road surface monitoring. In: Proceedings of the 6th international conference on mobile systems, applications, and services, 2008, pp.29–39. New York: ACM.
Rabhi A, M’sirdi NK, Fridman L, et al. Second order sliding mode observer for estimation of road profile. In: International workshop on variable structure systems, 2006, pp.161–165. New York: IEEE.
11.
RathJJVeluvoluKCDefoortM. Simultaneous estimation of road profile and tire road friction for automotive vehicle. IEEE Trans Veh Technol2015; 64: 4461–4471.
12.
Li Z, Kalabić UV, Kolmanovsky IV, et al. Simultaneous road profile estimation and anomaly detection with an input observer and a jump diffusion process estimator. In: American control conference (ACC), 2016, pp.1693–1698. New York: IEEE.
13.
Tudón-MartínezJCFerganiSSenameOet al.Adaptive road profile estimation in semiactive car suspensions. IEEE Trans Control Systems Technol2015; 23: 2293–2305.
14.
Doumiati M, Victorino A, Charara A, et al. Estimation of road profile for vehicle dynamics motion: Experimental validation. In: American control conference (ACC), 2011, pp.5237–5242. New York: IEEE.
15.
FauriatWMattrandCGaytonNet al.Estimation of road profile variability from measured vehicle responses. Veh Syst Dyn2016; 54: 585–605.
16.
WangZDongMQinYet al.Suspension system state estimation using adaptive Kalman filtering based on road classification. Veh Syst Dyn2017; 55: 371–398.
17.
Qin Y, Langari R, Wang Z, et al. Road profile estimation for semi-active suspension using an adaptive Kalman filter and an adaptive super-twisting observer. In: American control conference (ACC), 2017, pp.973–978. New York: IEEE.
18.
FliessMSira-RamírezH. An algebraic framework for linear identification. ESAIM: Control Optim Calcul Variat2003; 8: 151–168.
19.
FliessMJoinC. Model-free control. Int J Control2013; 86: 2228–2252.
20.
UlsoyAGPengHÇakmakciM. Automotive control systems, Cambridge: Cambridge University Press, 2012.
21.
JazarRN. Vehicle dynamics: Theory and application, New York: Springer, 2008, pp. 380–554.
22.
Zhang X, Yu W, Ma F, et al. Semi-active suspension adaptive control strategy based on hybrid control. In: Proceedings of the FISITA 2012 world automotive congress, 2013, pp.625–632. Berlin, Heidelberg: Springer.
23.
TurkaySAkcayH. A study of random vibration characteristics of the quarter-car model. J Sound Vib2005; 282: 111–124.
24.
HasbullahFFarisWFDarsivanFJet al.Ride comfort performance of a vehicle using active suspension system with active disturbance rejection control. Int J Veh Noise Vib2015; 11: 78–101.
25.
KaleemullahMFarisWFRashidMMet al.Comparative analysis of LQR and robust controller for active suspension. Int J Veh Noise Vib2012; 8: 367–386.
26.
HrovatD. Survey of advanced suspension developments and related optimal control applications. Automatica1997; 33: 1781–1817.
27.
ISO8608. Mechanical vibration–road surface profiles–reporting of measured data, Geneva, Switzerland: International Standardization Organization, 1995.
28.
He L, Qin G, Zhang Y, et al. Non-stationary random vibration analysis of vehicle with fractional damping. In: 2008 international conference on intelligent computation technology and automation (ICICTA), October 2008, Vol. 2, pp.150–157. New York: IEEE.
29.
PanHSunWJingXet al.Adaptive tracking control for active suspension systems with non-ideal actuators. J Sound Vib2017; 399: 2–20.
30.
Alvarez-SánchezE. A quarter-car suspension system: Car body mass estimator and sliding mode control. Procedia Technol2013; 7: 208–214.
31.
MikusińskiJ. Operational calculus. CUP Archive1967; 8.
32.
DoTMLeTC. Performance analysis of FFT filter to measure displacement signal in road roughness profiler. Int J Comput Electr Eng2013; 5: 356–356.
33.
D’Andréa-Novel B, Boussard C, Fliess M, et al. Commande sans modèle de la vitesse longitudinale d’un véhicule électrique. In: Sixième conference internationale francophone d’Automatique (CIFA 2010), Nancy, France, 2010.
34.
BakloutiAAntunesJDebutVet al.A method for the identification of dynamic constraint parameters in multi-supported flexible structures. Comptes Rendus Mécanique2017; 345: 239–247.
35.
Bolandhemmat H. Distributed sensing and observer design for vehicles state estimation. Thesis, University of Waterloo, Canada, 2009.
36.
DoumiatiMMartinezJSenameOet al.Road profile estimation using an adaptive Youla–Kučera parametric observer: Comparison to real profilers. Control Eng Pract2017; 61: 270–278.
