Research Papers

Optimal Vibration Control for Uncertain Nonlinear Sampled-Data Systems With Actuator and Sensor Delays: Application to a Vehicle Suspension

[+] Author and Article Information
Jing Lei

School of Mathematics and Computer Science,
Yunnan Nationalities University,
Kunming 650500, China;
Key Laboratory in Software
Engineering of Yunnan Province,
Kunming 650091, China
e-mail: elizabethia@126.com

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received October 25, 2011; final manuscript received October 2, 2012; published online February 21, 2013. Assoc. Editor: John B. Ferris.

J. Dyn. Sys., Meas., Control 135(2), 021021 (Feb 21, 2013) (13 pages) Paper No: DS-11-1332; doi: 10.1115/1.4023060 History: Received October 25, 2011; Revised October 02, 2012

The problem of optimal sampled-data vibration control for nonlinear systems with time delays and uncertainties is considered. With the purpose of simplifying the nonlinear optimal vibration control (NOVC) design, the original time-delay sampled-data system is converted into a discrete-time nondelayed system first, as well as the nonlinear and uncertain terms are treated as external excitations. Therefore, the design procedure for NOVC law is reduced and the successive approximation approach is sequentially developed in it. The obtained NOVC law is derived from a Riccati equation, a Stein equation, and sequences of adjoint vector difference equations. It is combined with a feedforward term, the nonlinearity and uncertainty compensator terms, and some control memory terms, which compensate for the effects produced by the disturbance, the nonlinearity and uncertainties, and the time delays. Moreover, the existence and uniqueness of NOVC law are proved and the stability of the closed-loop system is analyzed. In order to make the controller physically realizable, an observer is constructed and the corresponding dynamical control law is given. Furthermore, by this means, the NOVC law for a sampled-data quarter-car suspension model with actuator and sensor delays is designed. The results of numerical simulations illustrate that the NOVC gives satisfactory conclusions in effectiveness of suspension performance responses and feasibility of the proposed design approach.

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Wilson, D. A., Sharp, R. S., and Hassan, S. A., 1986, “The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions,” Veh. Syst. Dyn., 15(2), pp. 105–118. [CrossRef]
Elbeheiry, E. M., and Karnopp, D. C., 1996, “Optimal Control of Vehicle Random Vibration With Constrained Suspension Deflection,” J. Sound Vib., 189(5), pp. 547–564. [CrossRef]
Marzbanrad, J., Ahmadi, G., Zohoor, H., and Hojjat, Y., 2004, “Stochastic Optimal Preview Control of a Vehicle Suspension,” J. Sound Vib., 275(3–5), pp. 973–990. [CrossRef]
Mirzaei, M., Alizadeh, G., Eslamian, M., and Azadi, S., 2008, “An Optimal Approach to Nonlinear Control of Vehicle Yaw Dynamics,” Proc. Inst. Mech. Eng., Part I, 222(4), pp. 217–229. [CrossRef]
Du, H., and Zhang, N., 2007, “H∞ Control of Active Vehicle Suspensions With Actuator Time Delay,” J. Sound Vib., 301(1–2), pp. 236–252. [CrossRef]
Zuo, L., and Nayfeh, S. A., 2003, “Structured H2 Optimization of Vehicle Suspensions Based on Multi-Wheel Models,” Veh. Syst. Dyn., 40(5), pp. 351–371. [CrossRef]
Fischer, D., and Isermann, R., 2004, “Mechatronic Semi-Active and Active Vehicle Suspensions,” Control Eng. Pract., 12(11), pp. 1353–1367. [CrossRef]
Narayanan, S., and Senthil, S., 1998, “Stochastic Optimal Active Control of a 2-DOF Quarter Car Model With Nonlinear Passive Suspension Elements,” J. Sound Vib., 211(3), pp. 495–506. [CrossRef]
Hassanzadeh, I., Alizadeh, G., Shirjoposht, N. P., and Hashemzadeh, F., 2010, “A New Optimal Nonlinear Approach to Half Car Active Suspension Control,” IACSIT Int. J. Eng. Technol., 2(1), pp. 78–84.
Kim, C., and Ro, P. I., 1998, “A Sliding Mode Controller for Vehicle Active Suspension Systems With Non-Linearities,” Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.), 212(D2), pp. 79–92. [CrossRef]
Narayanan, S., and Raju, G. V., 1992, “Active Control of Non-Stationary Response of Vehicles With Nonlinear Suspensions,” Veh. Syst. Dyn., 21(1), pp. 73–88. [CrossRef]
Chen, Y. C., and Huang, A. C., 2005, “Adaptive Sliding Control of Non-Autonomous Active Suspension Systems With Time-Varying Loadings,” J. Sound Vib., 282(3–5), pp. 1119–1135. [CrossRef]
Choi, S.-B., and Han, S.-S., 2003, “H∞ Control of Electrorheological Suspension System Subjected to Parameter Uncertainties,” Mechatronics, 13(7), pp. 639–657. [CrossRef]
Gaspar, P., Szaszi, I., and Bokor, J., 2003, “Design of Robust Controllers for Active Vehicle Suspensions Using the Mixed μ Synthesis,” Veh. Syst. Dyn., 40(4), pp. 193–228. [CrossRef]
Tuan, H. D., Ono, E., Apkarian, P., and Hosoe, S., 2001, “Nonlinear H∞ Control for an Integrated Suspension System via Parameterized Linear Matrix Inequality Characterizations,” IEEE Trans. Control Syst. Technol., 9(1), pp. 175–185. [CrossRef]
Karlsson, N., Dahleh, M., and Hrovat, D., 2001, “Nonlinear H∞ Control of Active Suspensions,” Proceedings of American Control Conference, Arlington, Vol. 5, pp. 3329–3334.
Huang, A. C., and Chen, Y. C., 2004, “Adaptive Sliding Control for Single-Link Flexible-Joint Robot With Mismatched Uncertainties,” IEEE Trans. Control Syst. Technol., 12(5), pp. 770–775. [CrossRef]
Alleyne, A., and Hedrick, K., 1995, “Nonlinear Adaptive Control of Active Suspensions,” IEEE Trans. Control Syst. Technol., 3(1), pp. 94–101. [CrossRef]
Litak, G., Borowiec, M., Michael, I. F., and Szabelski, K., 2008, “Chaotic Vibration of a Quarter-Car Model Excited by the Road Surface Profile,” Commun. Nonlinear Sci. Numer. Simul., 13(7), pp. 1373–1383. [CrossRef]
Li, F., and Sun, J., 2011, “Controllability of Boolean Control Networks With Time Delays in States,” Automatica, 47(3), pp. 603–607. [CrossRef]
Gao, H., Chen, T., and Lam, J., 2008, “A New Delay System Approach to Network-Based Control,” Automatica, 44(1), pp. 39–52. [CrossRef]
Huang, D., and Nguang, S. K., 2008, “State Feedback Control of Uncertain Networked Control Systems With Random Time Delays,” IEEE Trans. Autom. Control, 53(3), pp. 829–834. [CrossRef]
Riccard, J. P., 2003, “Time-Delay Systems: An Overview of Some Recent Advances and Open Problems,” Automatica, 39(10), pp. 1667–1694. [CrossRef]
Du, H., Zhang, N., and Lam, J., 2008, “Parameter-Dependent Input-Delayed Control of Uncertain Vehicle Suspensions,” J. Sound Vib., 317(3–5), pp. 236–252. [CrossRef]
Chen, W. H., Ballance, D. J., and Gawthrop, P. J., 2003, “Optimal Control of Nonlinear Systems: A Predictive Control Approach,” Automatica, 39(4), pp. 633–641. [CrossRef]
Lu, P., 1995, “Optimal Predictive Control of Continuous Nonlinear Systems,” Int. J. Control, 62(3), pp. 633–649. [CrossRef]
Ali, F., and Padhi, R., 2011, “Optimal Blood Glucose Regulation of Diabetic Patients Using Single Network Adaptive Critics,” Opt. Control Appl. Methods, 32(2), pp. 196–214. [CrossRef]
Milasi, R. M., Yazdanpanah, M.-J., and Lucas, C., 2008, “Nonlinear Optimal Control of Washing Machine Based on Approximate Solution of HJB Equation,” Opt. Control Appl. Methods, 29(1), pp. 1–18. [CrossRef]
Padhi, R., Xin, M., and Balakrishnan, S. N., 2008, “Reduced-Order Suboptimal Control Design for a Class of Nonlinear Distributed Parameter Systems Using POD and θ-D Techniques,” Opt. Control Appl. Methods, 29(3), pp. 191–224. [CrossRef]
Cimen, T., and Banks, S. P., 2004, “Global Optimal Feedback Control for General Nonlinear Systems With Nonquadratic Performance Criteria,” Syst. Control Lett., 53(5), pp. 327–346. [CrossRef]
Cimen, T., and Banks, S. P., 2004, “Nonlinear Optimal Tracking Control With Application to Super-Tankers for Autopilot Design,” Automatica, 40(11), pp. 1845–1863. [CrossRef]
Jaddu, H., and Vlach, M., 2002, “Successive Approximation Method for Non-Linear Optimal Control Problems With Application to a Container Crane Problem,” Opt. Control Appl. Methods, 23(5), pp. 275–288. [CrossRef]
Göllmann, L., and Maurer, H., 2009, “Optimal Control Problems With Delays in State and Control Variables Subject to Mixed Control-State Constrains,” Opt. Control Appl. Methods, 30(4), pp. 341–365. [CrossRef]
Wei, G., Wang, Z., Shu, H., and Fang, J., 2006, “Robust H∞ Control of Stochastic Time-Delay Jumping Systems With Nonlinear Disturbances,” Opt. Control Appl. Methods, 27(5), pp. 255–271. [CrossRef]
Olbrot, A. W., 1978, “Stabilizability, Detectability, and Spectrum Assignment for Linear Autonomous Systems With General Time Delays,” IEEE Trans. Autom. Control, AC-23(5), pp. 887–890. [CrossRef]
Fiagbedzi, Y. A., and Pearson, A. E., 1986, “Feedback Stabilization of Linear Autonomous Time Lag Systems,” IEEE Trans. Autom. Control, AC-31(9), pp. 847–855. [CrossRef]
Mondie, S., and Michiels, W., 2003, “Finite Spectrum Assignment of Unstable Time-Delay Systems With a Safe Implementation,” IEEE Trans. Autom. Control, 48(12), pp. 2207–2212. [CrossRef]
Lei, J., 2007, “Research on Optimal Disturbance Rejection Methods for Systems With Control Delay,” M.E. dissertation, Ocean University of China, Qingdao, China (in Chinese).
Lei, J., 2010, “Study on Optimal Vibration Control for Time-Delay Systems With Application to Vehicle Suspension Systems,” D.E. dissertation, Ocean University of China, Qingdao, China (in Chinese).
Lei, J., 2011, “Suboptimal Vibration Control for Nonlinear Suspension Systems Based on In-Vehicle Networks,” Proceedings of 2011 International Conference on System Science and Engineering, Macau, China, pp. 239–244.
Sujit, K. M., 1977, “The Matrix Equation AXB+CXD=E,” SIAM J. Appl. Math., 32(4), pp. 823–825. [CrossRef]
Pedro, J. O., and Dahunsi, O. A., 2011, “Neural Network Based Feedback Linearization Control of a Servo-Hydraulic Vehicle Suspension System,” Int. J. Appl. Math Comput. Sci., 21(1), pp. 137–147. [CrossRef]
Du, H., Lam, J., and Sze, K. Y., 2003, “Non-Fragile Output Feedback H∞ Vehicle Suspension Control Using Genetic Algorithm,” Eng. Applic. Artif. Intell., 16(7–8), pp. 667–680. [CrossRef]
Lin, Y. C., and Khalil, H. K., 1992, “Two-Time-Scale Design of Active Suspension Control Using Acceleration Feedback,” Proceedings of 1st IEEE Conference on Control Applications, Dayton, OH, Vol. 2, pp. 884–889. [CrossRef]
Hrovat, D., 1997, “Survey of Advanced Suspension Developments and Related Optimal Control Applications,” Automatica, 33(10), pp. 1781–1817. [CrossRef]
Elbeheir, E. M., and Karnop, D. C., 1996, “Optimal Control of Vehicle Random Vibration With Constrained Suspension Deflection,” J. Sound Vib., 189(5), pp. 547–564. [CrossRef]


Grahic Jump Location
Fig. 1

Quarter-car model with active suspension

Grahic Jump Location
Fig. 2

Suspension responses under NOVC and OLS

Grahic Jump Location
Fig. 3

Suspension responses under NOVC and NDCC



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