0
Research Papers

Low-Complexity Passive Vehicle Suspension Design Based on Element-Number-Restricted Networks and Low-Order Admittance Networks

[+] Author and Article Information
Yinlong Hu

College of Energy and Electrical Engineering,
Hohai University,
Nanjing 211100, China
e-mail: yinlonghu@outlook.com

Michael Z. Q. Chen

School of Automation,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: mzqchen@outlook.com

1Corresponding authors.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received April 24, 2017; final manuscript received May 8, 2018; published online June 4, 2018. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 140(10), 101014 (Jun 04, 2018) (7 pages) Paper No: DS-17-1214; doi: 10.1115/1.4040294 History: Received April 24, 2017; Revised May 08, 2018

This paper is concerned with the low-complexity passive suspension design problem, aiming at improving vehicle performance in the meanwhile maintaining simplicity in structure for passive suspensions. Two methods are employed to construct the low-complexity passive suspensions. Using the first method, the number of each element is restricted to one, and the performance for all networks with one inerter, one damper, and one spring is evaluated, where best configurations for different vehicle settings are identified. Using the second method, low-order admittance networks whose orders of admittance functions are no larger than three are utilized. Design methods are proposed by directly using the positive realness conditions imposed on the admittance functions. The effectiveness of the proposed methods is numerically demonstrated, and the comparison between these two constructing methods is conducted.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Savaresi, S. M. , Poussot-Vassal, C. , Spelta, C. , Sename, O. , and Dugard, L. , 2010, Semi-Active Suspension Control Design for Vehicles, Elsevier, Amsterdam, The Netherlands.
Poussot-Vassal, C. , Spelta, C. , Sename, O. , Savaresi, S. M. , and Dugard, L. , 2012, “ Survey and Performance Evaluation on Some Automotive Semi-Active Suspension Control Methods: A Comparative Study on a Single-Corner Model,” Annu. Rev. Control, 36(1), pp. 148–160. [CrossRef]
Smith, M. C. , 2002, “ Synthesis of Mechanical Networks: The Inerter,” IEEE Trans. Autom. Control, 47(10), pp. 1648–1662. [CrossRef]
El Majdoub, K. , Ghani, D. , Giri, F. , and Chaoui, F. Z. , 2014, “ Adaptive Semi-Active Suspension of Quarter-Vehicle With Magnetorheological Damper,” ASME J. Dyn. Syst. Meas. Control, 137(2), p. 021010. [CrossRef]
Liu, Y. , and Zuo, L. , 2016, “ Mixed Skyhook and Power-Driven-Damper: A New Low-Jerk Semi-Active Suspension Control Based on Power Flow Analysis,” ASME J. Dyn. Syst. Meas. Control, 138(8), p. 081009. [CrossRef]
Fei, J. , and Xin, M. , 2012, “ Robust Adaptive Sliding Mode Controller for Semi-Active Vehicle Suspension System,” Int. J. Innovative Comput., Inf. Control, 8(1), pp. 691–700. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.460.4514&rep=rep1&type=pdf
Du, H. , Li, W. , and Zhang, N. , 2011, “ Semi-Active Variable Stiffness Vibration Control of Vehicle Seat Suspension Using an MR Elastomer Isolator,” Smart Mater. Struct., 20(10), p. 105003. [CrossRef]
Chen, M. Z. Q. , Hu, Y. , Li, C. , and Chen, G. , 2014, “ Semi-Active Suspension With Semi-Active Inerter and Semi-Active Damper,” 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa, Aug. 24–29, pp. 11225–11230. https://pdfs.semanticscholar.org/154b/a270fe37788f62728366201fef5d802b8a54.pdf
Hu, Y. , Chen, M. Z. Q. , Xu, S. , and Liu, Y. , 2017, “ Semi-Active Inerter and Its Application in Adaptive Tuned Vibration Absorbers,” IEEE Trans. Control Syst. Technol., 25(1), pp. 294–300. [CrossRef]
Sakthivel, R. , Arunkumar, A. , Mathiyalagan, K. , and Selvi, S. , 2014, “ Robust Reliable Control for Uncertain Vehicle Suspension Systems With Input Delays,” ASME J. Dyn. Syst. Meas. Control, 137(4), p. 041013. [CrossRef]
Mozaffari, A. , Doosthoseini, A. , and Azad, N. L. , 2016, “ Predictive Control of Suspension Systems Through Combining Dynamic Matrix and Constrained Variable Structure Controllers,” ASME J. Dyn. Syst. Meas. Control, 138(12), p. 121007. [CrossRef]
Li, P. , Lam, J. , and Cheung, K. C. , 2014, “ Multi-Objective Control for Active Vehicle Suspension With Wheelbase Preview,” J. Sound Vib., 333(21), pp. 5269–5282. [CrossRef]
Hu, Y. , Chen, M. Z. Q. , and Hou, Z. , 2015, “ Multiplexed Model Predictive Control for Active Vehicle Suspensions,” Int. J. Control, 88(2), pp. 347–363. [CrossRef]
Sun, W. , Gao, H. , and Kaynak, O. , 2015, “ Vibration Isolation for Active Suspensions With Performance Constraints and Actuator Saturation,” IEEE/ASME Trans. Mechatronics, 20(2), pp. 675–683. [CrossRef]
Cao, D. , Song, X. , and Ahmadian, M. , 2011, “ Editors' Perspectives: Road Vehicle Suspension Design, Dynamics, and Control,” Veh. Syst. Dyn., 49(1–2), pp. 3–28. [CrossRef]
Smith, M. C. , and Wang, F.-C. , 2004, “ Performance Benefits in Passive Vehicle Suspensions Employing Inerters,” Veh. Syst. Dyn., 42(4), pp. 235–257. [CrossRef]
Scheibe, F. , and Smith, M. C. , 2009, “ Analytical Solutions for Optimal Ride Comfort and Tyre Grip for Passive Vehicle Suspensions,” Veh. Syst. Dyn, 47(10), pp. 1229–1252. [CrossRef]
Hu, Y. , Chen, M. Z. Q. , and Shu, Z. , 2014, “ Passive Vehicle Suspensions Employing Inerters With Multiple Performance Requirements,” J. Sound Vib., 333(8), pp. 2212–2225. [CrossRef]
Papageorgiou, C. , and Smith, M. C. , 2006, “ Positive Real Synthesis Using Matrix Inequalities for Mechanical Networks: Application to Vehicle Suspension,” IEEE Trans. Control Syst. Technol., 14(3), pp. 423–435. [CrossRef]
Wang, F.-C. , and Chan, H.-A. , 2011, “ Vehicle Suspensions With a Mechatronic Network Strut,” Veh. Syst. Dyn., 49(5), pp. 811–830. [CrossRef]
Wang, F.-C. , and Su, W.-J. , 2008, “ Impact of Inerter Nonlinearities on Vehicle Suspension Control,” Veh. Syst. Dyn., 46(7), pp. 575–595. [CrossRef]
Chen, M. Z. Q. , Hu, Y. , Huang, L. , and Chen, G. , 2014, “ Influence of Inerter on Natural Frequencies of Vibration Systems,” J. Sound Vib., 333(7), pp. 1874–1887. [CrossRef]
Guo, S. , Liu, Y. , Xu, L. , Guo, X. , and Zuo, L. , 2016, “ Performance Evaluation and Parameter Sensitivity of Energy-Harvesting Shock Absorbers on Different Vehicles,” Veh. Syst. Dyn., 54(7), pp. 918–942. [CrossRef]
Wang, F.-C. , Liao, M. K. , Liao, B. H. , and Su, W. J. , 2009, “ The Performance Improvements of Train Suspension Systems With Mechanical Networks Employing Inerters,” Veh. Syst. Dyn., 47(7), pp. 805–830. [CrossRef]
Wang, F.-C. , Hong, M. F. , and Chen, C. W. , 2010, “ Building Suspensions With Inerters,” Proc. IMechE, Part C: J. Mech. Eng. Sci., 224(8), pp. 1605–1616. [CrossRef]
Chen, M. Z. Q. , Wang, K. , Li, C. , and Chen, G. , 2017, “ Realization of Biquadratic Impedances as Five-Element Bridge Networks,” IEEE Trans. Circuits Syst. I: Regular Papers, 64(6), pp. 1599–1611. [CrossRef]
Chen, M. Z. Q. , Wang, K. , Zou, Y. , and Lam, J. , 2013, “ Realization of a Special Class of Admittances With One Damper and One Inerter for Mechanical Control,” IEEE Trans. Autom. Control, 58(7), pp. 1841–1846. [CrossRef]
Wang, K. , Chen, M. Z. Q. , and Hu, Y. , 2014, “ Synthesis of Biquadratic Impedances With at Most Four Passive Elements,” J. Franklin Inst., 351(3), pp. 1251–1267. [CrossRef]
Lazar, I. F. , Neild, S. A. , and Wagg, D. J. , 2014, “ Using an Inerter-Based Device for Structural Vibration Suppression,” Earthquake Eng. Struct. Dyn., 43 (8), pp. 1129–1147. [CrossRef]
Hu, Y. , Chen, M. Z. Q. , Shu, Z. , and Huang, L. , 2015, “ Analysis and Optimization for Inerter-Based Isolators Via Fixed-Point Theory and Algebraic Solution,” J. Sound Vib., 346, pp. 17–36. [CrossRef]
Brzeski, P. , Pavlovskaia, E. , Kapitaniak, T. , and Perlikowski, P. , 2015, “ The Application of Inerter in Tuned Mass Absorber,” Int. J. Non-Linear Mech., 70, pp. 20–29. [CrossRef]
Jin, X. L. , Chen, M. Z. Q. , and Huang, Z. L. , 2016, “ Minimization of the Beam Response Using Inerter-Based Passive Vibration Control Configurations,” Int. J. Mech. Sci., 119, pp. 80–87. [CrossRef]
Yamamoto, K. , and Smith, M. C. , 2016, “ Bounded Disturbance Amplification for Mass Chains With Passive Interconnection,” IEEE Trans. Autom. Control, 61(6), pp. 1565–1574. [CrossRef]
Hu, Y. , and Chen, M. Z. Q. , 2015, “ Performance Evaluation for Inerter-Based Dynamic Vibration Absorbers,” Int. J. Mech. Sci., 99, pp. 297–307. [CrossRef]
Li, P. , Lam, J. , and Cheung, K. C. , 2015, “ Control of Vehicle Suspension Using an Adaptive Inerter,” Proc. Inst. Mech. Eng., Part D: J. Autom. Eng., 229(14), pp. 1934–1943. [CrossRef]
Shen, Y. , Chen, L. , Yang, X. , Shi, D. , and Yang, J. , 2016, “ Improved Design of Dynamic Vibration Absorber by Using the Inerter and Its Application in Vehicle Suspension,” J. Sound Vib., 361, pp. 148–158. [CrossRef]
Zhang, S. Y. , Jiang, J. Z. , and Neild, S. A. , 2017, “ Passive Vibration Control: A Structure-Immittance Approach,” Proc. R. Soc. A, 473(2201), p. 20170011. [CrossRef]
Newcomb, R. W. , 1966, Linear Multiport Synthesis, McGrawHill, New York.
Chen, M. Z. Q. , and Smith, M. C. , 2009, “ A Note on Tests for Positive-Real Functions,” IEEE Trans. Automat. Control, 54(2), pp. 390–393. [CrossRef]
Anderson, B. D. O. , and Vongpanitlerd, S. , 1973, Network Analysis and Synthesis: A Modern Systems Approach, Prentice Hall, Upper Saddle River, NJ.
Van Valkenburg, M. E. , 1965, Introduction to Modern Network Synthesis, Wiley, New York.
Bott, R. , and Duffin, R. J. , 1949, “ Impedance Synthesis Without Use of Transformers,” J. Appl. Phys., 20(8), p. 816. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

Explicit networks with one inerter, one damper, and one spring. The first row from left to right denotes C1, C2, C3, and C4 and the second row from left to right denotes C5, C6, C7, and C8.

Grahic Jump Location
Fig. 1

A quarter-car vehicle model

Grahic Jump Location
Fig. 3

Control diagram description

Grahic Jump Location
Fig. 14

The optimal networks for ride comfort performance where K = 80 kN/m: from left to right: first-order, second-order, and third-order admittances

Grahic Jump Location
Fig. 6

Optimal tire grip performance comparison for all networks with one inerter, one damper, and one spring

Grahic Jump Location
Fig. 7

Optimal damping coefficients c: left figure: for optimal ride comfort and right figure: for optimal tire grip

Grahic Jump Location
Fig. 8

Optimal inertances b: left figure: for optimal ride comfort and right figure: for optimal tire grip

Grahic Jump Location
Fig. 9

Optimal stiffnesses k: left figure: for optimal ride comfort and right figure: for optimal tire grip

Grahic Jump Location
Fig. 10

The optimal networks for tire grip performance where K = 80 kN/m: from left to right: first-order, second-order, and third-order admittances

Grahic Jump Location
Fig. 11

An alternative realization of the third-order admittance for the optimal tire grip performance where K = 80 kN/m: k = 1203.37 N/m, k1 = 549.16 kN/m, c1 = 3109.08 Ns/m, c2 = 3189.56 Ns/m, and b = 496.40 kg

Grahic Jump Location
Fig. 12

The ride comfort performance comparison between low-order admittance networks and the networks with one inerter, one damper, and one spring: upper figure: J1 and lower figure: percentage improvements over the networks with one inerter, one damper, and one spring

Grahic Jump Location
Fig. 13

The tire grip performance comparison between low-order admittance networks and the networks with one inerter, one damper, and one spring: upper figure: J3 and lower figure: percentage improvements over the networks with one inerter, one damper, and one spring

Grahic Jump Location
Fig. 4

Traditional passive struts without inerters. From left to right denotes TC1 and TC2.

Grahic Jump Location
Fig. 5

Optimal ride comfort performance comparison for all networks with one inerter, one damper, and one spring

Tables

Errata

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