Full Text:   <5297>

CLC number: O32

On-line Access: 2013-06-03

Received: 2012-06-29

Revision Accepted: 2013-01-30

Crosschecked: 2013-05-16

Cited: 10

Clicked: 9837

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2013 Vol.14 No.6 P.401-416


Proportional-integral-derivative control of nonlinear half-car electro-hydraulic suspension systems

Author(s):  John E. D. Ekoru, Jimoh O. Pedro

Affiliation(s):  . School of Mechanical, Aeronautical and Industrial Engineering, University of the Witwatersrand, Private Bag 03, WITS 2050, Johannesburg, South Africa

Corresponding email(s):   John.Ekoru@students.wits.ac.za

Key Words:  Force control, Proportional-integral-derivative (PID) control, Nonlinear half-car, Active vehicle suspension system (AVSS), Hydraulic actuator dynamics, Model uncertainty

John E. D. Ekoru, Jimoh O. Pedro. Proportional-integral-derivative control of nonlinear half-car electro-hydraulic suspension systems[J]. Journal of Zhejiang University Science A, 2013, 14(6): 401-416.

@article{title="Proportional-integral-derivative control of nonlinear half-car electro-hydraulic suspension systems",
author="John E. D. Ekoru, Jimoh O. Pedro",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Proportional-integral-derivative control of nonlinear half-car electro-hydraulic suspension systems
%A John E. D. Ekoru
%A Jimoh O. Pedro
%J Journal of Zhejiang University SCIENCE A
%V 14
%N 6
%P 401-416
%@ 1673-565X
%D 2013
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1200161

T1 - Proportional-integral-derivative control of nonlinear half-car electro-hydraulic suspension systems
A1 - John E. D. Ekoru
A1 - Jimoh O. Pedro
J0 - Journal of Zhejiang University Science A
VL - 14
IS - 6
SP - 401
EP - 416
%@ 1673-565X
Y1 - 2013
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1200161

This paper presents the development of a proportional-integral-derivative (PID)-based control method for application to active vehicle suspension systems (AVSS). This method uses an inner PID hydraulic actuator force control loop, in combination with an outer PID suspension travel control loop, to control a nonlinear half-car AVSS. Robustness to model uncertainty in the form of variation in suspension damping is tested, comparing performance of the AVSS with a passive vehicle suspension system (PVSS), with similar model parameters. Spectral analysis of suspension system model output data, obtained by performing a road input disturbance frequency sweep, provides frequency response plots for both nonlinear vehicle suspension systems and time domain vehicle responses to a sinusoidal road input disturbance on a smooth road. The results show the greater robustness of the AVSS over the PVSS to parametric uncertainty in the frequency and time domains.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Akcay, H., Turkay, S., 2009. Influence of tire damping on mixed H 2/H synthesis of half-car active suspensions. Journal of Sound and Vibration, 322(1-2):15-28. 

[2] Astrom, K.J., Hagglund, T., 2001. The future of PID control. Control Engineering Practice, 9(11):1163-1175. 

[3] Astrom, K.J., Hagglund, T., 2004. Revisiting the Ziegler-Nichols step response method for PID control. Journal of Process Control, 14(6):635-650. 

[4] Buckner, G.D., Schuetze, K.T., Beno, J.H., 2000. Active Vehicle Suspension Control Using Intelligent Feedback Linearization. Proceedings of the American Control Conference, 6:4014-4018. 

[5] Cetin, S., Akkaya, A.V., 2010. Simulation and hybrid fuzzy-PID control for positioning of a hydraulic system. Nonlinear Dynamics, 61:465-476. 

[6] Chantranuwathana, S., Peng, H., 2004. Adaptive robust force control for vehicle active suspension. International Journal of Adaptive Control and Signal Processing, 18(2):83-102. 

[7] Chen, H., Liu, Z.Y., Sun, P.Y., 2005. Application of constrained H control to active suspension systems on half-car models. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 127(3):345-354. 

[8] Chien, T.L., Chen, C.C., Chiu, H.C., Cheng, H.W., Chen, Y.C., 2008. Almost disturbance decoupling control of nonlinear MIMO uncertain system and application to half-car active suspension system. International Journal of Vehicle Design, 46(4):367-392. 

[9] Dahunsi, O.A., Pedro, J.O., 2010. Neural network-based identification and approximate predictive control of a servo-hydraulic vehicle suspension system. Engineering Letters, 18(4):357-368. 

[10] Dahunsi, O.A., Pedro, J.O., Nyandoro, O.T., 2009. Neural Network-based Model Predictive Control of a Servo-hydraulic Vehicle Suspension System. , Proceedings of the International IEEE Africon, 1-6. :1-6. 

[11] Dahunsi, O.A., Pedro, J.O., Nyandoro, O.T., 2010. System identification and neural network based PID control of servo-hydraulic vehicle suspension system. SAIEE Africa Research Journal, 101(3):93-105. 

[12] Du, H., Zhang, N., 2007.  H control of active vehicle suspensions with actuator time delay. Journal of Sound and Vibration, 301(1-2):236-252. 

[13] Du, H., Zhang, N., 2009. Fuzzy control for nonlinear uncertain electrohydraulic active suspensions with input constraint. IEEE Transactions on Fuzzy Systems, 17(2):343-356. 

[14] Du, H., Zhang, N., 2009. Static output feedback control for electrohydraulic active suspensions via T-S fuzzy model approach. Journal of Dynamic Systems, Measurement and Control, Transactions of ASME, 131(5):1-11. 

[15] Du, H., Zhang, N., 2010. Robust active suspension design subject to vehicle inertial parameter variations. International Journal of Automation and Computing, 7(4):419-427. 

[16] Ekoru, J.E.D., Dahunsi, O.A., Pedro, J.O., 2011. PID Control of a Nonlinear Half-car Active Suspension System via Force Feedback. , Proceedings of the International IEEE Africon, 1-6. :1-6. 

[17] Eski, I., Yildirim, S., 2009. Vibration control of vehicle active suspension system using a new robust neural network control system. Simulation Modelling Practice and Theory, 17(5):778-793. 

[18] Fateh, M.M., Alavi, S.S., 2009. Impedance control of an active suspension system. Mechatronics, 19(1):134-140. 

[19] Feng, J.Z., Li, J., Yu, F., 2003. GA-based PID and fuzzy logic control for active vehicle suspension system. International Journal of Automotive Technology, 4(4):181-191. 

[20] Fialho, I., Balas, G.J., 2002. Road adaptive active suspension using linear parameter-varying gain-scheduling. IEEE Transactions on Control Systems Technology, 10(1):43-54. 

[21] Fischer, D., Isermann, R., 2004. Mechatronic semi-active and active vehicle suspensions. Control Engineering Practice, 12(11):1353-1367. 

[22] Gao, H., Lam, J., Wang, C., 2006. Multi-objective control of vehicle active suspension systems via load-dependent controllers. Journal of Sound and Vibration, 290(3-5):654-675. 

[23] Gao, Z., 2002. From linear to nonlinear control means: a practical progression. ISA Transactions, 41(2):177-189. 

[24] Griffin, M.J., 2007. Discomfort from feeling vehicle vibration. Vehicle System Dynamics, 45(7-8):679-698. 

[25] Guclu, R., 2003. Active control of seat vibrations of a vehicle model using various suspension alternatives. Turkish Journal of Engineering and Environmental Sciences, 27(6):361-373. 

[26] Guglielmino, E., Edge, K.A., 2004. A controlled friction damper for vehicle applications. Control Engineering Practice, 12(4):431-443. 

[27] Guo, B., Liu, H., Luo, Z., 2009. Adaptive PID Controller Based on BP Neural Network. , Proceedings of the International Conference on Artificial Intelligence, 148-150. :148-150. 

[28] Hanafi, D., 2010. PID Controller Design for Semi-active Car Suspension based on Model from Intelligent System Identification. , Proceedings of the 2nd International Conference on Computer Engineering and Applications, 60-63. :60-63. 

[29] Hassanzadeh, I., Alizadeh, G., Shirjoposht, N.P., Hashemzadeh, F., 2010. A new optimal nonlinear approach to half car active suspension. IACSIT International Journal of Engineering and Technology, 2(1):78-84. 

[30] Hrovat, D., 1997. Survey of advanced suspension developments and related optimal control applications. Automatica, 33(10):1781-1817. 

[31] Huang, C.J., Lin, J.S., Chen, C.C., 2010. Road adaptive algorithm design of half-car active suspension system. Expert Systems with Applications, 37(6):4392-4402. 

[32] Ji, X.D., Wan, K.J., Hai, N.Y., 2007. Time Delay Force Control for Vehicle Active Suspension System. , Proceedings of the 26th Chinese Controls Conference, 640-645. :640-645. 

[33] Ji, X.J., Li, S.J., 2009. Design of the Fuzzy-PID Controller for New Vehicle Active Suspension with Electro-Hydrostatic Actuator. , Proceedings of the 4th IEEE Conference on Industrial Electronics and Applications, 60-63. :60-63. 

[34] Kumar, M.S., 2008. Development of an Active Suspension System for Automobiles using PID Controller. , Proceedings on the World Congress on Engineering, 1472-1477. :1472-1477. 

[35] Marusak, P.M., Kuntanapreeda, S., 2011. Constrained model predictive force control of an electrohydraulic actuator. Control Engineering Practice, 19(1):62-73. 

[36] ODwyer, A., 2006.  Handbook of PI an PID Controller Tuning Rules. Imperial College Press,London :

[37] Pedro, J.O., 2007.  H 2-LQG/LTR controller design for active suspension systems. R and D Journal of the South African Institution of Mechanical Engineering, 23(2):32-41. 

[38] Pedro, J.O., Dahunsi, O., 2011. Neural network based feedback linearization control of a servo-hydraulic vehicle suspension system. International Journal of Applied Mathematics and Computer Science, 21(1):137-147. 

[39] Priyandoko, G., Mailah, M., Jamaluddin, H., 2009. Vehicle suspension system using skyhook adaptive neuro active force control. Mechanical Systems and Signal Processing, 23(3):855-868. 

[40] Renn, J., Wu, T., 2007. Modelling and control of a new 1/4t servo-hydraulic vehicle active suspension system. Journal of Marine Science and Technology, 15(3):265-272. 

[41] Ryu, S., Kim, Y., Park, Y., 2008. Robust H preview control of an active suspension system with norm-bounded uncertainties. International Journal of Automotive Technology, 9:585-592. 

[42] Sam, Y.M., Hudha, K., 2006. Modelling and Force Tracking of Hydraulic Actuator for an Active Suspension System. , Proceedings of the IEEE Conference on Industrial Electronics and Applications, 1-6. :1-6. 

[43] Sammier, D., Sename, O., Dugard, L., 2003. Skyhook and H control of semi-active suspensions: some practical aspects. Vehicle System Dynamics, 39(4):279-308. 

[44] Savaresi, S.M., Poussot-Vassal, C., Spelta, C., 2010.  Semi-active Suspension Control Design for Vehicles. Butterworth-Heinemann,Boston :

[45] Szaszi, I., Gaspar, P., Bokor, J., 2002. Nonlinear Active Suspension Modelling using Linear Parameter Varying Approach. , Proceedings of the 10th Mediterranean Conference on Control and Automation, 1-10. :1-10. 

[46] The MathWorks, Inc., 2001. Signal Processing Toolbox for Use with Matlab® User’s Guide Version 5.1. , :

[47] Weber, P.A., Braaksma, J.P., 2000. Towards a North American geometric design standard for speed humps. ITE Journal, 70(1):30-34. 

[48] Williams, R.A., 1997. Automotive active suspensions Part 2: Practical considerations. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 211(6):427-444. 

[49] Yagiz, N., Hacioglu, Y., 2008. Backstepping control of a vehicle with active suspensions. Control Engineering Practice, 16(12):1457-1467. 

[50] Yoshimura, T., Kume, A., Kurimoto, M., Hino, J., 2001. Construction of an active suspension system of a quarter car model using the concept of sliding mode control. Journal of Sound and Vibration, 239(2):187-199. 

[51] Zhao, Q., Yin, J., Li, D., 2011. Intelligent Compound Control of Vehicle Active Suspension based on RBF Neural Network. Proceedings of the 3rd International Conference on Measuring Technology and Mechatronics Automation, 2:441-444. 

[52] Zuo, L., Nayfeh, S.A., 2003. Low order continuous-time filters for approximation of the ISO 2631-1 human vibration sensitivity weightings. Journal of Sound and Vibration, 265(2):459-465. 

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2022 Journal of Zhejiang University-SCIENCE