Abstract
The active suspension system has always been a topic of interest because of its ability to influence the ride quality by exerting independent forces on the suspension by the usage of separate actuators. Various strategies have been proposed over the years in order to estimate the appropriate control action. These strategies are typically feedback oriented and dependent on many factors like the control objective, the frequency of the excitation and system non-linearities that result in the formulation of a complex problem. A simulation-based study using a comprehensive quarter car model with an active suspension is beneficial to summarize the character of each of these approaches by comparing attributes like formulation, performance, robustness, tunability and requirements for implementation on real physical systems.
Since active suspensions use an on-board computer and sensor measurements to determine the control action, the enactment of a strategy is limited by the computational requirements and available measurements. This study aims to foresee such challenges when implementing modern control strategies like H∞ control or preview based approaches like Model Predictive Control (MPC) and Deep Learning methods. The latter will focus on both Supervised Learning (SL) and Reinforcement Learning (RL) approaches. These methods are firstly developed in a virtual environment and subsequently implemented on a physical quarter car setup excited by a servo-hydraulic actuator. Finally, a comparison of the performances of the different control approaches is presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
[1] L. Eckstein, Vertical and Lateral Dynamics of Vehicles, Aachen, 2014.
[2] S. Savaresi, C. Poussot-Vassal, C. Spelta, O. Sename and L. Dugard, Semi-Active Suspension Control Design for Vehicles, Elsevier, 2010.
[3] G. Zames, “Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses,” IEEE Transactions on Automatic Control, pp. 301-320, April 1981.
[4] MathWorks Inc., “Robust Control of an Active Suspension,” 2019. [Online]. Available: https://de.mathworks.com/help/robust/gs/active-suspension-controldesign.html.
[5] H. Chen and K.-H. Guo, “Constrained H∞ Control of Active Suspensions: An LMI Approach,” IEEE Transactions on Control Systems Technology, pp. 412-4221, 2005.
[6] N. M. Ghazaly, A.-N. Sharkawy, A. S. Ali and G. Abdel-Jaber, “H∞ Control of Active Suspension System for a Quarter Car Model,” International Journal of Vehicle Structures and Systems, pp. 81-87, January 2016.
[7] M. Yamashita, K. Fujimori, K. Hayakawa and H. Kimura, “Application of H∞ control to active suspension systems,” IFAC Proceedings Volumes, pp. 87-90, 1993.
[8] A. Alessio and A. Bemporad, “A Survey on Explicit Model Predictive Control,” in Nonlinear Model Predictive Control, Berlin, Heidelberg, Springer, 2009, pp. 345-369.
[9] K. Kouramas, N. Faísca, C. Panos and E. Pistikopoulos, “Explicit/multiparametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming,” Automatica 47, pp. 1638-1645, 2011.
[10] L. H. Cseko”, M. Kvasnica and B. Lantos, “Analysis of the explicit model predictive control for the semi-active suspension,” Periodica Polytechnica, pp. 41-58, 2010.
[11] J. Theunissen, A. Sorniotti, P. Gruber, S. Fallah, M. Dhaens, K. Reybrouck and C. Lauwerys, “Explicit model predictive control of active suspension systems,” Proceedings of the International Conference on Advanced Vehicle Powertrains, pp. 344-362, 2017.
[12] R. Dessort and C. Chucholowski, “Explicit model predictive control of semiactive suspension systems using Artificial Neural Networks (ANN),” 8th International Munich Chassis Symposium, 2017.
[13] V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra and M. Riedmiller, “Playing Atari with Deep Reinforcement Learning,” arXiv preprint arXiv:1312.5602, 2013.
[14] R. S. Sutton and A. G. Barto, Reinforcement Learning: An Introduction, London, England: The MIT Press, 2017.
[15] G. Frost, T. J. Gordon, M. N. Howell and Q. H. Wu, “Moderated Reinforcement Learning of Active and Semi-Active Suspension Control Laws,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, p. 249–257, 1 November 1992.
[16] M. Howell, G. Frost, T. Gordon and Q. Wu, “Continuous action reinforcement learning applied to vehicle suspension control,” Mechatronics, pp. 263,276, 1997.
[17] S. Tognetti, S. M. Savaresi, C. Spelta and M. Restelli, “Batch Reinforcement Learning for Semi-Active Suspension Control,” 18th IEEE International Conference on Control Applications, pp. 582-587, 8-10 July 2009.
[18] I. O. Bucak and H. Oz, “Vibration control of a nonlinear quarter-car active suspension by reinforcement learning,” International Journal of Systems Science, 2011.
[19] G. Koch, E. P. S. Spirk and B. Lohmann, “Design and Modelling of a Quarter-Vehicle Testrig for Active Suspension Control,” Technical Reports on Automatic Control, 21 July 2010.
[20] M. F. Soong, R. Ramli and A. Saifizul, “Between simplicity and accuracy: Effect of adding modeling details on quarter car vehicle model accuracy,” PLoS ONE 12(6), 2017.
[21] C. Zhang, O. Vinyals, R. Munos and S. Bengio, “A Study on Overfitting in Deep Reinforcement Learning,” CoRR, 2018.
[22] J. C. Doyle, K. Glover, P. P. Khargonekar and B. A. Francis, “State-Space Solutions to Standard H2 and H∞ Control Problems,” IEEE Transactions on Automatic Control, pp. 831-847, August 1989.
[23] M. Grant and S. Boyd, “CVX: Matlab Software for Disciplined Convex Programming, version 2.1,” March 2014. [Online]. Available: http://cvxr.com/cvx.
[24] M. Grant and S. Boyd, “Graph implementations for nonsmooth convex programs,” in Recent Advances in Learning and Control, Springer-Verlag Limited, 2008, pp. 95-110.
[25] L. Wang, Model Predictive Control System and Design Implementation using MATLAB, Springer, 2008.
[26] MathWorks, Inc., “Optimization Toolbox,” 2019. [Online]. Available: https://de.mathworks.com/help/optim/index.html.
[27] MathWorks, Inc., “Deep Learning Toolbox,” 2019. [Online]. Available: https://de.mathworks.com/help/deeplearning/.
[28] A. Gosavi, Simulation-Based Optimization: Parametric Optimization Techniques and Reinforcement Leanring, New York, NY: Springer, 2014.
[29] F. Gustafsson, Control of Inverted Double Pendulum using Reinforcement Learning, 2016.
[30] L. Zuo and S. Nayfeh, “Low order continuous-time filters for approximation of the ISO 2631-1 human vibration sensitivity weightings,” Journal of Sound and Vibration 265, pp. 459-465, 2003.
[31] E. Frazzolli, 6.241 Dynamic Systems and Control, Lecture 25: H∞ sysnthesis, Lecture Slides, Massachusetts Institute of Technology, 2011.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Fachmedien Wiesbaden GmbH, part of Springer Nature
About this paper
Cite this paper
Khandavalli, G.B., Kalabis, M., Wegener, D., Eckstein, L. (2020). Potentials of modern active suspension control strategies – from model predictive control to deep learning approaches. In: Pfeffer, P. (eds) 10th International Munich Chassis Symposium 2019. Proceedings. Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-26435-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-658-26435-2_16
Published:
Publisher Name: Springer Vieweg, Wiesbaden
Print ISBN: 978-3-658-26434-5
Online ISBN: 978-3-658-26435-2
eBook Packages: EngineeringEngineering (R0)