Model Predictive Control System Design using ARMAX Identification Method for Car-following Behavior

Document Type : Research Paper

Authors

1 Mechanical Engineering Department, K. N. Toosi University of Technology, Tehran

2 Department of Mechanical Engineering, Pardis Branch, Islamic Azad University

3 Mechanical Engineering Department, Shahid Rajaee Teacher Training University, Tehran

Abstract

The control of car following is essential due to its safety and its operational efficiency. For this purpose, this paper builds a model of car following behavior based on ARMAX structure from a real traffic dataset and design a Model Predictive Control (MPC) system. Based on the relative distance and relative acceleration of each instant, the MPC predicts the future behavior of the leader vehicle and according to this behavior, the acceleration of the follower vehicle is controlled. Validation of the presented controller is done by comparing the behavior of the controller with the human drivers. Results show that the MPC controller has a behavior much safer than that of real drivers and it can provide a pleasant trip for passengers.

Keywords

Main Subjects

References

[1]      Rothery, R. W., “Car Following Models: In Traffic Flow Theory”, Transportation Research Board, Vol. 165, pp. (4)1-(4)41, (1992).
 
[2]      Zhang, H. M., and Kim, T., “A Car-following Theory for Multiphase Vehicular Traffic Flow”, Transportation Research Part B: Methodological, Vol. 39, No. 5, pp. 385–399 (2005).
 
[3]      Mar, J., and Hung-Ta, L., “The Car-following and Lane-changing Collision Prevention System Based on the Cascaded Fuzzy Inference System”, IEEE Transactions on Vehicular Technology, Vol. 54, No. 3, pp. 910-924, (2005).
 
[4]      Pan, D., and Zheng, Y., “Optimal Control and Discrete Time-delay Model of Car Following”, IEEE 7th World Congress on Intelligent Control and Automation, Chongqing, China, pp. 5657-5661, (2008).
 
[5]      Peng, Y. F., Hsu, C. F., Chih-Min, L.,  and Kao, C. J., “Robust CMAC Back Stepping Longitudinal Control of Vehicle Platoons”, IEEE International Conference, Networking, Sensing and Control, Taipei, Taiwan, Vol. 1, pp. 571-576, (2004).
 
[6]      Zakian, V., “Control Systems Design: A New Framework”, Springer-Verlag, Berlin, (2005).
 
[7]      Limon, D., Alvarado, I., Alamo, T., and Camacho, E.F., “MPC for Tracking Piecewise Constant References for Constrained Linear Systems”, Automatica, Vol. 44, pp. 2382–2387, (2008).
[8]      Maciejowski, J. M., “Predictive Control with Constraints”, Prentice Hall, Harlow, England, (2002).
 
[9]      Baskar, L. D., Schutter, B. D., and Hellendoorn, H., “Model-based Predictive Traffic Control for Intelligent Vehicles: Dynamic Velocity Limits and Dynamic Lane Allocation”, IEEE Intelligent Vehicles Symposium, Eindhoven, Netherlands, pp. 174–179, (2008).
 
[10]  Bellemans, T., De Schutter, B., and De Moor, B., “Model Predictive Control for Ramp Metering of Motorway Traffic: A Case Study”, Control Engineering Practice, Vol. 14, No. 7, pp. 757–767, (2006).
 
[11]  Hegyi, A., De Schutter, B., and Hellendoorn, J., “Optimal Coordination of Variable Speed Limits to Suppress Shock Waves”, IEEE Transactions on Intelligent Transportation Systems, Vol. 6, No. 1, pp. 102–112, (2005).
 
[12]  Kamal, M. A. S., Mukai, M., Murata, J. and Kawabe, T., “On Board Eco-driving System for Varying Road-traffic Environments using Model Predictive Control”, IEEE International Conference on Control Applications (CCA), Yokohama, Japan, pp. 1636-1641, (2010).
 
[13]  Naus, G. J. L., Ploeg, J., Van de Molengraft, M. J. G., Heemelsand, W.P.M.H., and Steinbuch, M., “A Model Predictive Control Approach to Design a Parameterized Adaptive Cruise Control”, Automotive Model Predictive Control, Vol. 402, pp. 273-284, Springer-Verlag, Berlin Heidelberg, (2010).
 
[14]  Salehinia, S., “Predictive Control System Design for Car Following Behavior in Traffic Flow”, M.Sc. Thesis, Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran, (2012).
 
[15]  Kvapil, D., “Stability Analysis of State-space Models in MATLAB”, Journal of Applied Mathematics, Vol. 3, No. 2, pp. 189-198, (2010).
 
[16]  Tettamanti, T., Varga, I., Kulcsár, B. and Bokor, J., “Model Predictive Control in Urban Traffic Network Management”, IEEE 16th Mediterranean Conference on Control and Automation Congress Centre, Ajaccio, France, pp. 1538–1543, June, (2008).
 
[17]  Bemporad, A., and Morari, M., “Robust Model Predictive Control: A Survey”, Automatic Control Laboratory, Swiss Federal Institute of Technology (ETH), Springer, Switzerland, (2007).
 
[18]  Brookhuis, K. A., de Vries, G., and de Waard, D., “The Effects of Mobile Telephoning on Driving Performance”, Elsevier Journal of Accident Analysis and Prevention, Vol. 23, No. 4, pp. 309–316, (1991).
 
[19]  Caird, J.K., Willness, C.R., Steel, P., and Scialfa, C., “A Meta-analysis of the Effects of Cell Phones on Driver Performance”, Elsevier Journal of Accident Analysis and Prevention, Vol. 40, No. 4, pp. 1282-1293, (2008).
 
[20]  Terwen, S., Back, M., and Krebs, V., “Predictive Powertrain Control for Heavy Duty Truck”, In: Proceedings of the IFAC Symposium on Advances in Automotive Control, Salerno, Italy, Vol. 39, pp. 105-110, (2004).
 
[21]  Falcone, P., Borelli, F., Asgari, J., He, T., and Hrovat, D., “A Model Predictive Control Approach for Combined Braking and Steering in Autonomous Vehicles”, In: Proceedings of the IEEE Conference on Control and Automation, Athens, Greece, pp. 1-6, (2007).
 
[22]  Re, L., Ortner, P., and Alberer, D., “Chances and Challenges in Automotive Predictive Control”, Automotive Model Predictive Control Models, Methods and Applications, Vol. 402, pp. 1-22, (2010).
 
[23]  US Department of Transportation, NGSIM – Next Generation Simulation, http://www.ngsim.fhwa.dot.gov (2009).
 
[24]  The Federal Highway Administration Website: US 101 Highway (Hollywood Freeway), Dataset:http://www.fhwa.dot.gov/publications/research/operations/07030/index.cfm.
 
[25]  Khodayari, A., Ghaffari, A., Kazemi, R., and Braunsting, R., “A Modified Car-following Model Based on a Neural Network Model of the Human Driver Effects”, IEEE Transactions on Systems, Man, and Cybernetics, Part A-Systems and Humans, Vol. 42, No. 6, pp. 1440–1449, (2011).
 
[26]  Thiemann, C., Treiber, M., and Kesting, A., “Estimating Acceleration and Lane-changing Dynamics Based on NGSIM Trajectory Data”, Transportation Research Record: Journal of the Transportation Research Board, Vol. 2088, pp. 90-101, (2008).
 
[27]  Box, G. P., Jenkins, G. M., and Reinsel, G. C., “Time Series Analysis: Forecasting and Control”, 3rd ed. Prentice-Hall (1994).
 
[28]  Hamilton, J. D., “Time Series Analysis”, Princeton University Press, (1994).
 
[29]  Katayama, T., “Subspace Methods for System Identification”, Springer-Verlag, Berlin, (2005).
 
[30]  Ljung, L., “System Identification. Theory for the User”, 2nd ed. Prentice Hall, New York, (1999).
 
[31]  Soderstrom, T. and Stoica, P., “System Identification”, Prentice-Hall, New York, (1989).
 
[32]  Overschee, P., Van and De Moor, B., “Subspace Identification for Linear Systems. Theory–implementation–applications”, Kluwer Academic Publishers, (1996).
 
[33]  Zhu, Y., “Multivariable System Identification for Process Control”, Pergamon, London, (2001).
 
[34]  Jørgensen, J. B., Huusom, J. K., and Rawlings, J. B., “Finite Horizon MPC for Systems in Innovation Form”, 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC),Orlando, FL, USA, December 12-15, (2011).
 
[35]  Ljung, L., “System Identification ToolboxTM 8 User’s Guide”, The MathWorks, Inc. (2012).
 
[36]  Cohen, E. R., “An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements”, Measurement Science and Technology, Vol. 9, No. 6,  pp. 839-1026, June, (1998).
 
[37]  Wang, L., “Model Predictive Control System Design and Implementation using MATLAB”, Springer, Australia, (2009).
 
[38]  Bemporad, A., Morari, M., Dua, and Pistikopoulos, V., “The Explicit Linear Quadratic Regulator for Constrained Systems”, Automatica, Vol. 38, No. 1, pp. 3-20, (2002).
 
[39]  Pipes, L. A., “An Operational Analysis of Traffic Dynamics”, Journal of Applied Physics, Vol. 24, No. 3, pp. 274–281, (1953).
 
[40]  Nikolaou, M., “Model Predictive Controllers: A Critical Synthesis of Theory and Industrial Needs”, Elsevier Advances in Chemical Engineering, Vol. 1, No. 713, pp. 131–204, (2001).
 
[41]  Palumbo, G., and Pennisi, S., “Feedback Amplifiers-Theory and Design”, Springer, New York, (2003).
 
[42]  Ogata, K., “Modern Control Engineering”, Prentice Hall, New York, (2010).
 
Garcia, C.E., Prett, D.M., and Morari, M., “Model Predictive Control: Theory and Practice-A Survey”, Automatica, Vol. 25, No. 3, pp. 335–348, (1989).

Files

Share

How to cite

Statistics