The study of pedestrian evacuation in channels with different structures is important among optimizing
through efficiency, avoiding accidents and designing passageway. It is of significant reference to set up a specific
model on account of the real traffic system and design an appropriate controller to apply on it. This paper
establishes a macroscopic model for T-shaped channel with a number of controlled entrances basing on the law
of mass conservation. Then, with the method of cascade, a kind of sliding mode controller is designed to achieve
the control target of avoiding the blocking and maximizing the pedestrian flow of the whole model, the stability
of the system is proved by the Lyapunov stability theory, and the boundary layer method is applied to restrain
the chattering of the controller. Finally, simulation results show the efficiency of the sliding mode controller and
the improvement brought by the boundary layer method.
CHANG Lu, SHAN Liang, LI Jun, DAI Yuewei
. Sliding Mode Control of T-Shaped Pedestrian Channel[J]. Journal of Shanghai Jiaotong University(Science), 2020
, 25(4)
: 478
-485
.
DOI: 10.1007/s12204-020-2198-8
[1] HELBING D, MOLN′AR P. Social force model for pedestrian dynamics [J]. Physical Review E, 1995,51(5): 4282-4286.
[2] HELBING D, BUZNA L, JOHANSSON A, et al. Selforganized pedestrian crowd dynamics: Experiments,simulations, and design solutions [J]. Transportation Science, 2005, 39(1): 1-24.
[3] MA P J, WANG B H. The escape of pedestrians with view radius [J]. Physica A: Statistical Mechanics and Its Applications, 2013, 392(1): 215-220.
[4] HOU L, LIU J G, PAN X, et al. A social force evacuation model with the leadership effect [J]. Physica A:Statistical Mechanics and Its Applications, 2014, 400:93-99.
[5] MURAMATSU M, IRIE T, NAGATANI T. Jamming transition in pedestrian counter flow [J]. Physica A: Statistical Mechanics and Its Applications, 1999,267(3/4): 487-498.
[6] MURAMATSU M, NAGATANI T. Jamming transition of pedestrian traffic at a crossing with open boundaries [J]. Physica A: Statistical Mechanics and Its Applications, 2000, 286(1/2): 377-390.
[7] MA J. Study of the behavioral mechanism of selforganized pedestrian counter flow [D]. Hefei, China:University of Science and Technology of China, 2010(in Chinese).
[8] CHEN C K, LI J, ZHANG D. Study on evacuation behaviors at a T-shaped intersection by a force-driving cellular automata model [J]. Physica A: Statistical Mechanics and Its Applications, 2012, 391(7): 2408-2420.
[9] HENDERSON L F. The statistics of crowd fluids [J].Nature, 1971, 229(5284): 381-383.
[10] HELBING D. A fluid-dynamic model for the movement of pedestrians [J]. Complex System, 1992, 6(5):391-415.
[11] HOOGENDOORN S, BOVY P H L. Gas-kinetic modeling and simulation of pedestrian flows [J]. Transportation Research Record: Journal of the Transportation Research Board, 2000, 1710(1): 28-36.
[12] HENDERSON L F. On the fluid mechanics of human crowd motion [J]. Transportation Research, 1974, 8(6):509-515.
[13] HUGHES R L. The flow of large crowds of pedestrians[J]. Mathematics and Computers in Simulation, 2000,53(4/5/6): 367-370.
[14] HUGHES R L. The flow of human crowds [J]. Annual Review of Fluid Mechanics, 2003, 35: 169-182.
[15] XIONG T, ZHANG P, WONG S C, et al. A macroscopic approach to the lane formation phenomenon in pedestrian counterflow [J]. Chinese Physics Letters,2011, 28(10): 108901.
[16] LI R F. Study on passenger flow model at metro platform end based on fluid mechanics [D]. Beijing, China:Beijing Jiaotong University, 2012 (in Chinese).
[17] KACHROO P, ¨OZBAY K. Feedback control theory for dynamic traffic assignment [M]. London, UK: Springer,1999.
[18] SHENDE A, SINGH M P, KACHROO P. Optimal feedback flow rates for pedestrian evacuation in a network of corridors [J]. IEEE Transactions on Intelligent Transportation Systems, 2013, 14(3): 1053-1066.
[19] SHAN L, CHANG L, XU S Y, et al. Robot-assisted pedestrian flow control of a controlled pedestrian corridor[J]. International Journal of Advanced Robotic Systems, 2018, 15(6): 1-11.
[20] ZHANG C Q. Study on levels of service for pedestrian facility in MTR hubs [D]. Beijing, China: Beijing Jiaotong University, 2008 (in Chinese).
[21] SLOTINE J J, SASTRY S S. Tracking control of nonlinear systems using sliding surfaces, with application to robot manipulators [J]. International Journal of Control, 1983, 38(2): 465-492.
[22] RYU S H, PARK J H. Auto-tuning of sliding mode control parameters using fuzzy logic [C]//American Control Conference. Arlington, VA, USA: IEEE, 2001:618-623.
[23] ZHAO W J, LIU J Z. An improved method of sliding mode control with boundary layer [J]. Journal of System Simulation, 2015, 17(1): 156-158 (in Chinese).
[24] ZHANG S B, GUO Y. Distributed multi-robot evacuation incorporating human behavior [J]. Asian Journal of Control, 2015, 17(1): 34-44.
[25] JIANG C, NI Z, GUO Y, et al. Robot-assisted pedestrian regulation in an exit corridor [C]// IEEE/RSJ International Conference on Intelligent Robots and Systems. Daejeon, Korea: IEEE, 2016: 815-822.
[26] LU Y S, CHEN J S. Design of a global sliding-mode controller for a motor drive with bounded control [J].International Journal of Control, 1995, 62(5): 1001-1019.
[27] CHANG L, SHAN L, XU S Y, et al. State feedback control of T-shaped pedestrian channel [C]//Chinese Automation Congress. Jinan, China: IEEE, 2017:6845-6850.
