MPC Based Driver's Intention Prediction Method for Vehicle Stability Control

Transcription

1 nd International Conerence on Automation echanical and Electrical Engineering (AEE 7) PC Based Driver's Intention Prediction ethod or Vehicle Stability Control Shunhang Zheng Bangcheng Zhang Shaosong Li Luping Guo Guodong Wang Zheng Li and Xiaohui Lu Changchun University o Technology Changchun China Corresponding author Abstract Aiming at improving vehicle handling and stability perormance a model predictive control based vehicle yaw stability controller is designed via active ront steering system In this paper the erence yaw rate is varied in each prediction horizon which can predict the driver's intention And the steering system constraint is also taen into account The proposed PC controller is veriied on a Carsim simulation platorm under the sinusoidal input test maneuver Simulation results show the beneits o the control methodology used II SYSTE ODELING FOR CONTROL D ESIGN A Vehicle model A DOF vehicle model is considered as shown in Figure which utilizes small angle assumptions and the approximation that the tires on each axle can be lumped together A constant vehicle longitudinal velocity Ux is also assumed The equations o motion or this model can be written in state-space orm as: Keywords- model predictive control; vehicle stability control; active ront steering x (t ) I INTRODUCTION Yaw stability control system plays a signiicant role in vehicle lateral dynamics in order to improve the vehicle handling and stability perormances Active ront steering system (AFS) is an eective control system to improve handling stability and active saety perormance and it has been the research hotspots nowadays[] where the state variable is yaw rate ; the control input is ront steering angle ; the disturbance inputs is side slip angle The state matrix A input matrix Bu disturbance input matrix Bd as ollows: odel Predictive Control (PC) can predict the vehicle dynamics states in the uture and has advantage in dealing with multiple control objectives in the case o constraints [][3] Recent contributions to theory and algorithms have enlarged the application spectrum o real-time PC[][5] Several PC controllers have been proposed or the active ront steering control[][7] However in the presented PC based yaw stability controller the ideal yaw rate is set to be a ixed value in each control cycle which will cause poor controller perormance In this paper a variable erence methods is proposed In each prediction horizon the erence yaw rate is varied which can predict the driver's intention Ax(t ) Bu u (t ) Bd d (t ) A Bu Bd (l C UxIz l C lr Cr ) Iz (l C Iz lr Cr ) where m and I z are the vehicle mass and yaw moment o inertia respectively; C is the ront tire cornering stiness; Cr is the rear tire cornering stiness; l is the distance rom CG to ront axle; lr is the distance rom CG to rear axle The organization o this paper is as ollows In Section a vehicle model is built and a control problem is stated in detail In Section 3 a PC yaw rate stability controller based on variable erence introduced Section gives the simulation results to validate the eectiveness o the proposed controller or dierent cases The conclusion and uture wor are summarized in Section 5 Y u lr Fyr l X F y L FIGURE I DOF VEHICLE ODEL Copyright 7 the Authors Published by Atlantis Press This is an open access article under the CC BY-NC license ( 9

2 B Control Problem Statement From the viewpoint o vehicle dynamics the yaw rate are closely related to vehicle stability which are controlled by the ront steering angle And the ollowing two objectives are considered: dri U x good handling and stability smooth steering o vehicle Ux FIGURE II CONTROL SCHEE In addition some constraints should be taen into account Due to actuator saturation which can be considered as a physical constraint o system An upper bound on the steering angle magnitude as expressed by the ollowing inequality constraint In order to simpliy the design process the ollowing assumptions are made Carsim vehicle model can accurately represent the real vehicle in this simulation-based study The vehicle parameter values are accurate and constant throughout the simulation such as vehicle mass All the vehicle state inormation can be obtained accurately such as tire-road riction coeicient The ront wheel steering rate is constrained to obtain a smoother control command sequence A DOF erence model is designed to determine ideal motion state o vehicle And the desired yaw response is derived in [8] The vehicle longitudinal speed is maintained constant B Design o the Prediction Equation Aiming at solving the tracing problem the system model () is described as a discrete orm in (5) with the Euler method The sample time is int t / Ts where t is running time and Ts is a ixed step size x ( ) Theore on the basis o those discussed above the stability control problem is described as ollows: Aiming at eeping yaw stability o vehicle yaw rate tracs the desired oreover or avoiding control saturation and preservation o driver comort the ront wheel steering angle and the ront wheel steering angle rate are constrained y ( ) Cx ( ) Where Ac Ts e ATs Bcu e At dt Bu Bcd Ts e At dt Bd C= The discrete orm can be written as incremental orm in () as ollows in which system static error can be eliminated x ( ) Ac x( ) Bcu u ( ) Bcd d ( ) y ( ) C x( ) y ( ) III DESIGN OF ODEL PREDICTIVE CONTROLLER A Control Scheme In this section a model predictive controller is derived to solve the constrained tracing problem mentioned above The control scheme o the proposed control system is shown in Figure which contains several subsystems In the erence model subsystem the desired value o the vehicle yaw rate is calculated based on steering angle vehicle longitudinal velocity and tire-road riction coeicient The input o the vehicle is ront wheel steering angle The output o the vehicle are vehicle yaw rate vehicle side slip angle vehicle longitudinal velocity U x and tire-road riction coeicient Ac x ( ) Bcu u ( ) Bcd d ( ) For this control system at sample time the uture control input sequence U is the optimization vector in the ollowing cost unction and the predictive control output sequence is Y which can be deined as ollows: y u U u Y y u m m y p p where each vector o U() is an array o control inputs u and each vector o Y() is an array o system output P is deined as predictive horizon to extend the orecast o the system uture output and m is deined as control horizon

3 The sequence o the control input change U is calculated by u u u which is equal to zero beyond the control horizon They are ormed as ollows: erence value Past Future Normal PC Proposed PC u u U Predicted output y Open-loop input u u m m Closed-loop Output y C Driver's Intention Prediction Considering that the driver's intention is always changing continuously the erence yaw rate will be calculated in realtime on the basis o driver's intention In order to get better controller perormance the erence yaw rate value is set to be variable in predictive horizon Here R() is deined as output erence sequence The calculation or driver's intention is ormed as ollows: r ( ) r ( ) r ( r ( ) ) ( ) ( ( ) ( ) ( ( ) ( )) ( )) r ( P ) r ( P ) ( ) ( ( ) ( )) Closed-loop input u t t+tsm t+tsp Control horizon Prediction horizon FIGURE III PREDICTION THEORY D Design o the Optimization Function In order to achieve precise yaw rate control an objective unction is designed based on the tracing problem which is composed o two parts as ollows: () The main control requirement is to mae actual yaw rate trac the required erence R() The criterion or minimizing the deviation between predicted outputs and given erences is usually chosen in a quadratic orm Theore the irst cost unction is as ollows J r t+ Y R Q p R r r p i p where ( ) is the erence yaw rate rom erence model; ( ) is the erence yaw rate value at previous sample time and is weight coeicient which can adjust change rate o erence yaw rate and then aect the tracing perormance o vehicle Figure 3 describes how the algorithm wors in PC The red curve is based on the method proposed in this paper The blac curve is based on normal PC method It can be seen that the erence value changes in prediction horizon and the open-loop input is bigger than the normal PC method This means a better prediction o uture dynamics The beneits o this algorithm are clear which can provide more accurate optimization results and better responsiveness Q j where Q is a positive weight actor or adjusting tracing perormance and weight matrix Q=diag(Q) () In order to reduce the change rate o control action and ensure smooth steering a cost unction is ormed as ollows J U S j m j j S j Finally a total objective unction o the optimal control problem is deined over a receding horizon consisting o two parts ()() as ollows: J mpc J J Y R Q U S

4 In addition the constraints in (3)() can be handled with by PC in optimization process at each sample time The hard constraints o the control input and can be rewritten as ollows j j Yawrate (deg/s) erence Normal PC Proposed PC j m 3 5 time (s) (a) yaw rate E odel Predictive Control Law The linear optimization problem is solved by using a quadratic programming (QP) method[9] which can be deined as ollows: Front wheel angle (deg) min xt Hx g T x x Ex u( ) U( ) where u() is a set o optimal vectors or active steering angle IV SIULATION COPARISON AND ANALYSIS In this section simulation results are shown to demonstrate the validity o the proposed PC controller compared with normal PC controller The simulation is evaluated on Carsim vehicle model The control eects o the designed PC controller on sinusoidal input test maneuver at high speed is veriied The simulation conditions are as ollows: The vehicle speed is m/h The road surace is dry concrete with tireroad riction coeicient as 85 and driver input is the sinusoidal input Simulation results o vehicle yaw rate is shown in Figure (a) It can be seen that the normal PC controller have a bigger tracing error than the proposed PC controller based on variable erence yaw rate which means that the driver's intentions method has good perormance And Figure (b) describes the vehicle ront wheel angle at sinusoidal input maneuver The experiment result showed that proposed PC controller has aster response than the normal PC controller - - b where H is symmetric matrix; g Gradient vector E and b are constraint matrix According to PC control strategy the irst element o the U() is implemented and the calculation is repeated at each time instant Hence at time instant the resulting state eedbac control law is as ollows Driver input Normal PC Proposed PC Time (s) (b) ront wheel angle 8 FIGURE IV SIULATION RESULTS OF SINUSOIDAL INPUT TEST ANEUVER WHEN =85 V CONCLUSIONS This paper ocuses on yaw stability control via active ront steering and presents a driver's intention prediction method The erence yaw rate value is varied in prediction horizon which means that the proposed PC controller has better control accuracy The proposed PC controller is veriied on an Carsim simulation platorm under the sinusoidal input test maneuver at high speed Simulation results show the beneits o the control methodology used In the uture eectiveness o the control strategy will be validated in the currently being built vehicle test bench In order to achieve better control perormance urther study about the proposed PC controller is needed ACKNOWLEDGENT The wor is supported by the Jilin Province Science and Technology Found or Young Scholars (No7597JH; No5JH) and by the Key Technology and Development Program o Jilin Province (No75GX) REFERENCES [] [] Jin X J Yin G Li Y Li J Stabilizing Vehicle Lateral Dynamics with Considerations o State Delay o AFS or Electric Vehicles via Robust Gain Scheduling Control Asian Journal o Control Jiechao Liu Paramsothy Jayaumar Jerey L Stein & Tulga Ersal A study on model idelity or model predictive control-based obstacle avoidance in high-speed autonomous ground vehicles Vehicle Dynamics Control vol 5 no pp 9 5 August

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