driver model - iit hyderabad
TRANSCRIPT
Driver model
BIBIN S ME13M1004
SAMUKHAM SURYA ME13M1012
SANTHOSH KUMAR ME13M1007
VINU V ME13M1016
ANWAR SADATH ME12M14P0 00001
RAGHAVENDRA ADITYA ME10B007
MADHAVA RAMESH ME11B038
3D CAD Model Of Mahindra Scorpio
3D CAD Model Of Mahindra Scorpio
Introduction β’ A driver model is a mathematical model which replicates the
functionality of a driver( controlling , monitoring and stabilizing a vehicle )during various maneuvers .
Road Conditions
Required Trajectory
Driver
Air Road
Vehicle
Engine
Vibration, Noise etc.,
Trajectory
Steering Control
Brake
Accelerator
Chassis
Disturbances
π½ , π , π , π, π,ππ
ππ‘,π£2
π ,
π, π½, π
Simplified scheme of the simplified vehicle-Driver System
Driver Model
Vehicle
Process
Intended + Path -
Actual Path
πΏ, π£
Controller C(s)
Plant P(s) Desired + input -
Output
units
Driver β vehicle 1-D model
Proposed driver models
β’ Driver model(PID controller): β’ Simple linearized driver model with and without delay
β’ Path following driver model.
β’ Path following driver model which minimizes lateral deviation and heading error according to a previewed path function and improves stability by regulating yaw and lateral disturbances during maneuvers.
β’ Vehicle Model β’ Rigid body model under neutral steering condition.
β’ Simple linearized driver model with out delay
πΏ π‘ + π = βπΎπ π π‘ β π π‘
ππΏ(π‘) + πΏ π‘ = βπΎπ π π‘ β π π‘
π½π§π = πππ + ππΏπΏ +ππ§π
π½π§π β πππ + πππΎπ = ππΏπΎπππ π‘ + ππ§π
ππ >2 π½π§πΎπππΏ
πΎπ <ππ
2
4π½π§ππΏ
β’ Simple linearized driver model with delay
π πΏ
π = π΄
ππΏπ
+ π΅πππ + π΅πππ§π
π΄ =
πππ½π§
ππΏπ½π§ 0
0 β1π
βπΎππ
1 0 0
, π΅π=
1π½π§
00
, π΅π =π πΏ
π
π 3 + π1
πβ
ππ
π½π§π 2 β
ππ
ππ½π§π +
ππΏπΎπ
ππ½π§=0
πΎπ <ππ
2
π½π§ππΏ
π <π½π§ππ
2
ππ2 β π½π§ππΏπΎπ
Proportional Constant Vs Velocity @ different time delays
Simple linearized Driver model with Delay Yellow is the desired path Violet is the Actual path
x
y
Path
π₯ π¦
π
π
cos(Σ¨) Sin(Σ¨) Tan(Σ¨)/l
0
v1
0 0 0 1
v2 + =
Zβ = ππ§
ππ π΄ = 0 1 B = 0
0 0 1
Path fallowing driver model.
π = π£1cos (π )
1 β ππ(π )
π = π£1 sin π
π = π£1 tan π
π β
π π cos π
1 β ππ π
π π = πππ‘ππ
Zβ = Az + Bv
π§πππ§ + ππ£2 π2ππ ππ α΄
0
P(A + ππΌ) + (π΄π + πI)P β 1/r PBBβTP + Q = 0 V = -Kz
π = π(π π β πΎπ§)
Results
Implementation of delay into driver model
β’ A vehicle path following analysis and improvement of vehicle handling process
β’ Introduce control system to ensure the vehicle follows desired path
β’ Desired yaw rate and slip angle to get desired path
β’ Delay associated with diver , Neural response delay
β’ Sensor delay
β’ Consider preview distance
β’ The equations of vehicle dynamics are: β’ π π π¦ + ππ = πΉπ¦π πππ πΏπ + πΉπ₯π π πππΏ + πΉπ¦π πππ πΏπ + πΉπ₯π π πππΏπ
β’ Izπ = ππΉπ¦π πππ πΏπ + ππΉπ₯π π πππΏπ β ππΉπ¦π π πππΏπ β ππΉπ¦π πππ πΏπ
π¦ π = π π πππ + ππ¦ cosπ
π = π π£ β π π
Vehicle model
π 1 = π΄1π1 + πΈ1πΏ + π΅1ππ§ + πΎ (1
π π‘)
Driver model
β’ π» π =π π
πΈπ π =
β
π
π1π+1
π2π+1
1
πππ+1πβπππ reff: Rosettes 2003
β’ Lead constant ,lag constant, reaction and delay time.
β’ π¦ππ = π¦π + πΏ π
β’ First order Pade polynomial approximation
β’ πβπππ =1β
ππ
2π
1+ππ
2π
Human driver equation in time variant space.
β’ πΏ = π βπ¦ π + πΏπ +2π1
π2π¦ π + πΏπ +
1
πππ2 β ππ + π2 πΏ β πΏ
β’ W= β
π.1
ππ
1
π2
Closed Loop driver model
β’ π = π΄π + π΅ππ§ + πΎ1
π
β’ yaw rate and slip angle to close actual path curvature is taken as sinusoidal path
Controller
Introduce PID controller for
1. yaw rate
2. slip angle to get desired path
3. Optimization of Kp, Ki, Kd by GA
Optimal PID controller
+-
Driver model Vehicle model
Intended path actual path
Process
Vr, r
Matlab Simulink model
Conclusion
β’ Formulated driver model in order to make vehicle in desired path.
β’ 1- Simple model with delay case has been studied, and used PID controller
β’ Modeled in Simulink
β’ 2- No delay case has been studied by considering preview distance
β’ Optimized proportional controller has been used with the help of Riccati equation by minimizing cost function .
β’ Modeled and solved using Matlab ODE solver
β’ 3- Introduced delays to driver model and
β’ Modeled in Matlab Simulink along with mathematical modeling .
REFERENCE
β’ Giancarlo Genta, Lorenzo Morello 2009 βThe Automotive Chassis β Sysem Designβ.
β’ Wenjuan Jiang, Carlos Canudas-de-Wit, Olivier Sename and Jonathan Dumon 2011 βA new mathematical model for car drivers with spatial previewβ.
β’ Behrooz Mashadi, Mehdi Mahmoudi-Kaleybar, Pouyan Ahmadizadeh; Atta Oveisi 2014 βA path following driver/vehicle model with optimized lateral dynamic controller.β
β’ Rosettes, E.J , (2003) βA potential Field Framework for Active Vehicle Lane Keeping Assistanceβ.
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