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Multibody System Dynamics

, Volume 33, Issue 2, pp 207–228 | Cite as

Integrated robust controller for vehicle path following

  • Behrooz Mashadi
  • Pouyan AhmadizadehEmail author
  • Majid Majidi
  • Mehdi Mahmoodi-Kaleybar
Article

Abstract

The design of an integrated 4WS+DYC control system to guide a vehicle on a desired path is presented. The lateral dynamics of the path follower vehicle is formulated by considering important parameters. To reduce the effect of uncertainties in vehicle parameters, a robust controller is designed based on a μ-synthesis approach. Numerical simulations are performed using a nonlinear vehicle model in MATLAB environment in order to investigate the effectiveness of the designed controller. Results of simulations show that the controller has a profound ability to making the vehicle track the desired path in the presence of uncertainties.

Keywords

Vehicle path following 4WS DYC Robust control μ-Synthesis 

Notation

Alphabetic

A

State-space matrix

B

Input matrix

C

Output matrix

\(\mathbb{C}\)

Set of complex numbers

Cαf (Cαr)

Cornering stiffness of front (rear) tires

d

Output from perturbation block

D

Constant scaling matrix

E

Disturbance matrix

c.g.

Center of gravity

eu

Weighted control input

ez

Output weighted signal

Fyf (Fyr)

Lateral force of front (rear) tires

Fu

Upper LFT

Gsys

System nominal model

i

Scaled disturbance input

Iz

Vehicle moment of inertia around z axis

\(\operatorname{inf}\)

Infimum

Lf (Lr)

Distance from vehicle center of gravity to front (rear) axle

LFT

Linear fractional transformation

m

Vehicle mass

Mz

External yaw moment produced by DYC system

U

Controller input

p (\(\bar{p}\))

Uncertain (nominal) parameter

Q

Parameter nominal dispersion

r (\(\dot{r}\))

Lateral position (velocity) error

\(\dot{R}\) (\(\dot{R}_{d}\))

Vehicle real (desired) velocity

Set of real numbers

S

Sensitivity function

\(\operatorname{sup}\)

Supremum

u

Vehicle longitudinal velocity

ud

Desired longitudinal velocity

v

Vehicle lateral velocity

vd

Desired lateral velocity

V

Vehicle velocity

w

Input to perturbation block

W

Disturbance vector

Wz,Wu,Wρ

System output, control input, road input weighting functions

x,y,z

Coordinate system attached to the vehicle

X

State-space vector

Z

Output signal

Greek

αf (αr)

Side slip angle of front (rear) tires

βf (βr)

Angle of front (rear) tire velocity with longitudinal axis of vehicle

δ

Perturbation

δf (δr)

Front (rear) steering angle

ΔF

Fictitious uncertainty block

Δsys

Uncertain matrix

ρ

Radius of curvature of the desired path

μ

Structured singular value

\(\bar{\sigma}\)

Maximum singular value

ω

Frequency

ψ (\(\dot{\psi}\))

Yaw angle (rate)

ψd (\(\dot{\psi}_{d}\))

Desired yaw angle (rate)

ψe

Orientation error

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Behrooz Mashadi
    • 1
  • Pouyan Ahmadizadeh
    • 1
    Email author
  • Majid Majidi
    • 1
  • Mehdi Mahmoodi-Kaleybar
    • 2
  1. 1.School of Automotive EngineeringIran University of Science and TechnologyTehranIran
  2. 2.School of Mechanical EngineeringIran University of Science and TechnologyTehranIran

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