Modified Adaptive Control and Simulation for FourWheel Steering Vehicles

1
Modified Adaptive Control and Simulation for
Four-Wheel Steering Vehicles

• Speaker Wenqin Zhou

Based on the article Modified Adaptive Control
for Four-Wheel Steering Vehicle written by
Wenqin Zhou and Yingmin Jia, published on Proc.
of 14th Control and Decision Conference in China.
Pp. 168-171.
2
Outline

• Introduction
• Main content
• Models Design
• (a) Preview Control Model (b)
  Yaw Dynamics Model
• 2. Mode Reference Adaptive Controllers Design
• (a) Mode Reference Adaptive Controller
• (b) Modified Mode Reference Adaptive
  Controller
• Computer Simulation

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Introduction

• With the increased number of vehicles and speed,
  both the safety and stability of driving gain
  more and more attention.
• We try to stabilize the moving vehicle with
  uncertain parameters, by means of using the
  steering angle from the preview information as
  the input of the adaptive control's model. In
  order to improve the control performance, a
  modified adaptive control method is used and
  proved effective from the simulation.

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Paper Structure

• is the route information, is the
  steering angle, is the yaw rate, is the
  lateral position.
• Key words Adaptive Control, MRAC, MMRAC, Preview
  Control.

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Preview Control Model (1)

• We know the route . We want to use preview
  control to keep the vehicle on the desired route
  after preview time ( is the preview
  distance).

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Preview Control Model (2)

• Now the Driver Vehicle system preview control
  model with the drivers reaction delay time
  is as follows.

is the steering angle,
is the wheelbase,
is the lateral position of the vehicle,
is the lateral acceleration,
is the velocity,
is the curve radius,
is the transmission rate of the turning system.
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Preview Control Model (3)

• Analyze the preview control model under the
  different preview time .
• When is small, the system oscillates obviously,
  which means the driver is a new one. So gives
  us some hint about the drivers experience.

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Preview Control Model (4)

• Analyze the preview control model under the
  different drivers reaction delay time .
• When is big, the system has less stability.

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Yaw Dynamics Model (1)

We have a basic vehicle model2 as
(1)

) ,
is the yaw rate (
is the sideslip angle,
is the vehicles velocity,
(
)
is the front (rear) steering angle,
is the cornering stiffness of front tire (rear
tire),
(
)
is the vehicle mass,
(
is the distance between the center of gravity and
front axle (rear axle).
)
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Yaw Dynamics Model (2)

• Laplace Transfer on equation (1)
• Vehicle under the control of rear tires
• We want the sideslip angle to remain zero. From
  , we can get two equations
• We get the ideal model as

and





and
(2)
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Yaw Dynamics Model (3)

• Real model with uncertain parameters
• We get the real model ( with two unknown
  parameters ) as

and
, which is because the sideslip angle does

not always equal zero.
(3)
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Controller Design

• We want to make a controller to control the
  vehicle system to be stable. (i.e. to make the
  real vehicle model acts as the ideal one.)
• We choose Mode Reference Adaptive Control method.
  Because this method can adaptively control system
  and output efficiently when the input and
  disturbance will change.
• It will also keep the system stable and the error
  approaches 0.

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Mode Reference Adaptive Controller (1)

• The mode reference adaptive control figure

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Mode Reference Adaptive Controller (2)

• The state equations and
• The adaptive control law
• The parameter adjust law
• , ,
  ,
• The control law

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Modified Mode Reference Adaptive Controller (1)

• To MMRAC, we use , instead
  of .
• It can eliminate the errors from the uncertainty
  parameters and errors from inaccurate
  identification of parameters.
• It also keeps the stability and robustness of the
  system.

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Modified Mode Reference Adaptive Controller (2)

• The principle control figure is as follows

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Computer Simulation (1)

• From the ideal model and real model
• We use the steering angle from the preview
  control model as the adaptive models input,
  simulate under mode reference adaptive controller
  (MRAC) and Modified MRAC.

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Computer Simulation (2)

• Compared with MRAC, MMRAC can obviously improve
  the systems response performance, while keeping
  the stability and robustness.

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Computer Simulation (3)

• When added disturbance like noise, the advantage
  of the modified MRAC method is much more obvious.

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Main Reference

• 1 Yingmin Jia. Robust Control with Decoupling
  Performance for Steering and Traction of 4WS
  Vehicles under Velocity-Varying Motion. IEEE
  Transactions on Control Systems and Technology,
  8(2000), 3 554-569
• 2  Juergen Ackermann. Robust Decoupling, Ideal
  Steering Dynamics and Yaw Stabilization of 4WS
  Cars. Automatica, 30(1994), 11 1761-1768
• 3  Jing Sun. A Modified Model Reference
  Adaptive Control Scheme for Improved Transient
  Performance. IEEE Transaction on Automatic
  Control, 38(1993), 8 1255-1259
• 4  Aniruddha Datta, Petros A. Ioannou.
  Performance Analysis and Improvement in Model
  Reference Adaptive Control. IEEE Transaction on
  Automatic Control, 39(1994), 12 2370-2387