Dynamics and Optimal Control of Road Vehicles

✍ Scribed by D. J. N. Limebeer, Matteo Massaro

• Publisher: Oxford University Press
• Year: 2018
• Tongue: English
• Leaves: 477
• Category: Library

✦ Synopsis

Dynamics and Optimal Control of Road Vehicles uniquely offers a unified treatment of tyre, car and motorcycle dynamics, and the application of nonlinear optimal control to vehicle-related problems within a single book. This is a comprehensive and accessible text that emphasises the theoretical aspects of vehicular modelling and control. The book focuses on two major elements. The first is classical mechanics and its use in building vehicle and tyre dynamics models. The second focus is nonlinear optimal control, which is used to solve a range of minimum-time and minimum-fuel, as well as track curvature reconstruction problems. As is known classically, all of this material is bound together by the calculus of variations and stationary principles. The treatment of this material is supplemented with a number of examples that were designed to highlight obscurities and subtleties in the theory.

✦ Table of Contents

A History of Road Vehicles
Prehistory
Darwinian steering
The differential
Birth of the motor car
Early engines
Early road vehicles
Early car industry
Early bicycles
Driven bicycles
Transition to the ordinary
The ordinary
Rise of the safety bicycle
Further developments
Powered two-wheeled vehicles
First steam-powered machine
First motorcycle
Production motorcycles
Tyres
The first tyre
Detachable tyres
Tyre developments
Topics in Mechanics
Background
Equations of motion
Inertial reference frame
Newton's equations
Properties of the inertia tensor
Generalized coordinates
Constraints
Kinetic energy
Potential energy
Lagrange's equations
Lagrange's equations in quasi-velocities
Conservation laws
Energy
Linear momentum
Angular momentum
Hamilton's equations
Legendre transform
Canonical equations
Poisson brackets
Frames, velocity, and acceleration
Equilibria, stability, and linearization
Time-reversal symmetry and dissipation
Chaplygin's sleigh
T-symmetry of the Chaplygin sleigh
Dynamics of a rolling ball
Ball on an incline
Ball on an inclined turntable
Rolling disc
Introduction
Rolling constraints
Angular momentum balance
Equilibrium solutions
Lagrange's equation
Rolling stability
Tyres
Background
Tyre forces and slips
Sliding velocities
Steady-state behaviour: the brush model
Pure side slip
Pure longitudinal slip
Pure spin slip
Combined lateral and longitudinal slip
Combined lateral, longitudinal, and spin slip
Summary of analytical models
Steady-state behaviour: the `magic formula'
Pure slip
Combined slip
Behaviour in non-reference conditions
Effect of normal load
Effect of inflation pressure
Effect of road surface
Hydroplaning
Thermal effects
Unsteady behaviour: string model
Side slip and spin slip
Transfer function relationships
Unsteady magic formulae
Low-speed modelling
Advanced models
Precursory Vehicle Modelling
Background
Simple car model
Constant speed case
Accelerating and braking
Cornering
Timoshenko–Young bicycle
Introduction
Steering kinematics
Vehicle dynamics
Lagrange's equation
Linearized model
Lumped-mass bicycle
Equations of motion
Wheel shimmy
Simple case
A more realistic setup
Unicycle
The Whipple Bicycle
Background
Bicycle model
Model features
Linear in-plane dynamics
Linear out-of-plane dynamics
Intermediate variables
Equations of motion
Modal analysis
Gyroscopic influences
Control-theoretic implications
A feedback-system perspective
Model extensions
Acceleration
Frame flexibility
Pneumatic tyres
Ride Dynamics
Background
Road surface characteristics
Design objectives
Single-wheel-station model
Invariant equation
Interpolation constraints
State-space analysis
Suspension optimization
In-plane vehicle model
Invariant equations
Mode shapes
Reconciliation with single-wheel-station model
Transfer functions
Interpolation constraints
Full-vehicle model
Invariant equations
Mode shapes
Reconciliation with single-wheel-station model
Transfer functions
Rigid-chassis model
Further analysis
Advanced Vehicle Modelling
Background
Vehicle trim
Longitudinal load transfer in cars and motorcycles
Squat, dive, and pitch
Lateral load transfer in cars
Roll trim in motorcycles
Road modelling
Three-dimensional curves
Ribbons
Euler angles
Vehicle Positioning
Car modelling
Tyre friction
Load transfer
Non-negative tyre loads
Wheel torque distribution
Suspensions
Aerodynamic maps
Driver modelling
Motorcycle modelling
Tyre contact geometry
Side-slipping relaxed tyres
Structural flexibility
Rider
Aerodynamic forces
Suspensions
Power transmission
Motorcycle multibody model
Remarks on vibration modes
Optimal Control
Background
Fundamentals
Pontryagin minimum principle (PMP)
Unconstrained case
Boundary conditions
Constancy of the Hamiltonian
Bounded controls
Bounded states and controls
Dynamic programming
Dynamic programming recurrence formula
The Hamilton–Jacobi–Bellman equation
Singular arcs and bang–bang control
Example: Goddard's rocket
Example: braking wheel
Example: Fuller's problem
Regularization
Numerical methods for optimal control
Explicit simulation (time-marching)
Implicit simulation (collocation)
Indirect methods
Direct methods
KKT vs PMP
Mesh refinement
Example: track curvature reconstruction
Vehicular Optimal Control
Background
An illustrative example
Constant-incline case
Regenerative braking
Dissipative braking
Fuel-efficient driving
Formula One hybrid powertrain
Track model
Important three-dimensional influences
Powertrain
Vehicle model
Scaling
Non-smooth features
Regularization
Computing gradients
Problem setup
Results
Minimum time of a racing motorcycle
References
Main Index
Person Index