Cover
Dynamics and Optimal Control of Road Vehicles
Copyright
Preface
Acknowledgements
Contents
1. A History of Road Vehicles
1.1 Prehistory
1.1.1 Darwinian steering
1.1.2 The differential
1.2 Birth of the motor car
1.2.1 Early engines
1.2.2 Early road vehicles
1.2.3 Early car industry
1.3 Early bicycles
1.3.1 Driven bicycles
1.3.2 Transition to the ordinary
1.3.3 The ordinary
1.3.4 Rise of the safety bicycle
1.3.5 Further developments
1.4 Powered two-wheeled vehicles
1.4.1 First steam-powered machine
1.4.2 First motorcycle
14.3 Production motorcycles
1.5 Tyres
1.5.1 The first tyre
1.5.2 Detachable tyres
1.5.3 Tyre developments
2. Topics in Mechanics
2.1 Background
2.2 Equations of motion
2.2.1
Inertial reference frame
2.2.2
Newton's equations
2.2.3 Properties of the inertia tensor
2.2.4 Generalized coordinates
2.2.5 Constraints
2.2.6 Kinetic energy
2.2.7 Potential energy
2.2.8 Lagrange's equations
2.2.9 Lagrange's equations in quasi-velocities
2.3 Conservation laws
2.3.1 Energy
2.3.2 Linear momentum
2.3.3 Angular momentum
2.4 Hamilton's equations
2.4.1 Legendre transform
2.4.2 Canonical equations
2.4.3 Poisson brackets
2.5 Frames, velocity, and acceleration
2.6 Equilibria, stability, and linearization
2.7 Time-reversal symmetry and dissipation
2.8 Chaplygin's sleigh
2.8.1 T-symmetry of the Chaplygin sleigh
2.9 Dynamics of a rolling ball
2.9.1 Ball on an incline
2.9.2 Ball on an inclined turntable
2.10 Rolling disc
2.10.1 Introduction
2.10.2 Rolling constraints
2.10.3 Angular momentum balance
2.10.4 Equilibrium solutions
2.10.5 Lagrange's equation
2.10.6 Rolling stability
3. Tyres
3.1 Background
3.2 Tyre forces and slips
3.3 Sliding velocities
3.4 Steady-state behaviour: the brush model
3.4.1 Pure side slip
3.4.2 Pure longitudinal slip
3.4.3 Pure spin slip
3.4.4 Combined lateral and longitudinal slip
3.4.5 Combined lateral, longitudinal, and spin slip
3.4.6 Summary of analytical models
3.5 Steady-state behaviour: the `magic formula'
3.5.1 Pure slip
3.5.2 Combined slip
3.6 Behaviour in non-reference conditions
3.6.1 Effect of normal load
3.6.2 Effect of inflation pressure
3.6.3 Effect of road surface
3.6.4 Hydroplaning
3.6.5 Thermal effects
3.7 Unsteady behaviour: string model
3.7.1 Side slip and spin slip
3.7.2 Transfer function relationships
3.8 Unsteady magic formulae
3.8.1 Low-speed modelling
3.9
Advanced models
4. Precursory Vehicle Modelling
4.1
Background
4.2 Simple car model
4.2.1 Constant speed case
4.2.2 Accelerating and braking
4.2.3 Cornering
4.3 TimoshenkoβYoung bicycle
4.3.1 Introduction
4.3.2 Steering kinematics
4.3.3 Vehicle dynamics
4.3.4 Lagrange's equation
4.3.5 Linearized model
4.4 Lumped-mass bicycle
4.4.1 Equations of motion
4.5 Wheel shimmy
4.5.1 Simple case
4.5.2 A more realistic setup
4.6 Unicycle
5. The Whipple Bicycle
5.1 Background
5.2 Bicycle model
5.2.1 Model features
5.3 Linear in-plane dynamics
5.4 Linear out-of-plane dynamics
5.4.1 Intermediate variables
5.4.2 Equations of motion
5.4.3 Modal analysis
5.4.4 Gyroscopic influences
5.5 Control-theoretic implications
5.5.1 A feedback-system perspective
5.6 Model extensions
5.6.1 Acceleration
5.6.2 Frame flexibility
5.6.3 Pneumatic tyres
6. Ride Dynamics
6.1 Background
6.2 Road surface characteristics
6.3 Design objectives
6.4 Single-wheel-station model
6.4.1 Invariant equation
6.4.2 Interpolation constraints
6.4.3 State-space analysis
6.4.4 Suspension optimization
6.5 In-plane vehicle model
6.5.1 Invariant equations
6.5.2 Mode shapes
6.5.3 Reconciliation with single-wheel-station model
6.5.4 Transfer functions
6.5.5 Interpolation constraints
6.6 Full-vehicle model
6.6.1
Invariant equations
6.6.2 Mode shapes
6.6.3 Reconciliation with single-wheel-station model
6.6.4 Transfer functions
6.6.5 Rigid-chassis model
6.7 Further analysis
7. Advanced Vehicle Modelling
7.1
Background
7.2 Vehicle trim
7.2.1 Longitudinal load transfer in cars and motorcycles
7.2.2 Squat, dive, and pitch
7.2.3 Lateral load transfer in cars
7.2.4 Roll trim in motorcycles
7.3 Road modelling
7.3.1 Three-dimensional curves
7.3.2 Ribbons
7.3.3 Euler angles
7.4 Vehicle Positioning
7.5 Car modelling
7.5.1
Tyre friction
7.5.2 Load transfer
7.5.3 Non-negative tyre loads
7.5.4 Wheel torque distribution
7.5.5 Suspensions
7.5.6
Aerodynamic maps
7.6
Driver modelling
7.7 Motorcycle modelling
7.7.1
Tyre contact geometry
7.7.2
Side-slipping relaxed tyres
7.7.3
Structural flexibility
7.7.4
Rider
7.7.5
Aerodynamic forces
7.7.6
Suspensions
7.7.7
Power transmission
7.7.8
Motorcycle multibody model
7.7.9 Remarks on vibration modes
8. Optimal Control
8.1
Background
8.2
Fundamentals
8.3
Pontryagin minimum principle (PMP)
8.3.1
Unconstrained case
8.3.2
Boundary conditions
8.3.3
Constancy of the Hamiltonian
8.3.4
Bounded controls
8.3.5
Bounded states and controls
8.4
Dynamic programming
8.4.1
Dynamic programming recurrence formula
8.4.2
The HamiltonβJacobiβBellman equation
8.5
Singular arcs and bangβbang control
8.5.1
Example: Goddard's rocket
8.5.2
Example: braking wheel
8.5.3
Example: Fuller's problem
8.5.4
Regularization
8.6
Numerical methods for optimal control
8.6.1
Explicit simulation (time-marching)
8.6.2
Implicit simulation (collocation)
8.6.3
Indirect methods
8.6.4
Direct methods
8.6.5
KKT vs PMP
8.6.6 Mesh refinement
8.6.7
Example: track curvature reconstruction
9. Vehicular Optimal Control
9.1
Background
9.2
An illustrative example
9.2.1
Constant-incline case
9.2.2
Regenerative braking
9.2.3
Dissipative braking
9.3
Fuel-efficient driving
9.4
Formula One hybrid powertrain
9.4.1
Track model
9.4.2
Important three-dimensional influences
9.4.3
Powertrain
9.4.4
Vehicle model
9.4.5
Scaling
9.4.6
Non-smooth features
9.4.7
Regularization
9.4.8
Computing gradients
9.4.9
Problem setup
9.4.10
Results
9.5
Minimum time of a racing motorcycle
References
Main Index
Person Index