Mathematical Modelling, Nonlinear Control and Performance Evaluation of a Ground Based Mobile Air Defence System

Preface
Acknowledgements
Contents
Acronyms
1 Introduction
	1.1 Part 1: Kinematics, Dynamics and Nonlinear Control of the Mobile Air Defence System Subject to Holonomic and Nonholonomic Velocity Constraints
	1.2 Part 2: Performance Evaluation of the Mobile Air Defence System Against an Attacking Aerial Target
2 Overview of the Mobile Air Defence System
	2.1 Multibody System Representation  of the Mobile Air Defence System
	2.2 Vehicle Body (Body 5)
		2.2.1 Electric Motors EMγ0, EMαs and EMδv
	2.3 Wheels 1, 2, 3 and 4 (Body 1 to Body 4)
		2.3.1 Velocity Constraints
	2.4 Turret (Body 6)
		2.4.1 Electric Motor EMζ0
	2.5 Anti-Aircraft Gun (Body 7)
	2.6 Drive System and Differential Gearbox (Body 8)
		2.6.1 Velocity Constraint
	2.7 Steering System (Body 9)
		2.7.1 Geometric Constraints
		2.7.2 Velocity Constraints
	2.8 Rotor of the Turret Electric Motor EMγ0 (Body 10)
		2.8.1 Velocity Constraint
	2.9 Rotor of the AA Gun Electric Motor EMζ0 (Body 11)
		2.9.1 Velocity Constraint
	2.10 Definition of Generalized Co-Ordinates q and Generalized Velocities p
	2.11 Inertial Azimuth and Elevation Angles of a Vector
	2.12 Line-of-Sight Vector from the Mobile ADS to the AAT
	2.13 Aiming Vector of the AA Gun
	2.14 Inertial Position and Velocity of the AA Gun Muzzle
3 Kinematic Model of the Mobile Air Defence System
	3.1 Velocity Constraints of the Mobile ADS
	3.2 Kinematic Model of the Mobile ADS
	3.3 Decoupled Kinematic Models of the Vehicle System …
4 Dynamic Model and Nonlinear Control of the Mobile Air Defence System
	4.1 Basic Dynamic Model of the Mobile ADS
	4.2 Reduced Dynamic Model of the Mobile ADS
	4.3 Nonlinear Feedback Control of the Reduced Dynamic Model of the Mobile ADS
		4.3.1 Analysis of the Zero Dynamics
	4.4 Constrained Motion of the Controlled Dynamic Model of the Mobile ADS
	4.5 Generalized Constraint Forces
	4.6 Lagrange Multipliers
5 Operational Modes of the Mobile Air Defence System
	5.1 Asymptotic Tracking Results
	5.2 Vehicle Body Tracking Mode VM1: Vehicle Body is Maneuvering
	5.3 Vehicle Body Tracking Mode VM1A: Vehicle Body is Moving in a Straight Line
	5.4 Vehicle Body Tracking Mode VM2: Vehicle Body is Stationary
	5.5 AA Gun Tracking Mode GM1: AA Gun is Rotating Relative to the Vehicle Body
	5.6 AA Gun Tracking Mode GM1A: AA Gun Aiming Vector is Tracking the LOS Vector
	5.7 AA Gun Tracking Mode GM1B: AA Gun Aiming Vector is Tracking the Fire Control Vector
	5.8 AA Gun Tracking Mode GM2: AA Gun is not Rotating Relative to the Vehicle Body
	5.9 Main Operational Modes of the Mobile ADS
	5.10 Operational Mode OM1: Mobile ADS is Maneuvering
	5.11 Operational Mode OM1A: Vehicle Body is Moving in a Straight Line (VM1A) and the AA Gun is Rotating Relative to the Vehicle Body (GM1)
	5.12 Operational Mode OM1B: Vehicle Body is Moving in a Straight Line (VM1A) and the AA Gun is not Rotating Relative to the Vehicle Body (GM2)
	5.13 Operational Mode OM2: Vehicle Body is Stationary (VM2) and the AA Gun is Rotating Relative to the Vehicle Body (GM1)
	5.14 Operational Mode OM3: Vehicle Body is Stationary (VM2) and the AA Gun is not Rotating Relative to the Vehicle Body (GM2)
	5.15 Firing Rate of the AA Gun and Firing Times of the AA Projectiles
6 Point Mass Flight Dynamics Model  of the Anti-Aircraft Projectile
	6.1 Inertial Position and Velocity of the AA Projectile
	6.2 Point Mass Flight Dynamics Model of the AA Projectile
	6.3 Parameter Values for the Anti-Aircraft Projectile
	6.4 Parameter Values for the Mobile ADS
	6.5 Computation of the AA Projectile Trajectory with No Wind
	6.6 Computation of the AA Projectile Trajectory with a Cross Wind
7 The Fire Control Problem
	7.1 Fire Control Problem FCA
	7.2 Fire Control Problem Formulation Using Feasible Control
	7.3 Air Defence System Deployment and Attacking Aerial Target Engagement Scenario
	7.4 Computational Results for Fire Control Problem FCA: Vehicle Body of Mobile ADS is Completely Stationary
	7.5 Computational Results for Fire Control Problem FCA: Vehicle Body of Mobile ADS is Moving in a Straight Line at Constant Speed
8 Computation of the Impact Point  of the AA Projectile on the Body  of the Attacking Aerial Target
	8.1 Geometry of the Attacking Aerial Target
	8.2 Inertial Trajectory of the Attacking Aerial Target
	8.3 Computation of the Impact Point of the AA Projectile on the Body of the Attacking Aerial Target
	8.4 Vulnerability Model of the Attacking Aerial Target
	8.5 Computational Results
9 Computation of the Probability that the AA Projectile Will Impact the Body of the Attacking Aerial Target
	9.1 Stochastic Model of the Dispersion of the AA Projectiles Fired by the AA Gun
		9.1.1 Remarks on Applications of Stochastic Optimal Control
	9.2 Computation of the Probability that the AA Projectile Will Impact the Body of the Attacking Aerial Target, PhitT,k
	9.3 Computational Method NM1 for the Computation of PhitT,k
	9.4 Computational Method NM2 for the Computation of PhitT,k
	9.5 Probability of Destroying the AAT for the Case …
	9.6 Accumulative Probability of Destroying the AAT for the Case Where a Burst of AA Projectiles is Fired
	9.7 Computational Results
	9.8 Verification Method VMB for the Computation of the Probability PhitT,k
		9.8.1 Computational Results
Appendix A Kinematics of Constrained Rigid Multibody Systems Subject to Velocity Constraints that May Not be Independent
Appendix B Lagrange Equations for Constrained Rigid Multibody Systems Subject to Velocity Constraints that May Not be Independent
B.1  Dynamics of Constrained Rigid Multibody Systems
B.2  Lagrange Equations for Constrained Rigid Multibody Systems Subject to Velocity Constraints that May Not be Independent
B.3 On the Solution of Consistent Simultaneous Linear Equations
B.3.1  On the Solution of Consistent SLEs by Partitioning the Variables into Independent and Dependent Variables
B.3.2  On the Solution of Consistent SLEs by using the Moore-Penrose Generalized Inverse
Appendix  References
Index