Performance analysis and enhancement of proportional navigation guidance systems

Proportional navigation has long been an active area of research in the guidance and control community. It is easy to implement and effective in most applications. However, proportional navigation leads to poor observability problems when using bearings-only measurements. Bearings-only measurement systems are common in guidance and target tracking, as they are low-cost and free from jam noise. Proportional navigation guidance systems with bearings-only measurements are not only practically important, but also theoretically interesting and nontrivial, due to their time-varying dynamics, highly nonlinear measurements, and complex engagement geometry when the target is maneuverable. This thesis is concerned with observability enhancement and performance analysis of proportional navigation guidance systems. To tackle the low observability problem involved in proportional navigation systems with angle-only information, observability analysis is rigorously performed in order to grasp a better understanding of the essence of the problem. Necessary and sufficient conditions for system observability are firmly established, and are general enough to encompass most previous results. Extensions of these conditions are readily applicable to observability checks with practical guidance laws in closed loop. The observability analysis paves the way for improvement of system performance and development of new guidance laws. Among existing guidance laws proposed to improve system observability as well as interception performance, additive proportional navigation is a class of guidance that preserves the simplicity in design and realization, while enhancing system observability by incorporating a measure of information content. Based on the thermal noise model, a new form of additive observable proportional navigation is presented in this thesis. Analysis undertaken demonstrates that this new guidance law outperforms true proportional navigation, which is the most accepted guidance law, by offering a better possibility of observable systems and a larger region of interception. The effectiveness of this new control law is also confirmed by simulations. Bounds of system navigation constants to ensure interception are provided as guidelines for system design. To account for the finite acceleration capability of real-world guidance systems due to physical limitations, effects of acceleration saturation constraint are investigated. In contrast to the ideal system with infinite acceleration capability, more stringent requirements on system initial launch conditions and different bounds of design parameters must be met to achieve interception, using more total control effort. The degradation of system performance due to saturation constraint is verified by extensive simulations.Thesis (MESc) -- University of Adelaide, Dept. of Electrical and Electronic Engineering, 199

Proportional-Integral-Derivative Controller in Proportional Navigation Guidance

In this thesis, a Proportional-Integral-Derivative (PID) guidance scheme is discussed to improve the miss distance accuracy and the finite time stability problem in the Proportional Navigation Guidance (PNG). The primary goal of this study is to design the PID guidance that can accurately intercept the fast maneuvering target. The PID guidance is the extended version of the PNG with the integral and derivative terms in parallel. For the understanding of the conventional PNG model, the two-dimensional (2-D) engagement model of the missile and target is analyzed. Two characteristics are found in the PNG model: (1) its’ stability is kept in the finite time but becomes unstable at the vicinity of the interception and (2) the Line-of-sight angle rate (LOSR) increases as the target acceleration magnitude increases. To regulate the LOSR, the PID guidance is derived based on the servomechanism theory. The PID guidance model replaces the proportional gain of the conventional PNG model by the PID controller. A PID controller design using the numerical method through the iterative simulation is presented. For the various missile and target initial geometries, the capture region of the PID guidance is evaluated and compared with the conventional PNG model. In the end, the PID guidance model shows the improved miss distance accuracy, the extended stable time, and extended capture region when compared with the PNG model

Counter Weapon Control

In this work, pursuit-evasion differential game theory is applied to the target defense scenario. The targets, attackers, and the defenders positional information is assumed to be known to the players. With positional information, a computational efficient method of strategy synthesis can be derived applying a differential game theory approach. We demonstrate that when non-optimal strategies are employed by one of the players, e.g. Line Of Sight guidance, the outcome will favor the players that employ the optimal strategy given by the solution of the pursuit-evasion differential game

A novel dual-spin actuation mechanism for small calibre, spin stabilised, guided projectiles

© Cranfield University 2022. All rights reserved. No part of this publication may be reproduced without the written permission of the author and copyright holderSmall calibre projectiles are spin-stabilised to increase ballistic stability, often at high frequencies. Due to hardware limitations, conventional actuators and meth ods are unable to provide satisfactory control at such high frequencies. With the reduced volume for control hardware and increased financial cost, incorporating traditional guid ance methods into small-calibre projectiles is inherently difficult. This work presents a novel method of projectile control which addresses these issues and conducts a systems level analysis of the underlying actuation mechanism. The design is shown to be a viable alternative to traditional control methods, Firstly, a 7 Degree-of-Freedom (DoF) dynamic model is created for dual-spin pro jectiles, including aerodynamic coefficients. The stability of dual-spin projectiles, gov erned by the gyroscopic and dynamic stability factors is given, discussed and unified across available literature. The model is implemented in a Matlab/Simulink simulation environ ment, which is in turn validated against a range of academic literature and experimental test data. The novel design and fundamental operating principle are presented. The actuation mechanism (AM) is then mathematically formulated from both a velocity change (∆V ) and a lateral acceleration (a˜) perspective. A set of axioms are declared and verified using the 7-DoF model, showing that the inherently discrete system behaviour can be controlled continuously via these control variables, ∆V or a˜. Control state switching is simplified to be instantaneous, then expanded to be generically characterised by an arbitrarily complex mathematical function. A detailed investigation, parametric analysis and sensitivity study is undertaken to understand the system behaviour. A Monte Carlo procedure is described, which is used to compare the correction cap abilities of different guidance laws (GLs). A bespoke Zero-Effort-Miss (ZEM) based GLis synthesised from the mathematical formulation of the AM, with innately more know ledge of the system behaviour, which allows superior error correction. This bespoke GL is discussed in detail, a parametric study is undertaken, and both the GL parameters and PID controller gains are optimised using a genetic algorithm. Artificial Intelligence (AI) Reinforcement learning methods are used to emulate a GL, as well as controlling the AM and operating as a GL, simultaneously. The novel GLs are compared against a traditional proportional navigation GL in a nominal system and all GLs were able to control the AMs, reducing the miss distance to a satisfactory margin. The ZEM-based GL provided superior correction to the AI GL, which in turn provided superior correction over proportional navigation. Example CAD models are shown, and the stability analysis is conducted on the geometry. The CAD model is then used in CFD simulations to determine aerodynamic coefficients for use in the 7-DoF dynamic model. The novel control method was able to reduce the 95% dispersion diameter of a traditional ballistic 7.62mm projectile from 70mm to 33mm. Statistical data analysis showed there was no significant correlation or bias present in either the nominal or 7-DoF dispersion patterns. This project is co-sponsored by BAE Systems and ESPRC (ref. 1700064). The con tents of this thesis are covered by patent applications GB2011850.1, GB 2106035.5 and EP 20275128.5. Two papers are currently published (DOI: 10.1016/j.dt.2019.06.003, the second DOI is pending) and one is undergoing peer review..PH

Sensors, measurement fusion and missile trajectory optimisation

When considering advances in “smart” weapons it is clear that air-launched systems have adopted an integrated approach to meet rigorous requirements, whereas air-defence systems have not. The demands on sensors, state observation, missile guidance, and simulation for air-defence is the subject of this research. Historical reviews for each topic, justification of favoured techniques and algorithms are provided, using a nomenclature developed to unify these disciplines. Sensors selected for their enduring impact on future systems are described and simulation models provided. Complex internal systems are reduced to simpler models capable of replicating dominant features, particularly those that adversely effect state observers. Of the state observer architectures considered, a distributed system comprising ground based target and own-missile tracking, data up-link, and on-board missile measurement and track fusion is the natural choice for air-defence. An IMM is used to process radar measurements, combining the estimates from filters with different target dynamics. The remote missile state observer combines up-linked target tracks and missile plots with IMU and seeker data to provide optimal guidance information. The performance of traditional PN and CLOS missile guidance is the basis against which on-line trajectory optimisation is judged. Enhanced guidance laws are presented that demand more from the state observers, stressing the importance of time-to-go and transport delays in strap-down systems employing staring array technology. Algorithms for solving the guidance twopoint boundary value problems created from the missile state observer output using gradient projection in function space are presented. A simulation integrating these aspects was developed whose infrastructure, capable of supporting any dynamical model, is described in the air-defence context. MBDA have extended this work creating the Aircraft and Missile Integration Simulation (AMIS) for integrating different launchers and missiles. The maturity of the AMIS makes it a tool for developing pre-launch algorithms for modern air-launched missiles from modern military aircraft.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Capturability of augmented proportional navigation (APN) guidance with nonlinear engagement dynamics

Proportional Navigation (PN) and its variants are widely used guidance philosophies. However, in the presence of target maneuver, PN guidance law is effective only for a restrictive set of initial geometries. To account for target maneuvers, the concept of Augmented Proportional Navigation (APN) guidance law was introduced and analyzed in a linearized interceptor-target engagement framework presented in literature. However, there is no work in the literature, that addresses the capturability performance of the APN guidance law in a nonlinear engagement framework. This paper presents such an analysis and obtains the conditions for capturability. It also shows that a shorter time of interception is obtained when APN is formulated in the nonlinear framework as proposed in this paper. Simulation results are given to support the theoretical findings