Sinusoidal or weave maneuvers on the part of the target can make it particularly difficult for a pursuing missile to hit. Normalized design curves are presented so that the guidance system designer can easily assess the influence of weave maneuvers on missile system performance. These curves show how the target weave frequency and amplitude along with the interceptor guidance system tune constant and effective navigation ratio determine the size of the miss distance. Acceleration saturation effects also are considered as a further important influence on system performance. Finally, suggestions are made showing how to improve system performance.

Proportional navigation and weaving targets

The performance of a proportional navigation homing missile against a target performing a sinusoidal weave maneuver is evaluated. The missile's effectiveness is measured in terms of the root-mean-square miss distance over a set of engagements in which the initial phase of the target weave is uniformly distributed. Closed form solutions for the root-mean-square miss are derived for the case where the missile guidance system is modeled by a first-order lag and the lateral acceleration is unlimited. The analysis is then extended to include the effects of acceleration saturation and higher order missile dynamics. Comparisons are made between a first-order and a fifth-order guidance system, and the root-mean-square miss is determined numerically as a function of the interceptor's effective navigation gain, time constant and acceleration limit, and the target's weave amplitude and frequency. UTURE homing interceptor missiles will face new and unique challenges as the sophistication of the threat spectrum in- creases. Engagements against air targets can occur at both very low and very high altitudes, with the threats accidentally or intentionally performing weaving or spiraling maneuvers during their midcourse and terminal phases.1"4 The lateral displacement, acceleration ca- pability, and weave frequency of the target maneuver can greatly enhance the threat's ability to survive a counterattack. To counter this, the defensive missile must have sufficient lateral acceleration, guidance system time constant, and terminal homing time to achieve a high probability of intercept. Whereas the per- formance of the interceptor will be influenced by many scenario- dependent factors,5"8 a major consideration will be the fundamental response of the proportional navigation (PN) guidance system to the postulated target weave motion.9'10 In the general case, the target dynamics may involve arbitrary periodic motion in three dimensions. A useful starting point for analysis, however, is the response of the PN homing system to a single plane sinusoidal maneuver of constant amplitude and fre- quency. The phase angle of target weave, which is associated with initial conditions at the start of the missile's terminal guidance, can be treated as a random variable, uniformly distributed between 0 and 2n over a set of engagements. The missile's dynamics are approxi- mated by a simple first-order transfer function, and unlimited lateral acceleration capability is assumed. The miss distance can then be parameterized in terms of the effective PN navigation gain N, the missile time constant T, and the amplitude AT and frequency co of the target weave. This paper focuses on root-mean-square (rms) miss distance as a recommended measure of effectiveness in analyzing missile perfor- mance against weaving targets. This measure allows uncertainties in target phase characteristics to be accounted for in the terminal per- formance results. The weaving target problem was first addressed by Chadwick, 9 who determined analytical expressions for the rms miss distance of the single lag PN missile for values of N =2 and 3. Zarchan 10 employed adjoint theory and transfer function tech- niques to determine formulas for the peak miss distance against a weaving target for values of N between 3 and 6. The present paper derives general closed-form expressions for the rms miss distance against a sinusoidal target. New results are obtained for arbitrary

Root-mean-square miss distance of proportional navigation missile against sinusoidal target

Explicit formulas of optimal guidance for a linear, time-invariant, arbitrary-order, and acceleration constrained missile are derived. These formulas are given in terms of the missile's transfer function and acceleration constraint. Optimal, full-state feedback guidance laws are synthesized and compared to first-order approximation and the proportional navigation for minimum and nonminimum missile dynamics. Simulations on a third-order missile model show the relative gain from using the full-order guidance law vs the acceleration constraint as well as some robustness tests. HE optimal control theory has been used to derive modern/optimal guidance laws which have improved performance. The improved performance of these homing laws is achieved by a consideration of the detailed dynamics of the threat (target) and the interceptor (missile). However, it comes at the expense of increased complexity in realization (cost), sensitivity to knowledge of various parameters, etc. An extensive study of literature on guidance laws in general, and optimal guidance laws in particular, is performed by Pastrick et al.1 In various references,2'6 optimal guidance laws are derived for first- and second-order missiles, respectively. In our previous paper,7 the structure of optimal guidance laws for a linear, arbitrary high-order missile was considered. Mainly, we derived the closed-loop, general structure formulas of the guidance law. Further, we studied the behavior of the gains for minimum and nonminimum phase missiles and compared the performance of some sub-optimal approximations of the guidance laws. The effect of the acceleration constraint, which is imposed by the structural or aerodynamic limitations, on guidance laws and performance for a first-order missile is systematicall y treated by Anderson.8 In this paper we derive an optimal/moder n guidance law, on collision course, for a linear, time-invariant, arbitrary order and acceleration constrained missile. It is shown that, for a minimum phase missile, the optimal guidance law is the guidance law for an unconstrained missile with saturation on the commanded acceleration. However, for a nonminimum phase missile, this is only a suboptimal guidance law, and the optimal controller is more complicated. In the paper comparison of the proportional navigation, first-order approximation, and full-order guidance laws is performed on a third-order minimum and nonminimum phase model of a missile. The comparison is performed on a common basis. Moreover, the robustness of these guidance laws is subject to an analysis, namely, the sensitivity to uncertainty/ variation in parameters, radome refraction slope, and acceleration constraint is checked for minimum and nonminimum phase air frames. The main conclusions are that, for a minimum phase missile, the full-order guidance law does not give improved performance with respect to the first-order approximation,

Optimal Guidance for High-Order and Acceleration Constrained Missile

Advanced guidance missiles employ blended control of aero-fin and reaction-jet to improve the guidance performance against highly maneuverable targets. The blended control requires multiple inputs and multiple outputs (MIMO) control system design, the design process is much complex than that of conventional aero-fin autopilot. This paper describes a autopilot design for a missile with aero-fin and reaction-jet using the Coefficient Diagram Method (CDM). Performance and stability trade-off study using the CDM is summarized. It is shown that MIMO autopilot design problem can be decomposed into feedback and feedforward controller design problems. A reasonable form of the controller is suggested using the coefficient diagram. A feedback controller is designed using the algebraical approach. The form of the controller has the same form as the conventional design. A wash-out type feedforward controller achieving the minimum fuel consumption is designed using the same manner. It is shown that the feedforward controller can be designed independently of the feedback controller. Improved response and robustness against the reaction-jet force saturation of the designed control system is proven by the simulation.

http://star.sgst.cn/upload/attach/attach20100603110853fyvizqhmys.pdf

Autopilot Design for a Missile with Reaction-Jet Using Coefficient Diagram Method

In recent years, a number of technology and operational features have emerged which have had an impact on the design of control systems for tactical missiles. These have required the closer tuning of autopilots to both the guidance loop and the aerodynamic limits and, at the same time, new design and assessment methods have also been developed for control systems. It is the purpose of this paper to bring these developments together and show how the various aspects contribute to the overall design process which enables a missile autopilot to reach maturity.

Autopilots for Tactical Missiles: An Overview

Radome induced miss distance in aerodynamically controlled homing missiles

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

P. Zarchan

Author Tools

Chat about Author

Papers

Radome induced miss distance in aerodynamically controlled homing missiles