Chaoyong Li, Wuxing Jing, Hui Wang and Zhiguo Qi
To study the application of three‐dimensional differential geometric (DG) guidance commands to a realistic missile defense engagement, and the application of the Newton's…
Abstract
Purpose
To study the application of three‐dimensional differential geometric (DG) guidance commands to a realistic missile defense engagement, and the application of the Newton's iterative algorithm to DG guidance problems.
Design/methodology/approach
The classical differential geometry theory is introduced firstly to transform all the variables in DG guidance commands from an arc length system to the time domain. Then, an algorithm for the angle‐of‐attack and the sideslip angle is developed by assuming the guidance curvature command and guidance torsion command equal to its corresponding value of current trajectory. Furthermore, Newton's iteration is utilized to develop iterative solution of the stated algorithm and the two‐dimensional DG guidance system so as to facilitate easy computation of the angle‐of‐attack and the sideslip angle, which are formulated to satisfy the DG guidance law.
Findings
DG guidance law is viable and effective in the realistic missile defense engagement, and it is shown to be a generalization of gain‐varying proportional navigation (PN) guidance law and performs better than the classical PN guidance law in the case of intercepting a maneuvering target. Moreover, Newton's iterative algorithm has sufficient accuracy for DG guidance problem.
Originality/value
Provides further study on DG guidance problem associated with its iterative solution.
Details
Keywords
Chaoyong Li, Wuxing Jing, Hui Wang and Zhiguo Qi
The paper aims to provide further study on the development and analysis of flight control system for two‐dimensional (2D) differential geometric (DG) guidance and control system…
Abstract
Purpose
The paper aims to provide further study on the development and analysis of flight control system for two‐dimensional (2D) differential geometric (DG) guidance and control system based on the application of a set‐point weighting proportional‐integral‐derivative (PID) controller.
Design/methodology/approach
The commanded angle‐of‐attack is developed in the time domain using the classical differential geometry theory. Then, a set‐point weighting PID controller is introduced to develop a flight control system so as to form the 2D DG guidance and control system, and the gains of the PID controller are determined by the Ziegler‐Nichols method as well as the Routh‐Hurwitz stability criterion. Finally, the classical frequency method is utilized to study the relative stability and robustness of the designed flight control system.
Findings
The results demonstrate that the designed controller yields a fast responding and stable system which is robust to the high frequency parameters variation. Moreover, the DG guidance law is viable and effective in a realistic missile defense engagement.
Originality/value
This paper provides a novel approach on the development of DG guidance and control system associated with its stability analysis.
Details
Keywords
The purpose of this paper is to investigate the problem of the initial attitude detumbling and acquisition for micro‐satellite using geomagnetism with the aid of the pitch…
Abstract
Purpose
The purpose of this paper is to investigate the problem of the initial attitude detumbling and acquisition for micro‐satellite using geomagnetism with the aid of the pitch momentum bias, and the application of the feedback linearization method, H∞ and μ‐synthesize control theory in the robust attitude acquisition controller design.
Design/methodology/approach
The pitch flywheels establish the momentum bias state in the beginning of the detumbling stage and keep the momentum bias state thereafter. The geomagnetic change rate feedback detumbling controller is used to detumble the micro‐satellite and the gyroscope rigidity is utilized to capture orbital negative normal orientation in the detumbling and attitude acquisition phase. Feedback linearization method is adopted to obtain the linear attitude dynamics. Based on the feedback linearization model, a quasi proportion differential (PD) controller is designed, meanwhile H∞ and μ‐synthesis control theories are adopted to synthesis the robust attitude acquisition controllers.
Findings
The pitch momentum bias‐aided attitude detumbling and acquisition method make the capture of the orbital negative normal orientation faster and more accurate than the classical initial operation process. Quasi PD and H∞ have greater robustness than the classical PD attitude acquisition controller in normal geomagnetic case; quasi PD and μ‐synthesis have greater robustness than the classical PD attitude acquisition controller in magnetic storm case.
Originality/value
Provides pitch momentum bias‐aided attitude detumbling and acquisition method for the micro‐satellite and the robust attitude acquisition controller design technology.