PurposeTo 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/approachThe 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.FindingsDG 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/valueProvides further study on DG guidance problem associated with its iterative solution.

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This paper presents a detailed study of the two-dimensional (2D) differential geometric (DG) guidance problem, as well as its iterative solution and initial conditions. The DG guidance curvature command is transformed from an arc length system to the time domain using the classical DG theory. Subsequently, an algorithm for commanded angleof-attack is developed to formulate the DG guidance system, whose iterative solution is established based on Newton's iterative algorithm. Moreover, a flight control system is presented using the classical PID controller so as to form the DG guidance and control system. Finally, a new necessary initial condition is deduced to guarantee the capture of a high-speed target. Simulation results demonstrate that Newton's iterative algorithm works well and accurately in DG guidance problems and the proposed DG guidance law exhibits similar performance to the proportional navigation guidance (PNG) law in the case of intercepting a non-maneuvering target. However, the proposed method performs better than PNG in the case of intercepting a maneuvering target.

PurposeThe 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/approachThe 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.FindingsThe 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/valueThis paper provides a novel approach on the development of DG guidance and control system associated with its stability analysis.

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