The application of optimal control technqiues to advanced manned missions, volume 1

Two problems are presented in the area of optimal control and its application to the design of attitude control systems for advanced complex aerospace vehicles. The problems discussed are specification of performance criteria in terms of structural load minimization and/or maximum orbital payload injection requirements of the controlled vehicle; and formulation and solution of the optimization problem such that practical control systems are obtained

Optimal impact angle guidance for exo-atmospheric interception utilizing gravitational effect

This paper aims to develop a new optimal intercept angle guidance law for exo-atmospheric interception by utilizing gravity. A finite-time optimal regulation problem is formulated by considering the instantaneous zero-effort-miss (ZEM) and the intercept angle error as the system states. The analytical guidance command is then derived based on Schwarz's inequality approach and Lagrange multiplier concept. Capturability analysis using instantaneous linear time-invariant system concept is also presented to provide better insights of the proposed guidance law. Theoretical analysis reveals that the proposed optimal guidance law encompasses previously suggested optimal impact angle constrained guidance laws. Numerical simulations with some comparisons clearly demonstrate the effectiveness of the proposed guidance law

Generalized formulation of linear nonquadratic weighted optimal error shaping guidance laws

This study presents a novel extension to the theory of optimal guidance laws represented by the nontraditional class of performance indices: nonquadratic-type signal Lp" role="presentation">Lp norm for the input weighted by an arbitrary positive function. Various missile guidance problems are generally formulated into a scalar terminal control problem based on the understanding of the predictor–corrector nature. Then, a new approach to derive the optimal feedback law, minimizing the nonquadratic performance index, is proposed by using the Hölderian inequality. The proposed extension allows a more general family of formulations for the design of closed-form feedback solutions to various guidance problems to be treated in a unified framework. The equivalence between the proposed approach and other design methodologies is investigated. In general, the type of input norm mainly determines the variability of input during the engagement while trading off against the rate of error convergence. The analytic solution derived in this study is verified by comparison with the solution from numerical optimization, and the effect of the exponent p" role="presentation">p in the performance index on the trajectory and command is demonstrated by numerical simulations

Rapid near-optimal trajectory generation and guidance law development for single-stage-to-orbit airbreathing vehicles

General problems associated with on-board trajectory optimization, propulsion system cycle selection, and with the synthesis of guidance laws were addressed for an ascent to low-earth-orbit of an air-breathing single-stage-to-orbit vehicle. The NASA Generic Hypersonic Aerodynamic Model Example and the Langley Accelerator aerodynamic sets were acquired and implemented. Work related to the development of purely analytic aerodynamic models was also performed at a low level. A generic model of a multi-mode propulsion system was developed that includes turbojet, ramjet, scramjet, and rocket engine cycles. Provisions were made in the dynamic model for a component of thrust normal to the flight path. Computational results, which characterize the nonlinear sensitivity of scramjet performance to changes in vehicle angle of attack, were obtained and incorporated into the engine model. Additional trajectory constraints were introduced: maximum dynamic pressure; maximum aerodynamic heating rate per unit area; angle of attack and lift limits; and limits on acceleration both along and normal to the flight path. The remainder of the effort focused on required modifications to a previously derived algorithm when the model complexity cited above was added. In particular, analytic switching conditions were derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another for two cases: the case in which engine cycle operations can overlap, and the case in which engine cycle operations are mutually exclusive. The resulting guidance algorithm was implemented in software and exercised extensively. It was found that the approximations associated with the assumed time scale separation employed in this work are reasonable except over the Mach range from roughly 5 to 8. This phenomenon is due to the very large thrust capability of scramjets in this Mach regime when sized to meet the requirement for ascent to orbit. By accounting for flight path angle and flight path angle rate in construction of the flight path over this Mach range, the resulting algorithm provides the means for rapid near-optimal trajectory generation and propulsion cycle selection over the entire Mach range from take-off to orbit

Guidance, flight mechanics and trajectory optimization. Volume 11 - Guidance equations for orbital operations

Mathematical formulation of guidance equations and solutions for orbital space mission

A New Path Planning Guidance Law For Improved Impact Time Control of Missiles and Precision Munitions

A new missile guidance law is proposed for the control of impact time which provides an improved time-to-go calculation by removing error due to trajectory curvature and also provides a family of trajectories for trajectory planning purposes. Unlike conventional optimal guidance laws, the proposed law is non explicit in time-to-go and the linearization of the engagement kinematics in order to gain a closed form solution is not necessary

Modeling, Analysis, and Optimization Issues for Large Space Structures

Topics concerning the modeling, analysis, and optimization of large space structures are discussed including structure-control interaction, structural and structural dynamics modeling, thermal analysis, testing, and design