Engineering topics
Publications and source records attributed to Rajan, N..
Report discusses formulation of algorithm used in pointing proposed Space Infrared Telescope Facility at various celestial objects. Control system of telescope required to aim and keep telescope aimed within 0.15 arc second of intended target. In addition, required to perform 120 degree slews in 8 min and 7.5-arc-minute nods (nod is small-angle slew) within 20 s. Study concentrates on nod maneuver.
A preliminary first-order optical design for the Stratospheric Observatory for Infrared Astronomy (SOFIA) is presented. This is a Cassegrain design with a 3 meter diameter, approximately f/1 primary mirror. Phenomena limiting the image quality of the telescope are divided into 'seeing', optics, and guidance. An error budget is presented for these categories and specific effects contributing to each. The seeing effects from the shear layer between the telescope cavity and the external air are expected to be dominant. Results are presented on the necessary thermal, optical, structural and guidance requirements to maintain contributions of these phenomena below that of the shear-layer seeing.
The response of the Space Infrared Telescope Facility's attitude control system to a nod command is studied under a wide variety of conditions. Several engineering issues are explored: the effects of variations in the structural model, relocation of sensors and actuators, the influence of the fine guidance sensor sampling period, resolution and noise on the system response, torque and rate integrating gyro noise and disturbances. Simulation results using control moment gyros and reaction wheels as actuators are presented.
In the course of a simulation study of a candidate design for the Space Infrared Telescope Facility (SIRTF), an unusual phenomenon was observed. The uncompensated control system was unstable, but a numerical simulation with the fixed-step-size classical fourth-order Runge-Kutta method gave a stable response. This phenomenon is described in the setting in which it occurred. The Runge-Kutta simulation model is analyzed as a discrete linear system and shown to be stable, thus corroborating the numerical results.
The turret game is defined and solved to illustrate the nature of games of combat. This game represents a highly simplified version of air combat, yet it is sufficiently complex so as to exhibit a rich variety of combat phenomena. A review of the formulation of delta-combat games is included.
The identification of a new fast variable for three-dimensional flight dynamics is discussed. It is shown that the variable gives a value of the flightpath angle which is consistent with the velocity-altitude state equations and that the accuracy of single-perturbation analyses is increased by decreasing the magnitude of boundary-layer corrections. The values of the flightpath angle along the three-dimensional energy-state extremal are found to be lower by approximately an order of magnitude than those along the two-dimensional energy-state solution.
A mathematical formulation is proposed of a combat game between two opponents with offensive capabilities and offensive objective is proposed. Resolution of the combat involves solving two differential games with state constraints. Depending on the game dynamics and parameters, the combat can terminate in one of four ways: the first player wins; the second player wins; a draw (neither wins); or joint capture. In the first two cases, the optimal strategies of the two players are determined from suitable zero-sum games, whereas in the latter two the relevant games are nonzero-sum. Further, to avoid certain technical difficulties, the concept of a delta-combat game is introduced.
Combat is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives. With each opponent is associated a target in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously or in neither, a joint capture or a draw, respectively, is said to occur. Resolution of the encounter is formulated as a combat game; namely, as a pair of competing event-constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero-sum differential game. Otherwise the optimal strategies are computed from a resulting non-zero-sum game. Since optimal combat strategies frequencies may not exist, approximate of delta-combat games are also formulated leading to approximate or delta-optimal strategies. To illustrate combat games, an example, called the turret game, is considered. This game may be thought of as a highly simplified model of air combat, yet it is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit-evasion games.
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Combat games are formulated as zero-sum differential games with unilateral event constraints. An interior penalty function approach is employed to approximate optimal strategies for the players. The method is very attractive computationally and possesses suitable approximation and convergence properties.
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A transformation from the altitude and velocity state variables of three-dimensional flight mechanics to a new set of more desirable variables is found. The new variables provide a greater time-scale separation, decrease system coupling, and give better estimates of the fast-variable values along the reduced solution. One of the new variables is the often-used specific energy, whereas the other variable changes along a given trajectory, depending on the nature of the local reduced solution. Numerical examples are included.
Combat which is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives is outlined. A target set is associated with each opponent in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously, or in neither, a joint capture or a draw, respectively, occurs. Resolution of the encounter is formulated as a combat game; as a pair of competing event constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero sum differential game. Otherwise the optimal strategies are computed from a resulting nonzero sum game. Since optimal combat strategies may frequently not exist, approximate or delta combat games are also formulated leading to approximate or delta optimal strategies. The turret game is used to illustrate combat games. This game is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit evasion games.
A method is proposed for mapping the barrier, dispersal, and control-level surfaces for a class of minimum-time interception and pursuit-evasion problems. Minimum-time interception of a target moving in a horizontal plane is formulated in a coordinate system whose origin is at the interceptor's terminal position and whose x-axis is along the terminal line of sight. This approach makes it possible to discuss the nature of the interceptor's extremals, using its extremal trajectory maps (ETMs), independently of target motion. The game surfaces are constructed by drawing sections of the isochrones, or constant minimum-time loci, from the interceptor and target ETMs. In this way, feedback solutions for the optimal controls are obtained. An example involving the interception of a target moving in a straight line at constant speed is presented.
The problem of validating and verifying digital flight control system (DFCS) software is addressed in this paper. A new specification language DIVERS is proposed, and is the keystone of the approach. This language consists of keywords where each keyword represents an element in the block diagram of a DFCS. DIVERS has a dictionary which contains all the keywords a DFCS designer might need. Translator programs convert the system specifications into an executable, high-level language program. The features of translators are discussed and are elucidated by examples. This language is used to describe a typical flight software module.
The problem of minimum-time interception of a target flying in three dimensional space is analyzed with the interceptor aircraft modeled through energy-state approximation. A coordinate transformation that uncouples the interceptor's extremals from the target motion in an open-loop sense is introduced, and the necessary conditions for optimality and the optimal controls are derived. Example extremals are shown.
Two methods for analyzing the time-scale properties of aircraft trajectory optimization problems are presented. Time-scale properties must be identified before solutions can be obtained by using singular perturbation methods. Both methods only require a knowledge of the state equations, the aircraft characteristics, and the bounds on the state and control variables. Although these methods give only rough estimates of time-scale separation, they do not require that an 'exact' optimal trajectory be known, as do the more rigorous methods, and they are an improvement on the ad hoc methods currently in use. The two methods are applied to an example problem for a high performance aircraft.