Neighboring optimal guidance for aeroassisted orbital transfer
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Naidu, D. S.↗
Engineering topics
Naidu, D. S.
Publications and source records attributed to Naidu, D. S..
Orbital plane change maneuver with aerocruise
The synergistic plane change problem connected with orbital transfer employing aeroassist technology, is addressed. The mission involves transfer from high earth orbit to low earth orbit with plane change being performed within the atmosphere. The complete mission consists of a deorbit phase, atmospheric phase, and finally reorbit phase. The atmospheric maneuver is composed of an entry mode, a cruise mode, and finally an exit mode. During the cruise mode, constant altitude and velocity are maintained by means of bank angle control with constant thrust or thrust control with constant bank angle. Comparisons between these two control strategies bring out some interesting features.
Naidu, D. S.↗
Neighboring optimal guidance for aeroassisted noncoplanar orbital transfer
The fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in preference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions. The results are presented to a typical aeroassisted noncoplanar orbital transfer problem.
Naidu, D. S.↗
Guidance and Control strategies for aerospace vehicles
A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.
Hibey, J. L.↗
On the method of matched asymptotic expansions
The present evaluation of the method of asymptotic expansions (MAE) indicates that the various terms of the common solution of MAE can be generated as polynomials in stretched variables, without actually solving them from the outer solution, as is currently the practice. It is also noted that the common solution of the MAE and the intermediate solution of the singular-perturbation method are the same; these methods therefore yield identical results for a certain class of problems. Two illustrative problems are treated.
Naidu, D. S.↗
Fuel-optimal trajectories of aeroassisted orbital transfer with plane change
The problem of minimization of fuel consumption during the atmospheric portion of an aeroassisted, orbital transfer with plane change is addressed. The complete mission has required three characteristic velocities, a deorbit impulse at high earth orbit (HEO), a boost impulse at the atmospheric exit, and a reorbit impulse at low earth orbit (LEO). A performance index has been formulated as the sum of these three impulses. Application of optimal control principles has led to a nonlinear, two-point, boundary value problem which was solved by using a multiple shooting algorithm. The strategy for the atmospheric portion of the minimum-fuel transfer is to start initially with the maximum positive lift in order to recover from the downward plunge, and then to fly with a gradually decreasing lift such that the vehicle skips out of the atmosphere with a flight path angle near zero degrees.
Naidu, D. S.↗
Singular perturbation and time scale approaches in discrete control systems
After considering a singularly perturbed discrete control system, a singular perturbation approach is used to obtain outer and correction subsystems. A time scale approach is then applied via block diagonalization transformations to decouple the system into slow and fast subsystems. To a zeroth-order approximation, the singular perturbation and time-scale approaches are found to yield equivalent results.
Naidu, D. S.↗
Three-dimensional atmospheric entry problem using method of matched asymptotic expansions
The analysis of a three-dimensional atmospheric entry problem using the method of matched asymptotic expansions is considered. A composite solution is formed in terms of an outer solution, an inner solution and a common solution. The outer solution is obtained from the gravitationally dominant region, whereas the aerodynamically dominant region contributes to the inner solution. The common solution accounts for the overlap between the outer and inner regions. In comparison to previous work, this simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods.
Naidu, D. S.↗
Fuel-optimal trajectories for aeroassisted coplanar orbital transfer problem
The optimal-control problem arising in coplanar orbital transfer using aeroassist technology is addressed. The maneuver involves the transfer from high earth orbit to low earth orbit with minimum fuel consumption. Simulations are carried out to obtain a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the present work is the application of an efficient multiple shooting method for handling the difficult nonlinear two-point boundary value problem resulting from the optimization procedure.
Naidu, D. S.↗
Time-scale synthesis of a closed-loop discrete optimal control system
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Naidu, D. S.↗
Impact of atmospheric density scale height on the performance of aeroassisted coplanar orbital transfer vehicles
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Naidu, D. S.↗
On the method of matched asymptotic expansions
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Naidu, D. S.↗
Experience in distributed parameter modeling of the Spacecraft Control Laboratory Experiment (SCOLE) structure
The Spacecraft Control Laboratory Experiment (SCOLE) configuration is used to compare exact and approximate solutions of the partial differential equations which define its structural dynamics. The need for a proof model for evaluating competing control laws demands that solutions be generated which not only exhibit accurate modal characteristics, but precise static deflections as well. Because precise pointing is required, the motion of the end bodies of the Shuttle-attached antenna must be known with great accuracy. Modal models are attractive because of their stable solutions but require hundreds of modes to obtain a static deflection accuracy of only one percent. Although proportional damping in bending agrees well with experimental results using the SCOLE experimental apparatus, modes which involve both torsion and bending differ significantly from proportional damping. A lumped mass model is used to generate exact static deflections, but only approximate modal characteristics. Asymptotic solutions to the distributed parameter system approximate very accurately the modal characteristics at high mode numbers. Ways are examined for refining the approximate solutions by applying a first-order variation and by employing singular perturbation techniques which are usually limited to ordinary differential equations. The most accurate solutions of the distributed parameter model of SCOLE are obtained by combining exact and asymptotic solutions.
Taylor, L. W.↗
Guidance and control strategies for aerospace vehicles
A simplified method of matched asymptotic expansions was developed where the common part in composite solution is generated as a polynomial in stretched variable instead of actually evaluating the same from the outer solution. This methodology was applied to the solution of the exact equations for three dimensional atmospheric entry problems. Compared to previous works, the present simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods. The optimal control problem arising in the noncoplanar orbital transfer employing aeroassist was also addressed.
Hibey, Joseph L.↗
Singular perturbations and time scales (SPaTS) in discrete control systems-An overview
Recent developments in the theory of singular perturbations and time scales (SPaTS) in discrete control systems are reviewed. Sources of discrete models and the effect of the discretizing interval on the model are examined. The analysis of two-time scale systems is presented to bring out typical characteristic features of SPaTS. In the control of the two-time scale systems, the important issue of multirate sampling is addressed.
Naidu, D. S.↗
Time scale analysis of a closed-loop discrete optimal control system
A two-time scale discrete control system is considered. The closed-loop optimal linear quadratic (LQ) regulator for the system requires the solution of a full-order algebraic matrix Riccati equation. Alternatively, the original system is decomposed into reduced-order slow and fast subsystems. The closed-loop optimal control of the subsystems requires the solution of two algebraic matrix Riccati equations of order lower than that required for the full-order system. A composite, closed-loop suboptimal control is created from the sum of the slow and fast feedback optimal controls. Numerical results obtained for an aircraft model show a very close agreement between the exact (optimal) solutions and computationally simpler composite (suboptimal) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the closed-loop optimal control of digital flight systems.
Naidu, D. S.↗
Time scale analysis of a digital flight control system
In this paper, consideration is given to the fifth order discrete model of an aircraft (longitudinal) control system which possesses three slow (velocity, pitch angle and altitude) and two fast (angle of attack and pitch angular velocity) modes and exhibits a two-time scale property. Using the recent results of the time scale analysis of discrete control systems, the high-order discrete model is decoupled into low-order slow and fast subsystems. The results of the decoupled system are found to be in excellent agreement with those of the original system.
Naidu, D. S.↗
On-three time scale analysis
In the present consideration of a three-timescale system, a block diagonalization employing three-stage linear transformations is used to decouple the original system into slow, fast, and faster subsystems. A numerical algorithm is given to solve the resulting Ricatti-type equations, and the technique is verified for the case of a ninth-order example. The technique yields substantial computational requirment reductions, since it involves subsystems that are of a lower order than the original system.
Naidu, D. S.↗