Minimum-fuel, power-limited transfers between coplanar elliptical orbits
Explore the source record for details and available documents.
Haissig, Christine M.↗
Engineering topics
Mease, Kenneth D.
Publications and source records attributed to Mease, Kenneth D..
Aerospace plane guidance using time-scale decomposition and feedback linearization
Explore the source record for details and available documents.
Van Buren, Mark A.↗
Shuttle entry guidance revisited
The Shuttle entry guidance concept is reviewed which is aimed at tracking a reference drag trajectory that leads to the specified range and velocity for the initiation of the terminal energy management phase. An approximate method of constructing the domain of attraction is proposed, and its validity is ascertained by simulation. An alternative guidance law yielding global exponential tracking in the absence of control saturation is derived using a feedback linearization method. It is noted that the alternative guidance law does not improve on the stability and performance of the current guidance law, for the operating domain and control capability of the Shuttle. It is suggested that the new guidance law with a larger operating domain and increased lift-to-drag capability would be superior.
Mease, Kenneth D.↗
Canonical transformations for space trajectory optimization
Canonical transformations are developed between the Cartesian coordinates, equinoctial elements, trajectory variables, and orbital elements for coplanar space trajectory optimization problems. The canonical transformations permit the state and adjoint or their solution, transversality conditions, the optimal control, and integrals of the motion, to be transformed between any of the common sets of coordinates for planar space trajectory optimization problems. Variations on the canonical transformations shown are straightforward to develop given the group properties of the canonical transformations.
Haissig, Christine M.↗
A geometric approach to regulator and tracker design for an aerospace plane
The paper presents a nonlinear design approach drawing from singular perturbations, feedback linearization, and variable structure control, that leads to regulators with automatic gain scheduling which exhibit similar dynamic behavior over the entire flight envelope of the aerospace plane. Additionally, design approach provides for a systematic way to counter disturbance effects as well as modeling uncertainties. The unifying feature of the three nonlinear feedback control methodologies is that they all have a geometric interpretation. First, the translational dynamics are decomposed into reduced-order slow and fast dynamics by way of a formal singular perturbation analysis. After feedback linearization the fast dynamics are robustly stabilized via a variable structure control approach. The slow dynamics are stabilized using conventional proportional-integral compensation based on the nominal slow dynamics. A number of sample command and disturbance responses at opposite ends of the flight envelope are presented for a nonlinear aerospace plane model.
Van Buren, Mark A.↗
Minimum-fuel, power-limited transfers between coplanar elliptical orbits
Two techniques of computing coplanar, minimum-fuel, power-limited transfers are presented, based on approximate solutions obtained by the averaging method. For the first technique, the average solution provides estimates of the initial adjoint variables, and the second provides approximations of the optimal controls in feedback form. The accuracy of the techniques for computing coplanar, minimum-fuel, power-limited transfers is evaluated for a number of initial and final orbits.
Mease, Kenneth D.↗
Aerospace plane guidance using time-scale decomposition - A geometric approach
A method is proposed for developing the necessary guidance logic to steer single-stage vehicles into orbit. The minimum-fuel ascent problem is first considered to analyze the effects of dynamic pressure, acceleration, and heating constraints on guidance systems to thereby develop the guidance logic. The optimal solution consists of behavior with two time scales, and the control law is used to develop near-optimal guidance. The solution uses the slow manifold to delineate the control for minimum-fuel reduced-order trajectory and a separate control for tracking the optimal reduced-order trajectory. A family of fast manifolds is then employed to resolve the tracking problem via the feedback linearization methodology from nonlinear geometric control theory. The two-time-scale decomposition is found to produce a near-optimal ascent by tracking the applicable state-constraint boundary, as well as to simplify the control-design task.
Van Buren, Mark A.↗
Effect of heat rate constraint on minimum-fuel synergetic plane change
The synergetic plane change offers substantial fuel savings over the pure-propulsive alternative for certain noncoplanar orbital transfers. On the other hand, the thermal environment for a synergetic plane change vehicle can be quite severe. The minimum-fuel controls are computed approximately by parametrizing the controls and solving the resulting nonlinear programming problem. By considering several different levels of heat rate constraint, we characterize how the control strategy should be modified in order to keep the heat rate below the specified limit. Flight on the heat rate constraint boundary at high angle of attack is the key characteristic.
Mease, Kenneth D.↗
Thrust law effects on the longitudinal stability of hypersonic cruise
In the present analytical treatment of the cruising flight stability of an aerospacecraft in nearly circular orbit, on the basis of a thrust law which arbitrarily depends on altitude, speed, and angle of attack, attention is given to thrust law effects on the translational (height and phugoid) and rotational (angle of attack) modes. The partial derivatives of the propulsive forces in conjunction with the aerodynamic forces, with respect to speed and altitude, are noted to exert a major influence on the stability of translational dynamics; the partial derivative of the component of propulsive and aerodynamic forces which is perpendicular to vehicle velocity (with respect to the angle of attack) is a primary determinant of the damping of angle-of-attack oscillations, while the partial derivative of the sum about the center of mass of aerodynamic and propulsive pitching moments, with respect to the angle of attack, determines the corresponding period.
Markopoulos, Nikos↗
Comparison of solution approaches for minimum-fuel, low-thrust, power-limited orbital transfers
An initial assessment of the feasibility of a function space gradient method for computing solutions to minimum-fuel power-limited transfers encompassing a wide range of thrust to weight ratios is conducted. Three transfers between coplanar ellipses are used as test cases. The gradient method performs best at the high end of the thrust to weight ratio range. At the lower end, there is reduced sensitivity of the fuel consumption to the control profiles. The minimum fuel consumption and the trajectory are computed quite accurately but the control profiles are in error. An approximate analytical solution, obtained by Edelbaum using the method of averaging, is discussed.
Mease, Kenneth D.↗
Aerospace plane guidance using geometric control theory
A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.
Van Buren, Mark A.↗
Trajectory optimization and guidance for an aerospace plane
The first step in the approach to developing guidance laws for a horizontal take-off, air breathing single-stage-to-orbit vehicle is to characterize the minimum-fuel ascent trajectories. The capability to generate constrained, minimum fuel ascent trajectories for a single-stage-to-orbit vehicle was developed. A key component of this capability is the general purpose trajectory optimization program OTIS. The pre-production version, OTIS 0.96 was installed and run on a Convex C-1. A propulsion model was developed covering the entire flight envelope of a single-stage-to-orbit vehicle. Three separate propulsion modes, corresponding to an after burning turbojet, a ramjet and a scramjet, are used in the air breathing propulsion phase. The Generic Hypersonic Aerodynamic Model Example aerodynamic model of a hypersonic air breathing single-stage-to-orbit vehicle was obtained and implemented. Preliminary results pertaining to the effects of variations in acceleration constraints, available thrust level and fuel specific impulse on the shape of the minimum-fuel ascent trajectories were obtained. The results show that, if the air breathing engines are sized for acceleration to orbital velocity, it is the acceleration constraint rather than the dynamic pressure constraint that is active during ascent.
Mease, Kenneth D.↗
Thrust law effects on the long-period modes of aerospace craft
An analytical study is presented of the longitudinal long-period dynamics of an aerospace craft in a nearly circular orbit, with a thrust law depending arbitrarily on the speed and altitude. A plane of engine possibilities is first defined, with points corresponding to propulsion systems having prescribed thrust slopes with respect to speed and altitude. Approximate expressions for the characteristic roots and times are obtained by first identifying a small quantity in the coefficients of the characteristic equation, and then expanding in a perturbation series about the origin of the plane of engine possibilities, for which the solution is always known. These expressions agree very well with the exact solutions over a wide range of altitudes and thrust laws. The period of the oscillatory translational mode (phugoid) is found to be independent to first order of the thrust law, generalizing results found by previous investigators for specific thrust laws. The results apply to the speed range from hypersonic to orbital.
Markopoulos, Nikos↗
Minimum-fuel ascent to orbit using air-breathing propulsion
Single-stage vehicles using air-breathing propulsion hold promise for more economical delivery of payloads to orbit. The characterization of minimum-fuel trajectories over the range of possible engine and aerodynamic performance of such vehicles provides useful feedback to engine and vehicle designers and paves the way for the development of guidance logic. The minimum-fuel trajectory problem is formulated, propulsion system and aerodynamic models are presented, a numerical solution approach is described, and some preliminary results are discussed.
Van Buren, Mark A.↗
Orbital changes during hypersonic aerocruise
A novel mathematical approach that allows the analysis of orbital changes occurring during an aerocruise maneuver to be conducted in two distinct stages is presented. In the first stage, the aerodynamic turn is determined using a nondimensional form of the equations of motion that is free of singularities, and the way in which speed, altitude, angle of attack, and thrust direction should be chosen to maximize the aerodynamic turn for a given propellant expenditure is demonstrated. In the second analysis stage, the aerodynamic turn is translated into changes in the orbital elements with respect to the equatorial plane; analytic solutions for the initial arguments of latitude that maximize the change in inclination and in the longitude of the ascending node are given. As the initial inclination decreases toward zero, the optimal location moves from the apex toward the node.
Mease, Kenneth D.↗