A Pseudospectral Approach to High Index DAE Optimal Control Problems

Historically, solving optimal control problems with high index differential algebraic equations (DAEs) has been considered extremely hard. Computational experience with Runge-Kutta (RK) methods confirms the difficulties. High index DAE problems occur quite naturally in many practical engineering applications. Over the last two decades, a vast number of real-world problems have been solved routinely using pseudospectral (PS) optimal control techniques. In view of this, we solve a "provably hard," index-three problem using the PS method implemented in DIDO, a state-of-the-art MATLAB optimal control toolbox. In contrast to RK-type solution techniques, no laborious index-reduction process was used to generate the PS solution. The PS solution is independently verified and validated using standard industry practices. It turns out that proper PS methods can indeed be used to "directly" solve high index DAE optimal control problems. In view of this, it is proposed that a new theory of difficulty for DAEs be put forth.Comment: 14 pages, 9 figure

Electrical-Power Constrained Attitude Steering

AAS/AIAA Astrodynamics Specialist Conference, August 20-24, 2017, Stevenson, WA. Paper number: AAS 17-774wheel array over the course of a slewing maneuver by steering the attitude ofthe spacecraft, in situations where it is not possible to command the reaction wheel torque directly. To explore this avenue, a set ofconstrained nonlinear non-smooth LI optimal-control problems are formulated and solved. It is demonstrated that energy consumption, dissipative losses, and peak-power load, of the reaction-wheel array can each be reduced substantially, by controlling the input to the attitude control system through attitude steering, thereby avoiding software modifications to flight software

Minimum Power Slews and the James Webb Space Telescope

Spaceflight Mechanics 2017Power is a precious commodity in space flight. Reducing the power demands of reaction wheels during spacecraft attitude slews can have multiple benefits both in the up-front spacecraft design phase as well as during in-flight operations. In an effort to reduce power requirements of momentum control systems, many authors have contemplated the use of proxies for reaction wheel power to design minimal effort slews. Proxies for power are used because the power input equation is non-smooth leading to a seemingly unsolvable problem in optimal control. In this paper we show, through the application of various transformations and the introduction of appropriate functional constraints, that a smooth cost functional for reaction wheel input power can indeed be built. Standard techniques can then be used to solve and analyze the power optimal slew problem. The concept is applied to reduce the power requirements for a typical largeangle slew of the James Webb Space Telescope. The energy reduction(~ 20%) is obtained by finding a minimum power momentum distribution that achieves the necessary control effort while simultaneously reducing power input to the individual wheels

Energy Constrained Shortest-Time Maneuvers for Reaction Wheel Satellites

AIAA SPACE Forum 13 - 16 September 2016, Long Beach, California AIAA/AAS Astrodynamics Specialist ConferenceIn this paper we develop energy-metrics that are in-line with true energy costs incurred when performing a slew using reaction wheels. These energy-metrics are incorporated in constrained nonlinear optimal control formulations, which enable detailed analysis on the relationship between transfer-time and energy to be performed. Through numerical simulations, a nonlinear relationship between transfer time and minimal energy is used to help explain the tradeoff between transfer time and energy consumption. This analysis can provide important information for design and operations. In examining the relationship between transfer-time and minimal energy, we also analyze the difference between offeigenaxis and conventional eigenaxis maneuvering. It is demonstrated that, by deviating from rotations about an eigenaxis the transfer-time may be significantly decreased but without incurring more energy than an eigenaxis maneuver. Analogously, energy may be reduced for an eigenaxis maneuver

Relationships Between Maneuver Time and Energy for Reaction Wheel Attitude Control

The article of record may be found at https://doi.org/10.2514/1.G002843The dichotomy between minimum time and minimum effort is well known. Minimum-time solutions are synonymous with large effort, whereas minimum effort solutions imply large time horizons. Shortest-time attitude maneuvers are minimum-time slews for agile reorientation of space vehicles. Intuition and experience would suggest that such maneuvers are expensive in terms of effort. This paper will show that this is not the case: Agile maneuvers exist within the energy budget associated with conventional attitude control systems. Moreover, even for conventional slew strategies (such as eigenaxis), energy requirements can be reduced. The energy savings are realized via a reallocation of the control effort by exploiting null motions within the control space, over the maneuver trajectory. A cost functional for minimum-energy slews is developed that is in line with true energy cost associated with reaction wheel-based attitude control systems. This energy metric is incorporated into a family of constrained nonlinear optimal control formulations whose solutions present a relationship between transfer time and energy. Both agile (off-eigenaxis) slews and conventional (eigenaxis) slews are studied. A trade space between transfer time and energy is identified, which can be exploited for mission operations, planning, and design

A Pseudospectral Approach to High Index DAE Optimal Control Problems

Historically, solving optimal control problems with high index differential algebraic equations (DAEs) has been considered extremely hard. Computational experience with Runge-Kutta (RK) methods confirms the difficulties. High index DAE problems occur quite naturally in many practical engineering applications. Over the last two decades, a vast number of real-world problems have been solved routinely using pseudospectral (PS) optimal control techniques..