Bong Wie

BENCHMARK PROBLEMS FOR ROBUST CONTROL DESIGN

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Robust Time-Optimal Control of Uncertain Flexible Spacecraft

A new approach for computing time-optimal open-loop control inputs for uncertain flexible spacecraft is developed. In particular, the single-axis, rest-to-rest maneuvering problem of flexible spacecraft in the presence of uncertainty in model parameters is investigated. Robust time-optimal control inputs are obtained by solving a parameter optimization problem subject to robustness constraints. A simple dynamical system with a rigidbody mode and one flexible mode is used to illustrate the concept.

Time-optimal three-axis reorientation of a rigid spacecraft

New results are presented for the minimum-time rest-to-rest reorientation control problem of a rigid spacecraft with independent three-axis control. It is shown that in general the eigenaxis rotation maneuver is not time optimal. An inertially symmetric (e.g., spherical or cubical) rigid body is examined to demonstrate that an eigenaxis rotation about a control axis of even such a simple body is not time optimal. The computed optimal solution is bang-bang in all three control components and has a significant nutational component of motion. The total number of switches is found to be a function of the specified reorientation angle.

Rapid Multitarget Acquisition and Pointing Control of Agile Spacecraft

This paper describes the study results of developing an attitude control system for agile spacecraft which require rapid retargeting and fast transient settling. In particular, a nonlinear feedback control logic is developed for large-angle, rapid multi-target retargeting maneuvers subject to various physical constraints, including the actuator saturation, slew rate limit, control bandwidth limit, etc. Simulation results for an agile spacecraft equipped with control moment gyros demonstrate the effectiveness and robust performance of the proposed nonlinear feedback control system.

Feedback control logic for spacecraft eigenaxis rotations under slew rate and control constraints

The problem of reorienting a rigid spacecraft as fast as possible within the physical limits of actuators and sensors is investigated. In particular, a nonlinear feedback control logic which accommodates the actuator and sensor saturation limits is introduced. The nearminimum-time eigenaxis reorientation problem of the Xray Timing Explorer spacecraft under slew rate and control torque constraints is used as an example to demonstrate the effectiveness and simplicity of the proposed nonlinear feedback control logic.

New approach to attitude/momentum control for the Space Station

A new approach to control moment gyro (CMG) momentum management and attitude control of the space station is presented. The control algorithm utilizes both the gravity-gradient and gyroscopic torques to seek torque equilibrium attitude in the presence of secular and cyclic disturbances. It is shown that, depending on mission requirements, either pitch attitude or pitch-axis CMG momentum can be held constant. It is also shown that a combination of yaw attitude and roll-axis CMG momentum can be held constant, whereas a combination of roll attitude and yaw-axis CMG momentum cannot. As a result, the overall attitude and CMG momentum oscillations caused by cyclic aerodynamic disturbances are minimized. A state feedback controller with minimal computer storage requirements for gain scheduling is also presented. An inherent physical property of the coupled roll/yaw dynamics is discussed in terms of a transmission zero of a multivariable system.

Singularity analysis and visualization for single-gimbal control moment gyro systems

The singularity problem inherent in redundant single-gimbal control moment gyro (CMG) systems is examined. It is intended to provide a comprehensive mathematical treatment of the CMG singularity problem, expanding upon the previous work by Margulies, Aubrun, and Bedrossian. However, particular emphasis is placed on characterizing and visualizing the physical as well as mathematical nature of the singularities, singular gimbal angles, singular momentum surfaces, null motion manifolds, and degenerate null motions. The mathematical framework for characterizing the geometric property of singular surfaces is also established by applying the surface theory of differential geometry. Two and three parallel single-gimbal CMG configurations and a typical pyramid array of four single-gimbal CMGs (including a special case of 90-deg skew angle) are examined in detail to illustrate the various concepts and approaches useful for characterizing and visualizing the CMG singularities.

Robust time-optimal control of uncertain structural dynamic systems

A new approach for computing open-loop time-optimal control inputs for uncertain linear dynamical systems is developed. In particular, the single-axis, rest-to-rest maneuvering problem of flexible spacecraft in the presence of uncertainty in model parameters is considered. Robustified time-optimal control inputs are obtained by solving a parameter optimization problem subject to robustness constraints. A simple dynamical system with a rigid-body mode and one flexible mode is used to illustrate the concept.

Pulse-modulated control synthesis for a flexible spacecraft

The describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. The method provides a means of characterizing the pulse modulator in terms of its gain and phase for structural mode limit cycle analysis. Although the describing function method is inherently inexact and is not widely used in practice, a new way of utilizing it for practical control design problems is presented. It is shown that the approximations inherent in the method can be accounted as a modeling uncertainty for the nonlinear control robustness analysis. The pulse modulated control system of the INTELSAT 5 spacecraft is used as an example to illustrate the concept and methodology developed in the gaper. The nonlinear stability margins predicted by the describing function analysis are verified from nonlinear simulations.

Classical and robust H(infinity) control redesign for the Hubble Space Telescope

A control redesign problem of the Hubble Space Telescope for reducing the effects of solar array vibrations on telescope pointing jitter is investigated. Both classical and H, control design methodologies are employed for such a control problem with a non-colocated actuator and sensor pair. This paper successfully demonstrates the effectiveness of a dipole concept for precision line-ofsight pointing control in the presence of significant structural vibrations. Proposed controllers with two dipoles effectively reduce the effects of the solar array induced disturbances at 0.12 Hz and 0.66 Hz on pointing jitter.