Brij N. Agrawal

VIBRATION SUPPRESSION OF FLEXIBLE SPACECRAFT DURING ATTITUDE CONTROL

This paper presents a new approach to vibration reduction of >exible spacecraft during attitude control by using pulse width pulse frequency (PWPF) modulator for thruster Cring and smart materials for active vibration suppression. The experiment was conducted on the Naval Postgraduate School (NPS)s >exible spacecraft simulator (FSS), which consists of a central rigid body and an L-shape >exible appendage. A pair of on-oE thrusters are used to re-orient the FSS. To actively suppress vibrations introduced to the >exible appendage, embedded piezoelectric ceramic patches are used as both sensors and actuators to detect and counter react to the induced vibration. For active vibration suppression using the piezoelectric ceramic patches, positive position feedback (PPF) control targeting at the Crst two >exible modes of the FSS system is used. Experimental results demonstrate the eEectiveness of the control strategy of PWPF modulation for attitude control and PPF for active vibration suppression. ? 2001 Elsevier Science Ltd. All rights reserved

Spacecraft Vibration Reduction Using Pulse-Width Pulse-Frequency Modulated Input Shaper*

Minimizing vibrations of a flexible spacecraft actuated by on-off thrusters is a challenging task. This paper presents the first study of Pulse-Width PulseFrequency (PWPF) modulated thruster control using command input shaping. Input shaping is a technique which uses shaped command to ensure zero residual vibration of a flexible structure. PWPF modulation is a control method which provides pseudo-linear operation for an on-off thruster. The proposed method takes full advantage of the pseudo-linear property of a PWPF modulator and integrates it with a command shaper to minimize the vibration of a flexible spacecraft induced by on-off thruster firing. Compared to other methods, this new approach has numerous advantages: 1) effectiveness in vibration suppression, 2) dependence only on modal frequency and damping, 3) robustness to variations in modal frequency and damping, 4) easy computation and 5) simple implementation. Numerical simulations performed on an eight-mode model of the Flexible Spacecraft Simulator (FSS) in the Spacecraft Research and Design Center (SRDC) at US Naval Postgraduate School (NPS) demonstrate the efficacy and robustness of the method.

Shape control of a beam using piezoelectric actuators

This paper presents the analytical and experimental results on optimal placement of piezoceramic actuators for shape control of beam structures. The objective is to determine the optimum piezoceramic actuator locations and voltages to minimize the error between the desired shape and the achieved shape. The analytical model for predicting beam deformation due to a piezoelectric actuator is based on the Euler-Bernoulli model. The cost function has fifth-order polynomials in the actuator locations and second-order polynomials in actuator voltages. This difference resulted in difficulty in simultaneous optimization of actuator locations and voltages. Using embedded Nader and Mead simplex algorithms to separately optimize actuator locations and voltages was found to produce reliable results, converging to the same optimum solution for a variety of initial conditions. Experimental results show that the analytical model provides a reasonable prediction of actuator performance at low input voltage, but does not account for the nonlinear behavior of the piezoceramic and effects of hysteresis.

Light Propagation through Anisotropic Turbulence

A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales, it is valid only inside the inertial subrange, and it has a power-law slope that can be different from a Kolmogorov one. Using this power spectrum, in the weak turbulence condition, we analyze the impact of the power-law variations α on the long-term beam spread and scintillation index for several anisotropic coefficient values ς. We consider only horizontal propagation across the turbulence cells, assuming circular symmetry is maintained on the orthogonal plane to the propagation direction. We conclude that the anisotropic coefficient influences both the long-term beam spread and the scintillation index by the factor ς(2-α).

Experimental Robustness Study of Positive Position Feedback Control for Active Vibration Suppression

Abstract : POSITIVE position feedback (PPF) control was introduced by Goh and Caughey in 1985 to control vibrations of large exible space structures. A PPF controller has several distinguished advantagesas compared to then widely used velocity feedbackcontrol laws. It is insensitive to spillover, where contributions from unmodeled modes affect the control of the modes of interest. As a second-order low-pass lter, a PPF controller rolls off quickly at high frequencies and is well suited to controlling the lower modes of a structure with well separated modes. Because of these advantages, PPF controller along with smart materials, in particular PZT (lead zirconatetitanate) type of piezoelectricmaterial, has been applied to many exible systems to achieve active damping. The design of a PPF controller requires the natural frequency of a structure. In practice, the structuralnatural frequencymay not be known exactlyor itmay varywith time.When the frequencyused in thePPF controller is different from that of the structure, the performance of the PPF control will adversely affected. Despite that PPF control is widely researched in literature, robustness study of PPF control when natural frequency is inexactly known is not reported. This motivates the authors to conduct experimental study of robustness of PPF control in active vibration suppression of a smart exible structure.

Experiments on Command Shaping Control of a Manipulator with Flexible Links

Minimizingvibrationsofamaneuverede exiblemanipulatorisachallengingtask.Resultsarepresentedofaseries of experimental tests carried out on the Space Robot Simulator assembly, which has been set up at the Spacecraft Research and Design Center of the Naval Postgraduate School. The manipulator is planar with two rotational degrees of freedom and two links, of which either one or both can be e exible in bending. The manipulator e oats on air cushions on a granite table. The task of the experiments was to test the effectiveness of the command input shaping technique on the near-minimum-time tracking control of a e exible manipulator. A recently introduced sliding mode control method with smooth joint friction compensation was applied to track either an open- or a closed-reference end-effector path, mapped into joint space. This controller guarantees a very precise tracking of thejoint referencemotion, despite thehigh and poorlymodeled jointfriction torques. Satisfying results,intermsof vibration reduction, have been obtained on point-to-point trajectories and on closed-path trajectories. The results are compared with those obtained with a different command shaping technique.

Adaptive Control of Uncertain Hamiltonian Multi-Input Multi-Output Systems: With Application to Spacecraft Control

A novel adaptive control law for nonlinear Hamiltonian multi-input multi-output (MIMO) systems with uncertain parameters in the actuator modeling as well as the inertia and/or the Coriolis and centrifugal terms is developed. The physical properties of the Hamiltonian systems are effectively used in the control design and the stability analysis. The number of the parameter estimates is significantly lowered as compared to the conventional adaptive control methods. A smooth projection algorithm is applied to keep the parameter estimates inside a singularity-free region. The developed control scheme is applied for attitude control of a spacecraft with both the inertia and the actuator uncertainties.

Vibration suppression of a spacecraft flexible appendage using smart material

This paper presents the results of positive position feedback (PPF) control and linear-quadratic Gaussian (LQG) control for vibration suppression of a flexible structure using piezoceramics. Experiments were conducted on the US Naval Postgraduate Schools flexible spacecraft simulator (FSS), which is comprised of a rigid central body and a flexible appendage. The objective of this research is to suppress the vibration of the flexible appendage. Experiments show that both control methods have unique advantages for vibration suppression. PPF control is effective in providing high damping for a particular mode and is easy to implement. LQG control provides damping to all modes; however, it cannot provide high damping for a specific mode. LQG control is very effective in meeting specific requirements, such as minimization of tip motion of a flexible beam, but at a higher implementation cost.

Automatic Mass Balancing of Air-Bearing based Three-Axis Rotational Spacecraft Simulator

Abstract : Air-bearing-based spacecraft simulators are widely used to develop and verify spacecraft control techniques required by modern spacecraft applications. To create a spacelike environment with ground spacecraft simulators, the effects of gravity should be minimized. For a spherical air-bearing system with 3 rotational degrees of freedom, the center of rotation of the spacecraft simulator should be exactly aligned with the center of gravity. This paper presents the automatic mass balancing method, which compensates for the center of gravity offset from the center of rotation by actuating three proof masses on linear motion stages. Adaptive control of the automatic mass balancing system is used while the balancing masses are actuated in real time. The proposed techniques are implemented on the ground-based three-axis spacecraft simulator for the bifocal relay mirror spacecraft.

ADAPTIVE ANTENNA SHAPE CONTROL USING PIEZOELECTRIC ACTUATORS

Abstract This paper presents improved techniques for the shape control of composite material plates using piezoelectric actuators. The application of this work is for the shape control of spacecraft antenna to correct surface errors introduced by manufacturing, in-orbit thermal distortion, and moisture. A finite element model has been developed for a composite plate with distributed piezoelectric actuators and sensors. To improve the accuracy of the prediction of plate deformation, a simple higher-order deformation theory is used. The electric potential is treated as a generalized coordinate, allowing it to vary over the element. The applied voltages to the actuators are optimized to minimize the error between the desired shape and the deformed shape. Based on these techniques, two computer programs were developed on finite element modeling and optimization. The analytical results demonstrate the use of piezo-electric actuators for the active shape control of spacecraft antennas.