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Research Papers

# Robust Adaptive Attitude Tracking Control With $L2$-Gain Performance and Vibration Reduction of an Orbiting Flexible Spacecraft

[+] Author and Article Information
Qinglei Hu

Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, Chinahuqinglei@hit.edu.cn

J. Dyn. Sys., Meas., Control 133(1), 011009 (Dec 22, 2010) (11 pages) doi:10.1115/1.4001703 History: Received September 16, 2007; Revised April 05, 2010; Published December 22, 2010; Online December 22, 2010

## Abstract

This paper presents a dual-stage control system design method for flexible spacecraft attitude tracking control and active vibration suppression by an embedded smart material as sensors/actuators. More specifically, a conventional sliding mode controller with the assumption of knowing system parameters is first designed that ensures asymptotical convergence of attitude tracking error described by error quaternion and its derivative in the presence of bounded parameter variation/disturbance. Then it is redesigned, such that the need for knowing the system parameters in advance is eliminated by using an adaptive updating law. For the synthesis of the controller, to achieve the prescribed $L2$-gain performance criterion, the control gains are designed by solving a linear matrix inequality problem. Indeed, external torque disturbances/parametric error attenuations with respect to the performance measurement along with the control input penalty are ensured in the $L2$-gain sense. Even if this controller has the ability to reject the disturbance and deal with actuator constraint, it excites the elastic modes of flexible appendages, which will deteriorate the pointing performance. Then the undesirable vibration is actively suppressed by applying feedback control voltages to the piezoceramic actuator, in which the modal velocity feedback control method is employed for determining the control voltages. Numerical simulations are performed to show that attitude tracking and vibration suppression are accomplished, in spite of the presence of disturbances/parameter uncertainties and even control input constraint.

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## Figures

Figure 1

Attitude tracking control without vibration compensation. Case 1: proposed sliding mode control law (solid line); Case 2: modified sliding mode control law (dash-dot line); Case 3: PD control law (dotted line); Case 4: adaptive control law (dashed line). (a) Time response of angular velocity; (b) time response of control torque; (c) time response of attitude quaternion; (d) time response of vibration displacements and energy; (e) time response of error quaternion.

Figure 2

Attitude tracking control with vibration compensation. Case 1: proposed sliding mode control law+MVF (solid line); Case 2: modified sliding mode control law+MVF (dash-dot line); Case 3: PD control law+MVF (dotted line); Case 4: adaptive control law+MVF (dashed line). (a) Time response of angular velocity; (b) time response of control torque; (c) time response of attitude quaternion; (d) time response of vibration displacements and energy; (e) time response of error quaternion.

Figure 3

Time responses of estimated parameters. Case 1: proposed sliding mode control law (dotted line); Case 2: modified sliding mode control law (dashed line); Case 3: proposed sliding mode control law+MVF (solid line); Case 4: modified sliding mode control law+MVF (dash-dot line).

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