Robust coordinated control for large flexible spacecraft based on consensus theory

Abstract

A distributed coordinated robust control method is proposed in this paper for large flexible spacecraft with distributed actuators and sensors. By dividing the control framework into an attitude dynamic system and a structural vibration system, a consensus observer is designed to estimate the primary system's modal coordinates and the graph theory is used to develop a leader-follower consensus vibration controller to reduce the oscillation of the flexible structures. The robust optimal attitude controller with known averaged vibration modal parameters is also designed to overcome the influence of environmental disturbances and other system uncertainties. The integrated result is an effective pointing controller of large flexible spacecraft, which is also robust to failures and inconsistencies in the control system. A comparative study is presented to show the advantage of the decentralized design over the conventional centralized method. Simulation results are provided to demonstrate the performance of the proposed control method.

Introduction

Large flexible spacecraft often has dynamic characteristics such as low frequency, dense mode and strong geometric nonlinearity [1]. During the long-term operation of the spacecraft, the large flexible structure is prone to vibration because there are various uncertain factors such as the unbalanced external forces or fuel sloshing caused by the attitude maneuver. Due to the low damping of the structures and the lack of atmospheric damping in the space environment, it is difficult to self-attenuate such vibration, which may cause structural fatigue damage and even affect the overall stability of the spacecraft system.

The attitude control and active vibration suppression problem of large-scale space structure has always been a research focus in the aerospace area. The selection of appropriate control actuators and the design of the control law play a significant role in the high precision pointing and vibration suppression of flexible spacecraft. For the attitude control of a flexible spacecraft, the actuator is often set to be a thruster or an angular momentum exchange device. However, for the vibration suppression of flexible structures, many options of actuators have been proposed such as micro thruster [2], sliding mass [3,4], magnetic or electrohydraulic dampers [5], piezoelectric material [6], angular momentum exchange device [7] or hybrid damping schemes based on different actuators [8]. Among them, piezoelectric materials are widely adopted due to the advantages, including light weight, large response frequency bandwidth and easy to install.

The main difficulty for the controller design lies in the modeling error of the flexible structure and the nonlinearity introduced by the rigid-flexible coupling of the system. One of the current solutions to this problem is mainly based on the feedback linearization approach, which transforms the system into a linear model to achieve precise control [9]. However, this approach is less robust to uncertainty and does not take into account the actual response of the actuators. Another possible solution is proposed by treating the rigid-flexible coupling nonlinearity as an uncertainty of the system. For instance, Hu et al. [6] applied the H_∞ robust control to realize the vibration suppression of flexible plates. Lei et al. [10] proposed a robust gain-scheduling attitude control scheme for spacecraft with large rotational appendages. Li et al. [9] designed the variable universe adaptive fuzzy controller by using the periodic variable domain, which effectively suppresses the vibration of flexible solar panels. Jiang et al. [11] designed the control system of intelligent solar panels by using velocity feedback and linear quadratic regulator (LQR). At present, researchers have proven that many decentralized control methods can effectively suppress the vibration of large flexible structure. Examples of such controller can be given as hybrid positive feedback (HPF) [12], positive position feedback (PPF) control [13], modified positive velocity feedback control [14], minimum energy based control [15], Lyapunov function based nonlinear vibration control [16] and Pole-configuration-integral resonance control method [17]. Meanwhile, Li et al. [18], [19], [20] carried out the theoretical research and experimental verification on distributed vibration control of satellite solar panels and large intelligent truss structures. Cao et al. [21] designed a shape input & time delay controller by using piezoelectric actuator for a flexible satellite containing a main rigid body and some flexible appendages. Wang et al. [22] proposed a distributed cooperative controller, using proportional and differential feedback and the interaction feedback among adjacent control units to suppress vibration of the solar power satellite. The ``distributed'' control method can effectively reduce the design complexity of the controller and improve the calculation efficiency under the premise of realizing the overall structure control.

However, with the development of space technology, the scale of flexible structures is getting larger and larger, so that more and more actuators are needed. The distributed parameterized control system composed of decentralization is also getting larger. It is important to ensure that all actuators are working in perfect synchronization with one another. If an actuator is not synchronized with other actuators, the performance of the controller will be reduced and the stability of the system may be heavily disturbed. In the event of an actuator failure or sudden change, the performance of the control system may be inconsistent. Therefore, the synchronization performance of distributed subsystems should be deeply investigated in order to improve the fault tolerance and robustness of the control system. At present, the consensus principle based on graph theory has been investigated to control the attitude/position coordinated motion of multiple unmanned systems (cars, airplanes, robots, microsatellites) [23], [24], [25], [26], [27], [28]. However, few studies have been conducted on the design of distributed cooperative control strategies for the vibration suppression of large flexible structures. In recent years, Omidi et al. [29,30] applied the consensus theory to the vibration suppression problems of both clamped beam and cantilever beam. Compared with the centralized control method, better control results can be obtained. For the control of the distributed parameterization system, the actuators arranged in the large flexible structure are regarded as the control units, and then the consistency control is applied to converge the performance inconsistency between the agents to 0. However, there is no literature on the application of the consensus theory to the high-precision shape maintenance control of large flexible spacecraft systems.

Inspired by the above literature, a new robust coordinated control for large flexible spacecraft based on consensus theory is develop and implemented for vibration control of large-scale flexible structures enhanced by adopting the piezoelectric materials as actuators. Based on the singular perturbation theory, the control framework is divided into an attitude dynamic system and a structural vibration system according to the response frequency of different actuators, and the spacecraft is controlled in cycles. In the attitude-oriented control period, the attitude parameters are kept unchanged, and the dynamic model of the flexible structure is converted into a distributed-parametric form. Then, a new vibration controller is developed for flexible structures based on the theory of leader-follower consensus architecture, which uses the modal coordinates and velocity information estimated by a distributed optimal observer. Under the determined consensus dynamics, the consensus constraint makes the adjacent control agents cooperate with each other to achieve a good synchronization performance between actuators. This consensus control method brings additional robustness to the vibration suppression of the flexible structure, and compensates for the failure of the agent by referring to the adjacent agent. In order to realize high-precision pointing control of large flexible spacecraft, the vibration modal parameters are averaged during each attitude control period, and the robust optimal attitude controller is designed by considering the environmental disturbance and model errors. The controller is numerically evaluated in the end and responses of the system to a failure circumstance in controller input applied is investigated. A comparative study is presented to show the advantage of the consensus control design over the conventional centralized method. The rest of the paper is organized as follows: Section 2 presents the dynamic model of the flexible spacecraft, and a brief introduction to the Graph Theory. The controller design is addressed in detail in Section 3, and the simulation results are shown in Section 4 before the conclusion is drawn in Section 5.