Fault Detection for Satellite Attitude Control System with Computation Constraint

Driven by the satellite’s features such as closed-loop, limited storage space and computing capacity constraint, a fault detection scheme based on the coprime factorization and Youla parameterization is proposed for the on-orbit satellite attitude control system. Based on the SISO dynamic of the satellite in pitch direction and the MIMO one in roll/yaw direction, the residuals equal to  ˆ ( ) ( ) y k y k is generated by a simple computation using the plant input and control error signals without running the state observer in parallel, therefore the computing expense is reduced to a certain extent, and the related theorems are provided synchronously. Simulation results are presented to show the performance of the proposed fault detection algorithm. 1.INTRODUCTION With the development of space technologies, different types of satellites have been constructed and used for various space missions, such as position location, Earth observation, atmosphere data collection, and communication (Qing Wu and Mehrdad Saif, 2007). Equipment fault leading to scientific mission failure and high costs has been common strategic and critical problems that are reported in the recent scientific mission. For this reason, a lot of different FDI techniques have been considered. In (Venkateswaran et al., 2002), a FDI observer combined with a residual weighting matrix is used to consider the gyroscopes faults problem, and the proposed design procedure involves eigenstructure assignment. Directional nonlinear observers are used to detect and isolate faults in small satellites’ actuators in (Jensen and Wisniewski 2002); however, as it is outlined by the authors, there exist some conditions regarding the distribution functions of the disturbances and faults, which basically rely on rank conditions. A particle filtering method combined with a bank of Kalman filters is proposed to address the problem of FDI in spacecraft and planetary rovers in (De Freitas N., 2002). In (Qing Wu and Mehrdad Saif, 2007), a nonlinear observer which synthesizes second order sliding mode techniques and wavelet networks is proposed for abrupt and incipient fault in a multiple satellite formation flying system. In (Qing Wu and Mehrdad Saif, 2007), an iterative learning observer is designed to achieve estimation of time-varying thruster faults in satellite system. However, two reasons prevent these methods from applying to the satellite in reality. One reason is that some of the aforementioned methods are based on an open-loop model of the monitored system, although the FDI scheme is placed in a feedback loop and faults may be covered by control actions (D.Henry, 2008)). This motivates the integrated design of control and diagnosis schemes in which the design of controllers and fault detectors are formulated as a standard optimization problem(C. N. Nett, 1988; A. Marcos and G. J. Balas, 2005; H. H. Niemann and J. Stoustrup, 1997; H. H. Niemann and J. Stoustrup, 2003; M. L. Tyler and M. Morari, 1994; Schultalbers et al, 2010; S.X.Ding, 2009). However, because of the fact that the already-in-place attitude control system is certified and thus cannot be removed, this solution is hard to be applied here. The other one is that instead of some complex methods, the limited storage space and computing capacity constraint of the satellite computer need simple but effective fault diagnosis approaches that can monitor the satellite operating condition without any extra online computation. In this paper, because of the fact that the dynamics in pitch direction decouples from that in roll/yaw direction in linear model on the small angles assumption, the corresponding SISO model and the MIMO model are obtained respectively by considering the satellite kinematic and dynamic model simultaneously. Based on the models, instead of running the state observer, the coprime factorization of the plants and the Youla parameterization of the stabilizing controllers are used to conclude that the residual equivalent to ) ( ˆ ) ( s y s y  be generated by a simple computation using the plant input and control error signals that are available in the feedback control loop without any computing expense. 2. SATELLITE DESCRIPTION A satellite is assumed to be a rigid body with the momentum wheel providing torques. The linear model of the satellite dynamic is presented as follows (Yang Ciann-dong and Sun Yun-ping, 2002):                             2 1 1 2 3 2 3 1 2 2 1 3 2 2 3 1 2 3 2 1 3 ( ) 4 ( ) 3 ( ) ( ) ( ) I n I I I n I I T I n I I T I n I I I n I I T (1) where 1 2 3 , , I I I are the principal moments of inertia,    , , are the roll angle ,the pitch angle and the yaw angle respectively, and 1 2 3 , , T T T are the body-axis components of the external torques acting on the satellite, which usually Preprints of the 18th IFAC World Congress Milano (Italy) August 28 September 2, 2011 Copyright by the International Federation of Automatic Control (IFAC) 2103 contain control torques and environmental disturbance torques, however in this paper they only contain control torques, n is the orbital rate of the satellite. It is noticed that the pitch dynamics decouples from the roll/yaw dynamics in linear model on the small angles assumption, so the residuals of the pitch channel and the roll/yaw channel can be designed separately. For the pitch channel, by defining the state vector [ ] x     and the output vector  y x , we have the following SISO state-space representation of the equations:   2 1 2 1 2 1 3 2 0 0 3 ( ) 0