Papers by Keyword: Nonlinear Least-Squares

Abstract: his work is applied to the dynamics of rotational motion of artificial satellites, that is, itsorientation (attitude) with respect to an inertial reference system. The attitude determination involvesapproaches of nonlinear estimation techniques, which knowledge is essential to the safety and controlof the satellite and payload. Here one focuses on determining the attitude of a real satellite: CBERS-2(China Brazil Earth Resources Satellite). This satellite was launched in 2003 and were controlled andoperated in turns by China (Xi’an Control Center) and Brazil (Satellite Control Center). Its orbit isnear polar sun-synchronous with an altitude of 778km, crossing Equator at 10:30am in descendingdirection, frozen perigee at 90 degrees, and providing global coverage of the world every 26 days.The attitude dynamical model is described by nonlinear equations involving the Euler angles. Theattitude sensors available are two DSS (Digital Sun Sensor), two IRES (Infra-Red Earth Sensor), andone triad of mechanical gyros. The two IRES give direct measurements of roll and pitch angles with acertain level of error. The two DSS are nonlinear functions of roll, pitch, and yaw attitude angles. Thegyros furnish the angular measurements in the body frame reference system. Gyros are very importantsensors, as they provide direct incremental angles or angular velocities. They can sense instantaneousvariations of nominal velocities. An important feature is that it allows the replacement of complexmodels (different torques acting on the space environment) by using their measurements to turn thedynamical equations into simple kinematic equations. However gyros present several sources of errorof which the drift is the most troublesome. Such drifts yield along time an accumulation of errorswhich must be accounted for in the attitude determination process. Herein one proposes to estimatethe attitude and the drift of the gyros using the Least SquaresMethod. Results show that one can reachaccuracies in attitude determination within the prescribed requirements, besides providing estimatesof the gyro drifts which can be further used to enhance the gyro error model.

Abstract: The positioning performance of high-speed, high-accuracy light-weight motion control systems is usually restricted by the structure flexibility and model parameter-varying caused by load mass variation. It needs to develop novel motion control algorithm to eliminate the residual vibration in the end-effectors, as well as to be robust over the load mass variation. This paper addresses the first and crucial step of this problem, modeling and identification technique. The linear parameter-varying model of the system is constructed and analyzed. The parameters and affine function identification method based on nonlinear least-squares and principle component analysis technique is proposed. The validity of the proposed method is demonstrated through a lightweight machine experimental setup. It is general enough to be applicable to the dynamic behaviors analysis and gain-scheduling robust control design for industrial lightweight vibration suppression and motion control systems that possess flexible elements and variable loads.

Abstract: A regularization homotopy iterative method established for ill-posed nonlinear least squares problem. Two new regularization parameter selecting strategies are proposed, which are called direct search method and interval division method. The calculation results of nonlinear least squares problems show that the regularization homotopy iterative method and parameter selecting strategies proposed in this paper are correctly and applicable. And also calculation results of nonlinear adjustment of free networks with rank deficiency of Jianglong bridge pier displacement defor-mation monitoring control network show that the method not only decrease the iterative matrix con-dition number, but also make the condition number small fluctuation in full iterative process.