Thrusting maneuver control of a small spacecraft via only gimbaled-thruster scheme

The thrust vector control (TVC) scheme is a powerful method in spacecraft attitude control. Since the control of a small spacecraft is being studied here, a solid rocket motor (SRM) should be used instead of a liquid propellant motor. Among the TVC methods, gimbaled-TVC as an efficient method is employed in this paper. The spacecraft structure is composed of a body and a gimbaled-SRM where common attitude control systems such as reaction control system (RCS) and spin-stabilization are not presented. A nonlinear two-body model is considered for the characterization of the gimbaled-thruster spacecraft where, the only control input is provided by a gimbal actuator. The attitude of the spacecraft is affected by a large exogenous disturbance torque which is generated by a thrust vector misalignment from the center of mass (C.M). A linear control law is designed to stabilize the spacecraft attitude while rejecting the mentioned disturbance torque. A semi-analytical formulation of the region of attraction (RoA) is developed to ensure the local stability and fast convergence of the nonlinear closed-loop system. Simulation results of the 3D maneuvers are included to show the applicability of this method for use in a small spacecraft.     

The use of Gaussian equations of motions of a satellite for local gravity anomaly recovery

The orbital elements of a low Earth orbiting satellite and their velocities can be used for local determination of gravity anomaly. The important issue is to find direct relations among the anomalies and these parameters. Here, a primary theoretical study is presented for this purpose. The Gaussian equations of motion of a satellite are used to develop integral formulas for recovering the gravity anomalies. The behaviour of kernels of the integrals are investigated for a two-month simulated orbit similar to that of the Gravity field and steady-state ocean circulation explorer (GOCE) mission over Fennoscandia. Numerical investigations show that the integral formulas have neither isotropic nor well-behaved kernels. In such a case, gravity anomaly recovery is not successful due to large spatial truncation error of the integral formulas. Reformulation of the problem by combining the orbital elements and their velocities leads to an integral with a well-behaved kernel which is suitable for our purpose. Also based on these combinations some general relations among the orbital elements and their velocities are obtained which can be used for validation of orbital parameters and their velocities.     

The effect of spatial truncation error on variance of gravity anomalies derived from inversion of satellite orbital and gradiometric data

The spatial truncation error (STE) is a significant systematic error in the integral inversion of satellite gradiometric and orbital data to gravity anomalies at sea level. In order to reduce the effect of STE, a larger area than the desired one is considered in the inversion process, but the anomalies located in its central part are selected as the final results. The STE influences the variance of the results as well because the residual vector, which is contaminated with STE, is used for its estimation. The situation is even more complicated in variance component estimation because of its iterative nature. In this paper, we present a strategy to reduce the effect of STE on the a posteriori   variance factor and the variance components for inversion of satellite orbital and gradiometric data to gravity anomalies at sea level. The idea is to define two windowing matrices for reducing this error from the estimated residuals and anomalies. Our simulation studies over Fennoscandia show that the differences between the 0.5°×0.5°$0.5°\times 0.5°$ gravity anomalies obtained from orbital data and an existing gravity model have standard deviation (STD) and root mean squared error (RMSE) of 10.9 and 12.1 mGal, respectively, and those obtained from gradiometric data have 7.9 and 10.1 in the same units. In the case that they are combined using windowed variance components the STD and RMSE become 6.1 and 8.4 mGal. Also, the mean value of the estimated RMSE after using the windowed variances is in agreement with the RMSE of the differences between the estimated anomalies and those obtained from the gravity model.     

Limit cycle oscillation control of wing with static output feedback control method

This paper presents a static output feedback controller (SOFC) for aeroelastic control of a cantilevered rectangular wing in low subsonic flow. For this purpose, an optimal formulation of this control method is developed, and a solution method is proposed for the related matrix equation. This optimal solution is obtained by solving combined Lyapunov and Riccati equations. At first these equations are transformed into a set of nonlinear algebraic equations and then are solved with iterative Newton–Raphson?s method. This solution method is applicable to the full state feedback case. The controller is designed to extend flutter boundary and suppress limit cycle oscillation (LCO) of a low aspect ratio rectangular nonlinear structural wing. This structural nonlinearity is given by Von Karman plate theory. Both full and reduced order aerodynamic models are examined based on the modified vortex lattice theory. Results show combination of SOFC with reduced order aerodynamic model would be an effective choice for aeroelastic stabilization, and this controller has a very comparable result with linear quadratic regulator (LQR).