Estimator for Spacecraft Mass Property and Momentum Actuator Alignment under Influence of External Torque

Abstract

This paper presents an estimation scheme of mass property and momentum actuator alignment of the rigid-body spacecraft with considering external torque. In many previous researches, it is assumed that external torque acts on a spacecraft is negligible. This assumption makes it feasible to build an estimator based on constant angular momentum vector of rigid-body spacecraft in inertial frame. However, the influence of external torque increases dramatically in low orbit Earth observation mission because of gravity-gradient torque. This paper develops a novel estimator that formulates gravity-gradient torque to get exact system dynamics equation. The performance of an estimator is verified by high-fidelity simulator. Nomenclature= Direction cosine matrix from inertial frame (N) to body frame at time (k) = Transpose of matrix A 1 = m-by-m identity matrix = Inertial parameters = [ ] [ ] = Body-fixed inertial matrix ω = Body rate of spacecraft in body frame , = Inertial of th reaction-wheel n = Number of reaction-wheels = Rotational rate of th reaction-wheel = Alignment vector of th reaction-wheel in body frame , , , = Extended Kalman filter system dynamics relevant components (system dynamics, state, control input, and process noise respectively) , ℋ, = Extended Kalman filter measurement equation relevant components (system measurement: means measurement for variable x, measurement equation, and measurement noise respectively) h = Total angular momentum of spacecraft in inertial frame T = Rotational kinetic energy P = Actuator misalignment parameters = [ 11 12 21 22 ⋯ 2] ∆ = Error value of variable x ̂ = Best knowledge of variable x = Position vector from spacecraft to center of the Earth in body frame = Standard deviation of random variable , ℎ = Additional linearization errors of rotational kinetic energy and angular momentum respectively = Gravity constant (3.986012 × 10 6 3 2 ⁄ ) = Gravity-gradient torque at time time

Nonlinear Feed Forward Control of a Perturbed Satellite using Extended Least Squares Adaptation and a Luenberger Observer

“…The feedforward controller converts the desired trajectories to the corresponding torque inputs for the system actuators. This is achieved by using the non-linear dynamics of the system as described as T= [Φ] {Θ} [6,7] in Eqs. (3) to (5) showcasing the coupling of cross terms and is the matrix representation of the system dynamics which propagates the commanded trajectory as a torque command in the corresponding moment in time.…”

“…Equation (3) represents the original feed-forward control equation presented by Slotine [8], Fossen [9], Sands [10], Byeon [6], and Lavretski [11] for control in an idealized system. In this instance the "adaptation" is gained by using an internal feedback loop using a PD control scheme from error between the commanded d ω  and ω d .…”

“…RLS error adaptation is based on the traditional optimal estimator bounded by the brackets within Eq. (6). The expected increased performance in adaptation is due to the fact that the error between commanded and measured angular acceleration and velocity values are propagated forward using the predicted dynamics of the plant to estimate the error in the next time step.…”

“…Another method for adaptation in the feed forward controller extends the implementation of RLS from the original RLS implementation in Eqs. (6) and (7) by adding α, β and ε to the original Φ matrix. This creates the feed forward model as seen in Figure 4.…”

Analytical State Deviation Prediction Model for Improving the GuidancePrecision of Missile

“…The feedforward controller converts the desired trajectories to the corresponding torque inputs for the system actuators. This is achieved by using the non-linear dynamics of the system as described as T= [Φ] {Θ} [6,7] in Eqs. 3to 5showcasing the coupling of cross terms and is the matrix representation of the system dynamics which propagates the commanded trajectory as a torque command in the corresponding moment in time.…”