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Non-linear Control Law Design For Satellite Fixed Ground Target tracking
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Most modern-day spacecraft missions have specific pointing requirements, otherwise known as pointing modes. Hence, it is not possible to verify the performance of control algorithms and strategies in real process, the simulation environments can be used. In this paper a MATLAB /Simulink software simulation of spacecraft in large angle and fast maneuver with two different quaternion-based nonlinear controllers. These controllers are using a desired target rate directly without transformation into body frame in their structure of control laws. The simulation is performed for attitude model verification and control pointing performance comparison purposes. Quaternion model-based control design process is used for both regulation and tracking cases. In regulation control the spacecraft is required to maneuver to a desired fixed attitude and driving the angular velocity to zero, while the tracking task is to control the spacecraft to follow a desired time-varying trajectory or in other words desired propagated attitude with desired angular velocity. Three different control tasks cover all possible regulation and tracking cases are simulated to precisely define the capability of using such nonlinear control laws in achieving the required control pointing performance. The first control task represents pointing mode at which only desired fixed reference attitude with zero rate is required such as inertial pointing. The second control task represents the mode at which desired reference attitude with constant rate is required such as Earth pointing. The last control task represents the mode at which desired reference attitude with non-constant rate is required such as elliptical orbital object pointing. The simulation results clarify the applicability of using such control laws especially for the first two control tasks when precise control performance is searched. Nomenclature J = inertia matrix ω = body angular velocity vector c ω = commanded angular velocity vector u = control torque q = current attitude quaternion c q = commanded attitude quaternion q δ = quaternion error D, K = derivative and proportioanal gain matrices n ω = desired average natural frequency ξ = desired damping ratio
This book explores topics that are central to the field of spacecraft attitude determination and control. The authors provide rigorous theoretical derivations of significant algorithms accompanied by a generous amount of qualitative discussions of the subject matter. The book documents the development of the important concepts and methods in a manner accessible to practicing engineers, graduate-level engineering students and applied mathematicians. It includes detailed examples from actual mission designs to help ease the transition from theory to practice and also provides prototype algorithms that are readily available on the author’s website.
Subject matter includes both theoretical derivations and practical implementation of spacecraft attitude determination and control systems. It provides detailed derivations for attitude kinematics and dynamics and provides detailed description of the most widely used attitude parameterization, the quaternion. This title also provides a thorough treatise of attitude dynamics including Jacobian elliptical functions. It is the first known book to provide detailed derivations and explanations of state attitude determination and gives readers real-world examples from actual working spacecraft missions. The subject matter is chosen to fill the void of existing textbooks and treatises, especially in state and dynamics attitude determination. MATLAB code of all examples will be provided through an external website.
Various control design techniques are model dependent. They typically require knowledge of the inertia matrix. There are major challenges for each proposed controller to cope with spacecraft mission objective in terms of pointing and jitter requirements. These challenges include sensitivity to noise effects and/or modeling errors, while others are sensitive to external torque disturbances, such as torques induced by solar radiation pressure. Robust controllers have been developed to mitigate these sensitivities. In this paper, a robust nonlinear tracking control algorithm introduced previously in the open literature is modified and tolerated to be utilized with exchange momentum actuators, e.g. reaction wheels. The control law is using the commanded attitude rate, commanded attitude acceleration, attitude error quaternion and gyroscopic terms. Tracking error dynamics equivalent to satellite closed-loop time-varying nonlinear dynamic system is used alternatively to confirm that a globally stable tracking controller always exists. The proposed controller is applied to meet requirements of a tracking complex mode. Generation of the needed target attitude and attitude rate are derived in details. The motion and kinematics of the ground target relative to the in-orbit satellite is analyzed and described in orbit-referenced coordinates. The satellite dynamics are derived from first principles and reformulated also in orbit referenced coordinates.. A tracking scheme for the pointing axis along the body z-axis of satellite is highlighted. Considering attitude and orbit control system (AOCS) with ideal attitude and orbit determination sensors with symmetric satellite inertia, the validity of proposed controller and target data generator is demonstrated under MATLAB/SIMULINK environment. MATLAB optimization tool is used for optimal gains selection. Robustness of the globally stable modified control law to spacecraft inertia matrix uncertainty is also discussed. Simulation results show that the proposed control law can be used successfully onboard for fast tracking and is robust enough to keep the pointing accuracy within acceptable limits with considerable inertia uncertainty.
Many on-board payloads for monitoring, communication and Earth imaging have extensive requirements for target tracking maneuvers in many space missions. A quaternion-bas ed PID feedback control for ground-target tracking of a three-axis stabilized Earth-pointing satellite is systematically analyzed. Based upon the orbital measurement of the satellite position and velocity by an accurate GPS receiver, we present a general method to compute the quaternion error and its integral error with respect to the commanded ground target for any selected pointing axis of the satellite. In addition, an optimal way to derive the desired angular velocity reference for tracking is discussed in detail. Three-axis reaction wheels are employed to demonstrate the feasibility of this control algorithm on a imaginary low-Eartheccentric-orbit satellite. A special tracking scheme for the pointing axis along the body z-axis of the satellite was also investigated. This scenario can be readily applied in real-time for practical target tracking with high accuracy.
A new non-linear tracking control algorithm based on an attitude error quaternion is studied in this paper. The control law developed here uses the commanded attitude rate without transformation into the body frame. The direct use of the commanded attitude rate simplifies the calculation of its derivative, which is used in the control law. The solutions and the equilibrium points of the closed-loop system, which is a time-varying non-linear system, are obtained in different scenarios. In order to analyse the stability of the system and the tracking performance, two different forms of perturbation dynamics with seven state variables are introduced. Local stability and performance analysis shows that the eigenvalues of the linearized perturbation dynamics are determined only by the gain matrices in the control algorithm and the inertia matrix. The existence of globally stable tracking control is proved using a Lyapunov function. Simulation results show that the spacecraft can track the commanded attitude and rate quickly for a non-zero acceleration rate command.
This paper deals with spacecraft attitude control using sliding
mode techniques. Two distinctions of the proposed method from most
reported methods are: 1) the measure of attitude error used is
intrinsically defined, Euclidean-geometric, and intuitive; and 2) a
novel, dynamically nonlinear sliding function is used that results in a
simple control law. As an example we consider the ground station
tracking of UASat
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