Equations of motion for the triaxial attitude control testbed

2003 ◽  
Author(s):  
Sangbum Cho ◽  
Jinglai Shen ◽  
N.H. McClamroch ◽  
D.S. Bernstein
Keyword(s):  
Attitude Control ◽  
Equations Of Motion

Optimal Stabling of Attitude Maneuver for a Special Satellite With Reaction Wheel Actuators

2010 ◽  
Author(s):  
Seyed Hasan Miri Roknabadi ◽  
Mohamad Fakhari Mehrjardi ◽  
Mehran Mirshams
Keyword(s):  
Attitude Control ◽  
Equations Of Motion ◽  
Low Energy ◽  
Dynamic Equations ◽  
Satellite Motion ◽  
Reaction Wheel ◽  
State Equations ◽  
Time Consumption ◽  
Attitude Maneuver ◽  
Simulation Results

This paper presents an optimal attitude maneuver by Reaction Wheels to achieve desired attitude for a Satellite. At first, Dynamic Equations of motion for a satellite with just three Reaction Wheels of its active actuators are educed, and then State Equations of this system are obtained. An optimal attitude control with the LQR method has exerted for a distinct satellite by its Reaction Wheels. As a result simulation has presented an optimal effort by calculated Gain matrix to achieve desired attitude for chosen Satellite. It shows that satellite becomes stable in desired attitude with a low energy and time consumption. Furthermore equations derivation, coupling of electrical Reaction Wheel equations with dynamic equations of satellite motion, linearizes them and Reaction wheel saturation avoidance approaches are innovative. Simulation results, accuracy of achieving desired attitude and satellite stability support this statement.

Analysis and Attitude Control of Spacecraft with Input Uncertainty

2011 ◽  
Vol 268-270 ◽  
pp. 2041-2047
Author(s):  
Sheng Qi Chen ◽  
Jun Zhou
Keyword(s):  
Control System ◽  
Nonlinear Equations ◽  
Attitude Control ◽  
Equations Of Motion ◽  
Variable Structure ◽  
Integral Form ◽  
Control Mode ◽  
Attitude Control System ◽  
Non Linear ◽  
Command Signals

A moving mass control of rotating spacecraft is a kind of new control mode, it differs from other control modes because it generates an angle of attack and an angle of sideslip directly from the mass motion.The nonlinear equations of motion for rotating Maneuverable Spacecraft are derived. the variable structure attitude controller is presented according to the nonlinear equations, It’s based on two-timescale separation and with two loops, faster loop and slower loop respectively. Inertial uncertainties and aerodynamic moment uncertainties are considered simultaneously, In order to track the command signals perfectly, the sliding surface is of integral form, results of the simulation shows that this kind of attitude control system is potentially practical and robust in the presence of inertial uncertainties of guided missile and uncertainties of aerodynamic moments. Compared with the common attitude control system, it has the following advantages:(1) non linear model is directly controlled,(2)it has robust. Because the non-linear factor is considered, it has the practical use for the engineering field.

Shared Fuzzy Control of Multiple Quadrotor UAVs With Time-Dependent Delay and Bounded Control-Input Constraint

2015 ◽  
Author(s):  
Mark D. Johnson ◽  
Mohammad A. Ayoubi
Keyword(s):  
Fuzzy Control ◽  
Attitude Control ◽  
Fuzzy Controller ◽  
Equations Of Motion ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Control Input ◽  
Maximum Magnitude ◽  
Time Varying ◽  
Bounded Control

We propose a shared fuzzy controller for position and attitude control of multiple quadrotor unmanned aerial vehicles (UAVs). Using the nonlinear governing equations of motion and kinematics of a quadrotor, we develop a Takagi-Sugeno (T-S) fuzzy model for a quadrotor. Then, we consider time-varying delays due to wireless connectioninto the T-S fuzzy model. We use the sufficient stability condition based on the Lyapunov-Krasovskii stability theorem and the parallel distributed compensation (PDC) technique to determine the fuzzy control law. For practical purposes, we include actuator amplitude constraint into the design process. The problem of designing a shared fuzzy controller is cast in the form of linear matrix inequalities (LMIs). A feasible solution region is found in terms of maximum magnitude and rate of time-varying delay. In the end, the stability, performance, and robustness of the proposed shared fuzzy controller are examined via numerical simulation.

Controllability of a square solar sail with movable membrane tips

2017 ◽  
Vol 231 (6) ◽  
pp. 1065-1075 ◽  
Author(s):  
Bo Fu ◽  
Gilbert Gede ◽  
Fidelis O Eke
Keyword(s):  
Attitude Control ◽  
Equations Of Motion ◽  
Numerical Approach ◽  
Solar Sail ◽  
Linearization Method ◽  
Displacement Method ◽  
Nonlinear Equations Of Motion ◽  
High Degree ◽  
Wing Tip ◽  
Tip Displacement

This paper presents a controllability study for a square solar sail that uses the wing tip displacement method for its attitude control. The goal is to determine whether this method of attitude control guarantees full control authority over normal attitude maneuvers that would be expected during a typical solar sail mission. The controllability of a given state is determined by first linearizing the full nonlinear equations of motion of the craft about the chosen state, and then applying the classical controllability test to the resulting linear model. This process is then repeated enough times to adequately span the allowable states of the vehicle. Because of the nature of the expressions for the control torques, direct analytical linearizations are not practical; and a full numerical approach is inefficient because of the sheer volume of computations involved. A hybrid linearization method that judiciously combines analytical and numerical approaches was therefore adopted. Results obtained show that the sailcraft is controllable throughout the tested region. A study of the influence of various actuator failure scenarios on controllability revealed that the wing tip displacement method of attitude control exhibits a very high degree of redundancy. The system’s controllability only becomes seriously impaired if more than half of its actuators fail.

scholarly journals Nonlinear Attitude Control Of Underactuated Spacecraft

2021 ◽  
Author(s):  
Alexander Frias
Keyword(s):  
Optimal Control ◽  
Angular Velocity ◽  
Attitude Control ◽  
Inertial Frame ◽  
Equations Of Motion ◽  
The Body ◽  
Time Varying ◽  
Ultimate Boundedness ◽  
Error Norm ◽  
Attitude Error

This dissertation investigates the nonlinear control of the attitude for an underactuated rigid-body spacecraft system in the body-orbital and inertial frames. The problem involving the stabilization of the body-orbital attitude of an underactuated output-feedback system is examined. Using sliding mode control in conjunction with finite-time nonlinear observer, a novel observer-based control law is rigorously analyzed and proven to achieve attitude convergence. Under time-varying disturbances, inertia matrix uncertainties, and high initial errors, the proposed novel law achieves attitude convergence for three-axis stability and ultimate boundedness within 5 degrees and 0.01 deg/s, for attitude error norm and angular velocity norm, respectively. Next, the attitude control problem is rigorously analyzed in the inertial frame, where the underactuated rigid-body spacecraft system equations of motion are highly nonlinear, and the linearized equations of motion are not controllable. To this end, a generalized velocity-free time-varying state feedback controller is developed to achieve globally exponential stability with respect to the homogenous norm and proven to provide ultimate boundedness of all signals with 5 degrees attitude error norm and 0.5 rad/s angular velocity error norm. Finally, the inertial frame attitude stabilization problem is treated as an optimal control problem. For this case, the Legendre pseudospectral method is used to discretized the spacecraft dynamics into Legendre-Gauss-Lobatto (LGL) node points, where the Lagrange polynomial interpolation is applied to obtain a suitable candidate optimal control sequence. Model predictive control is used to implement the optimal control in predefined control windows sequentially to achieve three-axis stability for a rest-to-rest maneuver within 0.3 orbit.

Investigation of Optimal Control With a Minimum-Fuel Consumption Criterion for a Fourth-Order Plant With Two Control Inputs; Synthesis of an Efficient Suboptimal Control

1965 ◽  
Vol 87 (1) ◽  
pp. 39-57 ◽  
Author(s):  
A. J. Craig ◽  
I. Flu¨gge-Lotz
Keyword(s):  
Feedback Control ◽  
Fuel Consumption ◽  
Fourth Order ◽  
Attitude Control ◽  
Equations Of Motion ◽  
Suboptimal Control ◽  
Optimal Solutions ◽  
State Variables ◽  
Time Control ◽  
Heuristic Analysis

Application of Pontryagin’s optimal principle to control system problems eventually requires that a two-point boundary-value problem be solved. For plants whose equations of motion are greater than second order this represents a formidable barrier in realizing a practical feedback control. When the criterion for optimization is minimum-fuel consumption, choice of time for solution may be used as a free parameter, and this plus consideration of the efficiency of application of control leads to an approximate method which avoids this difficulty. A heuristic analysis of the geometry of state-space trajectories, using true optimal solutions as a guide, provides laws for constructing a feedback control from the state variables. It further provides a knowledge of the bounds of performance of the mechanized suboptimal control and an estimate on the performance of a minimum-time control for comparison purposes. As an example, the method is applied to the problem of minimum-fuel attitude control of an earth-orbiting satellite, a fourth-order plant with two controls.

INVESTIGATION OF IN-ORBIT DISTURBING LOADS INDUCED ON SPACECRAFT DUE TO ELASTIC DEPLOYING ARM

2013 ◽  
Vol 13 (04) ◽  
pp. 1250081 ◽  
Author(s):  
P. BAGHERI GHALEH ◽  
S. M. MALAEK
Keyword(s):  
Control System ◽  
Attitude Control ◽  
Orbital Motion ◽  
Equations Of Motion ◽  
Orbital Plane ◽  
True Anomaly ◽  
Attitude Control System ◽  
Coupled Equations ◽  
Flexible Appendage ◽  
Lateral Displacements

The loads induced on the spacecraft orbiting the Earth by the deploying elastic arm are investigated. The coupled equations of motion of the arm with the vehicle orbital mechanics are used to describe the 3D dynamic behavior of the flexible-appendage and the related disturbing loads induced on the spacecraft. To this end, an equivalent dynamical system is derived for the arm by applying an attached Non-Newtonian Reference Frame which is subjected to the orbital motion and geocentric pointing maneuver of the spacecraft. With the help of the Assumed Modes Method, the behavior of the arm attached to the spacecraft in Keplerian orbits is studied. The results show that deploying the arm in some specific directions relative to the orbital plane leads to serious coupling between two lateral displacements. In addition, the effects of specific orbital parameters on arm responses and resulting induced loads are studied for the cases of "True Anomaly of spacecraft at deployment time, and Eccentricity of elliptical orbits". The prediction of disturbing loads induced on spacecraft helps design the robust attitude control system. Further, the positioning accuracy of the payloads (installed on the arm-tip) can be estimated by employing the obtained arm responses in the orbital motion, which enables us to determine the undesirable motions and predict any required control system for the arm.

scholarly journals Extended Kalman Filter Based Estimations for Satellite Attitude Control System

2021 ◽  
Vol 10 (5) ◽  
pp. 57-67
Author(s):  
D. Y. Dube ◽  
S. N. Sharma ◽  
H. G. Patel
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Attitude Control ◽  
Satellite Communication ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
Atmospheric Conditions ◽  
Attitude Control System ◽  
Stochastic Disturbance ◽  
Satellite Attitude

This paper mainly focuses on the maneuver of the satellite in orbit. A non-linear multi-inputs multi-outputs model has been derived from Newton-Euler equations of motion. The dynamics is presented with control methodologies allowing the Extended Kalman Filter (EKF) to iteratively provide improved data sets with zero errors. As the system is distracted from the atmospheric swings which are random hence the problem of stochastic disturbance is furnished. A set of differential equations of two dimensional Ito stochastic type is used for modeling the said disturbances (before t = 4s is recorded). The attitude parameters are recorded in RT-LAB setup with the Extended Kalman Filter (EKF) providing adequately superior estimation outcome which thereby makes the filter more appealing. With the presence of Gaussian noise in both dimension and system, Extended Kalman Filter gives the correct estimates. It’s collaboration with hardware setup RT-LAB is commendable. Hence, an Extended Kalman Filter which deals with such nonlinear models proves to be a higher choice for achieving best online results. A comparison reflecting the tracking and stable control of the satellite for the designed advanced adaptive robust controller (AARC) for two situations is plotted. The priority of making the system stable in the presence of stochastic disturbance is also visited. Also, the use of three different values of the confounding variables revealed that the control weighting line is completely diminished thereby boosting the tracking when the satellite is in orbit. Moreover, the previous research involves methods to improve satellite communication on ground station, this paper deals with exact positioning of concerned satellite attitude parameters and its validation tested experimentally on OPAL-RT hardware. To sum up, the development of advanced adaptive robust controllers have encouraged the stability and accuracy of systems considering the varying atmospheric conditions. The simulation results predict perfect tracking of output with respect to the desired set-point in the presence of stochastic disturbance for the proposed controller.

Cooperative parameter estimation of a nonuniform payload by multiple quadrotors

Robotica ◽  
2021 ◽  
pp. 1-20
Author(s):  
Farhad Arab ◽  
Farzad A. Shirazi ◽  
Mohammad Reza Hairi Yazdi
Keyword(s):  
Attitude Control ◽  
Equations Of Motion ◽  
Estimation Algorithm ◽  
Adaptive Controller ◽  
Dynamic Equations ◽  
Physical Parameters ◽  
Constraint Forces ◽  
Outer Loop ◽  
Simulation Results

Abstract Thispaper addresses the problem of carrying an unknown nonuniform payload by multiple quadrotor agents. The load is modeled as a rigid body with unknown weight and position of Center of Gravity (CG) for the agents, and is included in their dynamic equations of motion. The agents and the load are assumed to be connected to each other by taut ropes. The Udwadia–Kalaba equation is used to calculate the constraint forces on the ropes acting on each quadrotor. Inner-loop and outer-loop controllers for quadrotors position and attitude control are presented. For the outer loop, an estimation algorithm based on the invariance and immersion adaptive control is utilized to estimate the unknown physical parameters of the payload including mass and CG position without using multi-axes force/torque sensors. The inner-loop controller employs an adaptive controller. Simulation results, for two and four agents carrying a nonuniform rod and cubic payload, show the effectiveness of the proposed algorithm. A case study is also performed to investigate the effect of quadrotors positioning on flight endurance of the cooperative aerial team carrying a nonuniform payload.

scholarly journals General Planar Motion Modeling and Control of a Smart Rigid-Flexible Satellite Considering Large Deformations

2021 ◽  
Author(s):  
Hossein Ghorbani ◽  
Ramin Vatankhah ◽  
Mehrdad Farid
Keyword(s):  
Differential Equations ◽  
Attitude Control ◽  
Large Deformations ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Planar Motion ◽  
Transverse Displacement ◽  
Large Rotation ◽  
Modeling And Control ◽  
Flexible Appendages

Abstract In this paper, the motion of a smart rigid-flexible satellite by considering large deformations for its flexible appendages in general planar motion is modeled. Therefore, the satellite can experience translational and rotational motions also its flexible appendages can vibrate arbitrarily in the motion plane. Two control forces perpendicular to each other and one control torque are responsible for controlling the motion of the satellite on the desired trajectories. Also, piezoelectric actuators and sensors suppress vibrations and estimate the transverse displacement of the satellite's flexible appendages, respectively. The coupled ordinary-partial differential equations of motion, equations of the sensors, and boundary conditions of the system are obtained using extended Hamilton's principle. Then, these equations are discretized using the Galerkin method. The discretized equations of motion are a set of coupled nonlinear ordinary differential equations due to the consideration of the large rotation angle of the satellite and large deformations for its flexible appendages. Adaptive super-twisting global nonlinear sliding mode controller is designed to satisfy the control objectives including position and attitude control, as well as suppressing vibrations of the flexible appendages in the presence of uncertainties and external disturbances. Eventually, numerical simulations are presented to illustrate the effectiveness of the proposed controller.

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