外扰力矩作用下附三转子航天器混沌动力学分析

研究外部扰动力矩作用下航天器的混沌姿态运动,引入Deprit正则变量建立系统的Hamilton结构.应用Melnikov方法预测系统产生的稳定流形和不稳定流形的横截相交,得到系统产生混沌姿态运动的条件.研究表明:随着转子转动惯量的增加,引起系统出现混沌姿态运动的激励频率的范围逐渐减小.最后,对相空间轨线的数值模拟表明理论分析的可靠性.     

基于飞轮的偏置动量卫星周期干扰补偿方法

为了提高偏置动量卫星姿态控制精度,针对三轴稳定偏置动量卫星滚动/偏航回路周期干扰力矩补偿问题,提出了一种基于反作用飞轮的滚动/偏航回路周期干扰力矩补偿方案.采用频率分离法,分析了周期干扰力矩对卫星滚动/偏航回路姿态控制精度的影响.设计了周期干扰力矩的飞轮补偿方案,该干扰力矩补偿方案由安装在卫星滚动/偏航轴上的反作用飞轮实现.仿真结果表明,所设计的飞轮补偿方案提高了滚动/偏航轴的控制精度,从而验证了飞轮补偿方案的可行性和有效性.     

偏置动量轮控卫星姿态控制

研究了轮控的三轴稳定的偏置动量卫星姿态控制问题。卫星的俯仰回路采用偏置动量轮，滚动／偏航轴上各安装一个反作用飞轮来完成姿态控制。小姿态角下俯仰回路可以单独设计，利用测量的俯仰角来实现其姿态控制；滚动／偏航回路利用滚动信息，采用基于偏航观测器的滑模控制器设计。磁力矩器提供的磁矩与地磁场作用产生的力矩实现了飞轮的动量卸载。对卫星姿态控制系统进行的仿真研究结果表明，所设计的控制方案在飞轮输出力矩工作范围内，可使卫星达到很高的姿态控制精度。     

Application of Symbolic Computation Methods for Investigation of Stationary Motions of an Axisymmetric Satellite

With the help of computer algebra methods properties of the algebraic system that determines stationary motions of an axisymmetric satellite moving along a circular orbit subject to gravitational and active damping moments are investigated. The main attention is paid to the study of the conditions for the existence of stationary satellite motions. Computer algebra methods based on the algorithm for the construction of Gröbner bases are applied to reduce the satellite stationary motion system of six algebraic equations in six variables to a single algebraic equation in one variable that determines all stationary motions of the satellite. A classification of domains with equal numbers of stationary solutions is carried out using algebraic methods for constructing discriminant hypersurfaces. The effectiveness of various algorithms for constructing Gröbner bases for the solution of the problem under consideration was compared.     

一类磁性刚体航天器的混沌控制研究

采用基于误差线性系统稳定性准则的混沌控制方法,控制具有结构内阻尼的磁性刚体航天器在重力场与磁场共同作用下在圆形轨道的混沌姿态运动.讨论了航天器姿态运动方程中部分参数的取值对于运动姿态的影响,给出了这些参数通过倍周期分岔或逆倍周期分岔通往混沌的途径.当参数使系统做混沌姿态运动时,采用上述方法将混沌运动控制至周期-4轨道,并实现周期-1、2、4轨道之间转换的灵活控制.此外,分析了控制参数的变化对于控制效果的影响,并分别给出了控制至不同轨道时的输入扰动范围及控制参数范围.仿真结果表明,该方法能够实现混沌姿态运动在预定周期轨道间的灵活控制,且输入扰动量小、控制速度快、具有高精度,从而验证了该方法在航天器混沌姿态运动控制方面的有效性.     

带可控臂的绳系卫星短距释放实验研究

通过绳系卫星轨道面内运动的天-地动力学相似,利用地面物理仿真平台实验研究绳系卫星短距离释放的控制问题.首先建立带控制臂的绳系卫星系统非线性动力学方程,获得天-地动力学相似条件,采用比例-微分反馈控制方法,对受控绳系卫星的姿态运动进行数值仿真.其次,利用地面物理仿真平台实现绳系卫星的天-地动力学相似环境,通过单根刚性臂实现卫星姿态运动和系绳摆动的两自由度运动控制.实验和数值对比结果表明,借助控制臂可以有效的对绳系卫星的释放进行控制.     

Satellite attitude stabilization using solar radiation pressure and magnetotorquer

The paper presents three-dimensional (3-D) attitude stabilization of a geosynchronous satellite. The solar radiation pressure is considered for the satellite pitch and roll stabilization while the yaw attitude is stabilized by a magnetotorquer. The general formulation of the system comprised of a satellite body, two solar flaps, and a magnetotorquer is obtained through Euler's equations. The linearized system model is derived and then the control laws are developed for suitable rotations of solar flaps and variations in magnetic moment. The numerical simulation of the governing nonlinear system equations of motion establishes the feasibility of achieving the desired 3-D satellite attitude. The controllers are successful in stabilizing the satellite attitude even in the presence of orbital eccentricity and variations in system parameters.     

On the motion of a mobile robot with roller-carrying wheels

The motion equations of a robot on a horizontal surface on three roller-carrying wheels of omni directional type are derived without account of possible slippage. An exact solution of the equations is found when at the direct-current motors moving the wheels a constant voltage is supplied. The problem of minimizing the torques of electric motors is considered and steady-state motion modes are specified for which the torques of electric motors and energy expenses are minimum. The reckoning system for the robot traveled distance is described.     

欠驱动刚体航天器姿态运动规划的遗传算法

研究欠驱动刚体航天器姿态的非完整运动规划问题．航天器利用3个动量飞轮可以控制其姿态和任意定位,当其中一轮失效,航天器姿态通常表现为不可控．在系统角动量为零的情况下,系统的姿态控制问题可转化为无漂移系统的运动规划问题．基于优化控制理论,提出了求解欠驱动刚体航天器的姿态运动控制遗传算法,并且数值仿真表明：该方法对欠驱动航天器姿态运动的控制是有效的．     

A non-linear parameter identification approach with applications†

This article is concerned with the identification of unknown parameters for a proposed non-linear time-variant, multivnriable model, that is observed in an additive statistically known white Gaussian noisy environment. The estimation problem is investigated by partitioning the system into subsequent sub-systems to yield a computationally more pragmatical solution. An optimal predictor-corrector maximum-likelihood state estimator and a stochastic hill-climbing procedure are delineated for solving the identification problem. Two particular applications are furnished to illustrate the suggested technique. In the first application, the approach presented is carried out to determine the inertia constant and damping coefficient of a synchronous machine in an unsteady operation, The second application is devoted to tho evaluation of the moments of inertia for a rigid body rotating about its principal axes and subject to external random disturbances and control torques. It is highlighted for the two preceding applications that, though the equations of motion are non-linear in the unknown quantities and/or tho state variables, the solutions obtained via partitioning are expressible in a linear form.     

Chaotic satellite attitude control by adaptive approach

In this article, chaos control of satellite attitude motion is considered. Adaptive control based on dynamic compensation is utilised to suppress the chaotic behaviour. Control approaches with three control inputs and with only one control input are proposed. Since the adaptive control employed is based on dynamic compensation, faithful model of the system is of no necessity. Sinusoidal disturbance and parameter uncertainties are considered to evaluate the robustness of the closed-loop system. Both of the approaches are confirmed by theoretical and numerical results.     

Time-optimal reorientation for rigid satellite with reaction wheels

This article introduces a time-optimal reorientation manoeuvre controller with saturation constraints on both reaction wheels’ torques and angular momentum. The proposed control scheme consists of two parts. The first part is an open-loop time-minimum reorientation trajectory generated by the Legendre pseudospectral method. Actuator dynamics, saturations on control torques and angular momentums of reaction wheels are taken into account in generating the open-loop optimal trajectory. The second part is a closed-loop tracking control law to track the optimised reference trajectory based on attitude error dynamics with reaction wheel dynamics. Numerical simulations show that reaction wheel dynamics play an important role in attitude manoeuvres. The proposed controller performs better for rest-to-rest reorientation manoeuvre than other existing methods.     

Application of computer algebra methods for investigation of stationary motions of a gyrostat satellite

With the help of computer algebra methods, properties of a non-linear algebraic system that determines the equilibrium orientations of a gyrostat satellite moving along a circular orbit were investigated. The main attention is paid to the study of equilibrium orientations of the satellite with given principal central moments of inertia and given gyrostatic torque in special cases, when the projection of the vector of gyrostatic torque is located in one of the principal central planes of inertia of the satellite. Computer algebra method based on the algorithm for the construction of a Gröbner basis were applied to reduce the satellite stationary motion system of nine algebraic equations with nine variables to a single algebraic equation in one variable that determines all the equilibrium orientations of the satellite. Bifurcation curves in the space of system parameters that determine boundaries of domains with a fixed number of equilibria of the satellite were obtained symbolically. A comparative analysis of the effectiveness of different algorithms of Gröbner bases computation in solving the problem was carried out.     

Image-Based Attitude Control of a Remote Sensing Satellite

This paper deals with the image-based control of a satellite for remote sensing. Approach is demonstrated by simulation where the position of the satellite is obtained with the Simplified General Perturbations Version 3 model and its orientation by simulating its dynamic and kinematic models. For a known position and orientation of the satellite the images are obtained using the satellite’s onboard camera, simulated by the Google Earth application. The orientation of the satellite is governed by reaction wheels, which produce the required moments to the satellite. The image-based control law using SIFT image features is applied to achieve an automatic reference-point observation on the Earth’s surface. Main contributions of the paper are the following: use of the same sensor for Earth observation and attitude control, simplicity of the approach, no need for explicit calibration of camera parameters and good tracking accuracy. Demonstrated simulation results and performance analysis confirm the approach applicability.     

Satellite dynamics due to gravity and constant torques

We consider the dynamics of the rotational motion of a satellite moving in the central Newtonian force field in a circular orbit due to gravity and constant torques. We propose a method for determining all positions of equilibrium (equilibrium orientations) of a satellite in the orbital coordinate system given the values of the vector of constant torque and the major central moments of inertia; we obtained the conditions for the existence of these positions. We classify the domains with an equal number of equilibrium positions using algebraic methods for the construction of discriminant hypersurfaces. The results obtained in this study can be used to construct gravitational control systems for the orientation of artificial Earth satellites.     

Control of the angular orientation of the platform of a uniaxial wheeled module moving without slippage over an underlying surface

A method for controlling the angular orientation with respect to the horizon plane of the platform of a uniaxial wheeled module moving without slippage over the underlying surface is considered. For a module involving a one-axis gyroscope, a compensating flywheel, and a stabilizing weight, equations of motion are derived, which describe the module as a nonholonomic system due to the absence of slippage of its wheels over the underlying surface. The conditions for the “force of undisturbability” of the platform by the inertial forces upon its arbitrary translational-rotational motion and the conditions for “informational undisturbability” by the inertial forces of the accelometric sensor of the deviation of the platform from the horizon plane are determined. The analytical relationships determining the conditions for the absence of slippage of the wheels are found. By numerical simulation, rational values of the coefficient in the laws governing the moments of forces developed by the control elements of the structure are obtained. The effectiveness of these laws is confirmed by the results of simulating the control processes over the angular motion of the platform of the module along a typical trajectory of its motion over the underlying surface.     

重力梯度卫星大角度姿态机动的变结构控制

针对重力梯度稳定小卫星的大角度姿态机动问题,采用四元数来描述卫星的姿态,通过选择一类滑动流形,设计了变结构控制律,得到了在大角度姿态机动中卫星的姿态角、姿态角速度以及三个反作用飞轮转速的变化规律.理论分析和数值仿真都表明了该控制律具有渐近稳定性和鲁棒性.     

环形天线结构的复杂动力学研究

部分改进高维系统的广义Melnikov方法研究含参非线性动力系统的混沌问题,并应用于研究环形天线结构的混沌运动等复杂非线性动力学行为.通过定义恰当的横截面,发展适用于研究五维含参非线性动力系统的Melnikov方法,获得系统发生Smale马蹄意义下混沌运动区域及判定定理.将所得理论结果应用于研究面内激励与横向激励共同作用下环形天线结构的混沌运动,得到系统发生混沌运动的不稳定区域及相应的参数控制条件.探讨阻尼系数、参数激励对系统动力学行为的影响,并利用数值模拟方法给出其相图构型,验证理论结果的正确性.     

一类弦-梁耦合非线性振动系统的动力学数值模拟研究

本文研究了一类具有参数激励和外激励弦-梁耦合非线性系统.首先,运用多尺度法分析弦-梁耦合非线性系统的响应,求得系统平均方程.其次,基于求得的方程,以系统的阻尼系数作为分叉参数,并对系统平衡点的稳定性进行分析,得到平衡点的分叉曲线.为了验证理论预测的正确性数值模拟了不同分叉参数下的相空间轨线.利用四阶龙格库塔方法验证了弦-梁耦合非线性系统混沌运动的存在性,从数值模拟看出系统存在单倍周期运动、多倍周期运动和混沌运动.     

A minimum-fuel mode for steady-state attitude control of an earth-orbiting spacecraft

Steady-state reaction control of the attitude of a spacecraft in the presence of environmental disturbance torquesTis usually accomplished by using the thrusters to establish limit-cycle motion of acceptable amplitudes about all three axes. For such strategies, the greatest lower bound for the propellant consumption is proportional tointmin{t1}max{t2}|T|dt. The results presented in this paper show that when the disturbances are not unidirectional, the environment, consisting of gravity-gradient and aerodynamic torques, can be used to reduce this lower bound significantly. The linearized equation which describes the dynamics of an inertially referenced satellite has a periodic coefficient matrix and forcing vector. The existence of forced periodic solutions of such equations is established, and an algorithm for determining an initial point on the trajectory of these solutions in state space is provided. This defines a "natural" limit cycle, i.e., both turning points of this motion are produced by the environment. In particular, the periodic rotational motion about two of the spacecraft axes is produced by the aerodynamic torque, an effect which is usually neglected.