{"title":"非受控扰动中部分变量控制问题的反馈线性化方法","authors":"V. Vorotnikov, A. Vokhmyanina","doi":"10.15622/SP.61.3","DOIUrl":null,"url":null,"abstract":"The paper studies a problem of guaranteed transfer within a finite amount of time of a nonlinear dynamical system subjected to uncontrolled disturbances to a state where a given part of the variables equals zero. The bounded controls are offered to be generated by means of a feedback in form of nonlinear functions of phase variables of a given nonlinear controlled system of differential equations. The method of exact feedback linearization of the nonlinear system is used. As a result, the solution of the original nonlinear problem is narrowed down to solve the linear game-theoretic antagonistic control problem. Sufficient conditions are obtained with ensure that the problem has a guaranteed solution for the given domain of initial conditions. \nAs an example, problem of the space turn of an asymmetric rigid bode (spacecraft) is considered within the framework of the method. Three reaction wheels are employed to produce necessary torque in the axes of the spacecraft. External uncontrolled disturbances, that have no statistical description, are taken into consideration in the process of reorientation. In this case the initial nonlinear controlled systems consists of dynamic Euler equations and Rodriges – Hamilton kinematic equations based on the quaternion parameterization of attitude kinematics. Two problems of the space turn of the spacecraft are considered. 1) The rest - to - rest reorientation problem. 2) The space turn from a stationary state to a given angular position; it is not assumed that the turn takes the spacecraft to a stationary state. The proposed approach allows common positions to give some already well-known solutions of these problems. A new solution of the reorientation problem is also given. For this new solution an estimation of the admissible domain of uncontrolled disturbances is found. Results of a numerical calculations are considered.","PeriodicalId":53447,"journal":{"name":"SPIIRAS Proceedings","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Feedback Liniarization Method for Problem of Control of a Part of Variables in Uncontrolled Disturbances\",\"authors\":\"V. Vorotnikov, A. 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引用次数: 9
摘要
研究了非线性动力系统在有限时间内受不可控扰动的保证转移到给定部分变量为零的状态的问题。给出了用给定的非线性微分方程控制系统相变量非线性函数的反馈形式产生有界控制的方法。对非线性系统采用精确反馈线性化方法。将原非线性问题的求解范围缩小为求解线性博弈论对抗控制问题。得到了在给定初始条件域上保证问题有保证解的充分条件。以非对称刚体(航天器)的空间转向问题为例进行了分析。三个反作用轮被用来在航天器的轴上产生必要的扭矩。在重定向过程中考虑了没有统计描述的外部不受控制的干扰。在这种情况下,初始非线性控制系统由基于姿态运动学四元数参数化的动态欧拉方程和罗德里格斯-汉密尔顿运动学方程组成。考虑了航天器空间转向的两个问题。1) rest - to - rest重新定位问题。2)空间从静止状态转到给定角度位置;不假设转弯会使航天器进入静止状态。建议的方法允许共同立场给出这些问题的一些众所周知的解决方案。给出了一种新的重定向问题的解法。对于这个新解,给出了不受控制扰动容许域的估计。考虑了数值计算的结果。
Feedback Liniarization Method for Problem of Control of a Part of Variables in Uncontrolled Disturbances
The paper studies a problem of guaranteed transfer within a finite amount of time of a nonlinear dynamical system subjected to uncontrolled disturbances to a state where a given part of the variables equals zero. The bounded controls are offered to be generated by means of a feedback in form of nonlinear functions of phase variables of a given nonlinear controlled system of differential equations. The method of exact feedback linearization of the nonlinear system is used. As a result, the solution of the original nonlinear problem is narrowed down to solve the linear game-theoretic antagonistic control problem. Sufficient conditions are obtained with ensure that the problem has a guaranteed solution for the given domain of initial conditions.
As an example, problem of the space turn of an asymmetric rigid bode (spacecraft) is considered within the framework of the method. Three reaction wheels are employed to produce necessary torque in the axes of the spacecraft. External uncontrolled disturbances, that have no statistical description, are taken into consideration in the process of reorientation. In this case the initial nonlinear controlled systems consists of dynamic Euler equations and Rodriges – Hamilton kinematic equations based on the quaternion parameterization of attitude kinematics. Two problems of the space turn of the spacecraft are considered. 1) The rest - to - rest reorientation problem. 2) The space turn from a stationary state to a given angular position; it is not assumed that the turn takes the spacecraft to a stationary state. The proposed approach allows common positions to give some already well-known solutions of these problems. A new solution of the reorientation problem is also given. For this new solution an estimation of the admissible domain of uncontrolled disturbances is found. Results of a numerical calculations are considered.
期刊介绍:
The SPIIRAS Proceedings journal publishes scientific, scientific-educational, scientific-popular papers relating to computer science, automation, applied mathematics, interdisciplinary research, as well as information technology, the theoretical foundations of computer science (such as mathematical and related to other scientific disciplines), information security and information protection, decision making and artificial intelligence, mathematical modeling, informatization.