基于位置—加速度反馈的广义二阶系统特征结构配置问题研究

发布时间：2018-10-29 17:12

【摘要】：广义系统与正常系统相比,在形式上更具一般性,应用范围更广,对广义系统的研究也取得了一些成果,航空航天控制,振动控制,机器人的控制等问题又都可以用二阶动力学系统的控制和设计问题来刻画。因此,本文选择广义二阶动力学系统作为研究对象。随着实际工程对高精度的需求,对于传统特征结构配置的创新正成为研究热点。在设计广义二阶动力学系统控制器时,可以通过对鲁棒性能指标的优化,使闭环系统具有期望的特性。本文利用特征结构配置的参数化方法对广义二阶系统进行了反馈控制,在质量-弹簧-阻尼系统当中得到验证,并改善系统的响应特性。本文主要探讨的问题分为以下两点:1)根据广义系统的特性,提前设定控制律的形式,即位置-加速度反馈,利用反馈消除脉冲的影响。结合右互质分解,推导反馈控制器的参数化形式。2)为了使系统受到扰动能尽量保持原有特性,提出相应的鲁棒性能指标,提高闭环系统的鲁棒性。针对上述问题,完成的创新工作有以下三点:一、基于位置-加速度反馈解决广义二阶动力学系统的特征结构配置问题。位置-加速度反馈控制律作用于广义系统时,可以改变系统的动态阶,消除广义系统脉冲响应的影响。而且对于一些类型的系统,特别是大的柔性结构,使用加速度计测量系统的动态响应比位置和速度传感器更加准确。二、允许闭环系统特征值未知,并基于右互质分解和矩阵初等变换,利用提出的特征结构参数化方法,推导广义二阶动力学系统的特征向量矩阵和反馈增益控制器的参数化表达式,该参数化的表达式为系统提供的自由度可以用于该系统的鲁棒性设计。该算法具有简单有效,计算量小,求解精度高的优点,能够比较有效地用于广义二阶动力学系统控制器的设计。三、提出一个新的测量广义二阶系统灵敏度的性能指标,提高系统的鲁棒性。使闭环系统的特征值在指定区域内的同时,也希望特征值对于参数的扰动不敏感。与以往不同的是,该性能指标对位置和加速度反馈增益矩阵也进行了优化设计,防止系统被代入大幅值的控制输入。
[Abstract]:Compared with normal systems, singular systems are more general in form and wider in scope of application. Some achievements have been made in the study of singular systems, such as aerospace control, vibration control, The control problem of robot can be described by the control and design of the second order dynamic system. Therefore, the generalized second order dynamical system is chosen as the research object in this paper. With the demand of high precision in practical engineering, the innovation of traditional feature structure configuration is becoming a research hotspot. In the design of the controller of generalized second-order dynamical system, the closed-loop system can have the desired characteristics by optimizing the robust performance index. In this paper, the feedback control of generalized second-order system is carried out by the parameterized method of eigenstructure collocation, which is verified in mass-spring-damping system, and the response characteristic of the system is improved. The main problems discussed in this paper are as follows: 1) according to the characteristics of the singular system, the form of the control law is set in advance, that is, the position-acceleration feedback, and the feedback is used to eliminate the influence of the pulse. The parameterized form of the feedback controller is derived by combining the right co-prime decomposition. 2) in order to keep the original characteristics of the system disturbed as much as possible, the corresponding robust performance index is proposed to improve the robustness of the closed-loop system. In order to solve the above problems, the innovative work is as follows: first, based on position-acceleration feedback, the eigenstructure configuration problem of generalized second-order dynamical systems is solved. When the position-acceleration feedback control law is applied to the singular system, the dynamic order of the system can be changed and the impulse response of the singular system can be eliminated. For some types of systems, especially for large flexible structures, the dynamic response of the system measured by accelerometers is more accurate than that of position and velocity sensors. Secondly, the eigenvalues of the closed-loop system are allowed to be unknown, and the parameterization method of the eigenstructure is proposed based on the right co-prime decomposition and the elementary transformation of the matrix. The parametric expressions of eigenvector matrix and feedback gain controller for generalized second-order dynamical systems are derived. The degree of freedom provided by the parameterized expressions can be used in the robust design of the system. The algorithm has the advantages of simple and effective, low computational complexity and high accuracy. It can be used in the design of the controller of generalized second-order dynamical system more effectively. Thirdly, a new performance index for measuring the sensitivity of singular second order system is proposed to improve the robustness of the system. The eigenvalue of the closed-loop system is not sensitive to the parameter perturbation while the eigenvalue is in the specified region. Different from the past, the performance index also optimizes the position and acceleration feedback gain matrix to prevent the system from being substituted into the control input of the large value.
【学位授予单位】：东北电力大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13

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