【作者】 丁吉；

【导师】 程光明；

【作者基本信息】 吉林大学 ， 机械电子工程， 2007， 硕士

【摘要】 振动的主动控制技术是当今振动工程领域内倍受重视的一项高新技术。本文所研究的基于悬臂梁振动的主动控制技术,主要采用有限元方法建立系统的动力学模型,通过二次型最优控制理论建立控制规律,使用压电驱动器作为控制执行器,对悬臂梁的一阶振动进行了抑制。主要包括以下内容:1.介绍了弹性力学中,有限单元法的分析过程,并分析了应用有限元法对梁进行单元划分时应遵循的原则。介绍了梁单元动力学有限元方程的建立方法,推导了梁单元质量矩阵、刚度矩阵表达式,同时给出了阻尼矩阵的确定方法。2.介绍了最优控制理论中线性二次型问题目标泛函的描述形式,分析了性能指标中各指标所代表的工程意义,并介绍了二次型问题中的无限时间状态调节器,给出了其目标泛函的表达形式及最优控制的求解方法。3.基于能量准则确定了压电驱动器的粘贴位置,应用模态可控度原理检验了传感器位置对系统可控度的影响,确定了传感器的检测位置。建立了含压电覆层的悬臂梁质量、刚度矩阵。采用P.Mario动态凝聚法,建立了由两个主自由度表示的悬臂梁动力学有限元模型。采用二次型最优控制性能指标,对悬臂梁的控制规律进行了设计。4.基于LabVIEW软件平台,设计了控制系统的主程序和前面板。应用所设计的控制系统,对初始扰动和持续外激励作用下,悬臂梁一阶振动的抑制进行了初步的实验研究,比较了振动主动控制实施前后系统衰减到平衡位置的时间和一阶阻尼比的大小。在此基础上,又通过实验研究了控制规律中Q、R选取的不同对结构一阶阻尼比的影响。更多还原

【Abstract】 Recently, the technique of the active vibration control is a kind of new technique in the area of vibration engineering. In the area of aviation and spaceflight, for the reason of specific requirement to the structure weight, the techinique of the active vibration control, which use the light piezoelectric material, has the development superiority. The technique of the active vibration control of cantilever beam set up dynamic equation with finite element analysis, finds the way of control with the theory of quadratic optimization control and controls the first stage of vibration of cantilever beam by means of inputting the energy into the system with piezoelectric actuator. This paper discusses the following:1. This paper introduces the analysis process of beam with finite element analysis, including the structure dispersal, unit analysis and whole structure analysis. It introduces the rule of unit partition with finite element analysis and the foundation of finite element equation of beam unit, deduces the expression of quality matrix and rigidity matrix of beam unit, introduces the identifying method of damp matrix.2. This paper introduces the character of linearity quadratic optimization control and the describing way of aim function and the engineering meaning of each index in the capability index. On the base of it, it introduces infinite time condition adjuster of quadratic optimization control and gives expressions of aim function.3. Basing on the energy rule, we identify the paste position of piezoelectric actuator, basing on the theory of mode control degree, we examine the effect of the position of sensory to the control the system and identify the position of the sensory is at the end of the beam. After we have analysized beam unit with the finite element analysis, we set up quality matrix and rigidity matrix of beampasting with piezoelectric material. By using the technique of P.mario’s dynamic contract, we set up the dynamic model of cantilever beam using two main freedoms. We design the control rule of cantilever beam with quadratic optimization control and deduce the expression of it.4. Through the experiments, we identify the relationship between the voltage of piezoelectric actuator and equivalent force beared at the end of cantilever beam. Using the software of LABVIEW, we design the main process and front panel of the control system. By using the control system we design, it constrains freedom vibration disturbed at the beginning of cantilever beam. We draw the response curves under the condition of control and uncontrol, compare the ratio of damp and the attenuation time under the condition of control and uncontrol. Ratio of damp increase to 8.4 multiple and the attenuation time is 2.6 seconds under the condition of control. It constrains the force vibration of the cantilever beam and the magnitude of vibration decrease to that of 48.2%. This proves that the control is efficient to the vibration. Finally, we research the effect to the control efficiency under the condition of different choice of Q and R, draw a three-dimensional curve of the relationship of Q, R and ratio of damp.更多还原