摘要
现代机械向高速、精密、轻型和低噪声等方向发展,为了提高机械产品的动态性能、工作品质,必须十分重视机构动力学的研究。特别对于高速运行的机器人,在外力与惯性力作用下,构件的弹性变形不可忽略,它不仅影响了机构的轨迹精度和定位精度,破坏系统运行的稳定性和可靠性,同时降低了工作效率和整机的使用寿命。对有害动态响应的消减是机械动力学研究的重要问题。本文以柔性机器人机构为研究对象,对其动力学建模、优化综合和振动主动控制的理论和方法进行系统地分析和研究,主要内容如下:
提出一种建立一般柔性并联机构的模型的子结构方法。该方法的主要思想是根据并联机构是由若干独立运动支链、静平台和动平台组成的特点,将并联机构的运动支链视为柔性子结构,静平台和动平台作为刚性子结构,分别建立它们的运动方程,然后将子结构的运动方程组合成系统的运动方程。它的特点是引入刚性子结构,推导出相邻刚性子结构和弹性子结构之间的几何和运动约束关系。使用动平台质心的微位移和微转角作为系统广义坐标,减少了系统自由度数,简化了模型并便于计算它们。两个算例的动力学分析结果验证了模型的有效性。
对一种新型高速并联机械手,在弹性动力学层面上以系统的动态性能为目标对其截面参数进行优化设计。采用有限元法建立系统的弹性动力学方程,研究分析了系统第一阶固有频率对截面参数的灵敏度,并据此确定优化设计变量。分别选择基频或重量指标作为目标函数进行优化设计,最后的优化结果都能满足设计要求,能使机构有较小的重量又有较高固有频率。提出的思路和方法可应用于其他机构的优化设计。
以一种新型两自由度柔性并联机械手为对象,利用假设模态法和拉格朗日乘子法,得到系统的动力学方程为微分—代数方程组,为了设计控制器,采用坐标分块法消除拉格朗日乘子,得到关于独立变量的二阶微分方程组。由于它是非线性和时变的,采用变结构控制策略设计控制器,通过选择合适的关节控制规律,使机械手能够跟踪期望轨迹,又能有效抑制弹性构件的振动。仿真分析的结果表明该控制器的可行性和有效性。
以一种新型两自由度柔性并联机械手为对象,在含有压电元件的有限元模型基础上,基于实模态理论和滑模变结构理论,研究其振动主动控制。采用有限元法和模态理论建立系统的动力学模型。根据系统的性能要求,采用最优化方法确定滑移面,基于Lyapunov直接法设计滑模控制器,并且考虑了作动器输入电压的界限。仿真结果表明,该控制器可以有效地抑制柔性构件产生的弹性振动,减小了并联机械手的动平台的位置误差,验证了该控制器的可行性和有效性。
以一柔性5杆机械手为研究对象,应用线性二次型高斯最优控制研究其振动主动控制。采用了一种表征作动能量的可控性指标和表征观测信号能量的可观性指标来确定作动器和传感器的最优位置。在计算线性二次反馈增益矩阵时,分别使用以状态量和输出响应为性能指标。将在模态坐标下的外力、惯性力和量测噪声视为白噪声信号,构造出Kalman状态估计器,连接状态估计器和反馈增益矩阵形成二次型Gauss控制器。仿真分析结果表明设计的两种控制器都能有效地抑制柔性机械手振动响应,通过比较分析,在以输出响应性能为指标的控制器的控制效果更好。
应用模型预测控制理论设计控制器抑制一柔性5杆机械手振动响应。根据系统状态空间方程推导出系统的预测模型,以此得到预测模型的未来输出值。将模态力和量测噪声作为不确定性外部扰动,并视为白噪声,采用Kalman滤波估计器估计出系统状态量。以控制电压及其变化率为约束条件,将系统性能指标和约束条件化为一个标准二次规划优化问题,最后通过求解这一优化问题来得到最优控制输出。仿真分析结果表明了模型预测控制方法对柔性机械手振动响应抑制是有效的,取得了较为满意的控制效果。
以柔性5杆机械手为研究对象,应用H_∞控制理论和μ综合方法设计具有鲁棒性的控制器抑制其振动响应。在设计H_∞控制器时,将模态力和量测噪声为不可确定性外部扰动,分别选择模态位移信号和输出应变信号为评价信号,并根据实际信号的幅值和频率特性选择合适的加权函数,形成一个最小灵敏度问题。考虑系统结构参数的不确定性,如固有频率、阻尼比和作动器参数,利用μ综合方法设计控制器。为了验证控制器的有效性,分别在频域和时域内分析它们。分析的结果表明:两个控制器都能够抑制模态力对输出应变的影响;所有控制器都能在系统不确定性情况下满足控制要求,具有一定的鲁棒性;μ控制器的控制性能和鲁棒性较好于H_∞控制器。最后,比较分析了滑模变结构控制、线性二次型高斯控制、模型预测控制和H_∞控制及μ综合控制这几种控制方法在柔性机器人机构振动主动控制应用方面的优缺点和异同点,并分别从时域和频域不同的角度比较分析它们的性能。
为验证所设计的控制器的有效性,对柔性5杆机械手进行振动主动控制试验。试验分为三个部分:第一个部分为机械手的刚体运动控制;第二个部分为实验模态测试,获得系统固有频率和阻尼比,修正理论模型;第三个部分为振动控制试验。试验数据分析表明,所设计的控制器能够有效地抑制机械手的弹性振动响应。
In order to improve dynamic performance and quality of mechanism, we must pay more attention to mechanism dynamic as modern machinery is developing into high-speed, precise, lightweight and low-noise one. Especially for a high-speed operating robot, the elastic deformation of its component is not ignored under the external force and inertia force. The elastic deformations not only affect trajectory accuracy and positioning precision, destroy the system stability and reliability, but also reduce productivity and machine life. It is an important issue for mechanism dynamic to reduce its hazardous dynamic response. In the paper, theory and methods on the dynamical modeling, optimization, and active vibration control of flexible robot mechanism is systematically analyzed and studied. The main contributions in this thesis are listed as follows:
A sub-structure modeling method is presented for a general flexible parallel robot. The main idea of the method is that according to the structure character of parallel robot comprised by some independent moving chain, static platform and moving platform, the kinematic substructure is treated as flexible one, the static and moving platform is rigid. Its dynamic equations are established, respectively, and then the system motion equations are obtained by combining all the motion equations of the sub-structure. The characters of the method are as follows: rigid substructure is introduced; the geometric and motion constraint relationship between rigid substructure and flexible one is derived. The model is simplified by using the micro-displacement and micro rotation of the moving platform center as system generalized coordinates to reduce its degrees of freedom and calculate conveniently them. The dynamic analysis results of two examples show the validity of the model.
For a novel 2-DoF flexible parallel manipulator, the optimal design of sectional parameters is carried out in order to acquire the best dynamic characteristics within the category of elastodynamic. The finite element method is applied to obtain the dynamic equations of the system. The sensitivity analysis of the first order natural frequency with respect to sectional parameters is investigated to determine the optimization design variables. Fundamental frequency or weight is selected as objective function respectively; the final optimization results can meet the design requirements, that is, the manipulator have less weight and a relatively high natural frequency. Ideas and methods presented in the paper can be applied to optimize the design of other mechanisms.
For a novel 2-DoF flexible parallel manipulator, the dynamic equations of the system were derived by using assumed mode method and Langrange multiplier method. It is a differential algebraic equation. In order to design a controller, the coordinate-partitioned method is used to convert the differential algebraic equations into a second-order differential equations. Beacause the equations are non-linear and time-varying the variable structure control method is applied to design the controller in order to acquire desired trajectory and attenuate the elastic deformation of flexible parts by selecting the appropriate joint control law. The simulation results show the feasibility and effectiveness of the controller.
Mode theory and variable structure control are applied to design active vibration controller for a novel 2-DoF flexible parallel manipulator with piezoelectric actuators and sensors. The sliding surface is determined by using optimization method according to the performance demand of the system, and sliding controller is designed by applying Lyapunov direct method, and taking account of actuator input voltage limits. The simulation results show the controller can effectively attenuate elastic vibration caused by flexible parts, and reduce the displacement errors of mobile platform of the parallel manipulator, and it is feasible and effective.
Linear quadratic Gaussian optimal control is applied the active vibration control of the flexible five-link manipulator. The optimum positions of the actuators and sensors are determined by applying a controllable and observable indicator characterized by the energy of actuator and measurement signal. The state variables and the output response are used as the performance index in the calculation of the linear quadratic feedback gain matrix. The external force and inertia force in modal coordinate is treated as white noise, a Kalman state estimator is constructed and connects the state estimator and feedback gain matrix to obtain quadratic Gauss controller. The simulation results show the two controllers can effectively suppress the vibration of flexible manipulator, and through comparative analysis, the controller with output performance can obtain better control effects.
Model predictive control is applied to suppress elastic vibration response of a flexible five–link robot. According to the system state space equation, its prediction model is derived so as to obtain the future output value of prediction model. The modal force and measurement noise is non-deterministic external disturbance, and are treated as white noise, a Kalman filter estimator to estimate the system states. Considering the control voltages and its change rates as constraints, the system performance index and the constraints is formed into a quadratic programming optimization problem, and finally the optimal control outputs are acquired. The simulation results show that it is effective of the model predictive control method to attenuate vibration response of flexible manipulator, and achieve satisfactory control effects.
H_∞control theory andμsynthesis is applied to design robust controller to suppress elastic vibration response of a flexible five–link robot. During the design of H_∞controller, the modal force and measurement noise is uncertain external disturbances, modal displacement signal and output response signals are selected as the evaluation signal respectively, and using amplitude and frequency characteristics of actual signal select the appropriate weighting function to form a minimum sensitivity problem. Considering the uncertainty of structural parameters, such as natural frequency, damping ratio and actuator parameters, theμcontroller is designed by usingμsynthesis approach. In order to verify the validity of the controller, the analysis from the frequency domain and time domain are carried out, respectively. Analysis results show that: The two controllers are designed to inhibit the influence of mode force on output strain; The controllers can meet control requirements with uncertainty, and denote that all controllers have some robustness; The control performance and robustness ofμcontroller is better than the H_∞controller. Finally, the comparative analysis of the sliding mode variable structure control, linear quadratic Gaussian control, model predictive control, H_∞control andμcontrol are performed. The advantages and disadvantages, and the similarities and differences of these control method apllied to active vibration control of flexible robot mechanism are analyzed respectively. The control performance compariatve analysis of these controllers is carried out from the point of view of time domain and frequency domain.
In order to verify the validity of the designed controller, the experiment on active vibration control of a flexible five-link manipulator is carried out. The experiment is divided into three parts: The first part is the rigid motion control of the manipulator; The second part is experimental modal testing to access to natural frequency and damping ration of the system, and modify the theoretical model; The third part is the experiment for the vibration control. The experimental data shows the designed controller can effectively suppress the elastic vibration of the manipulator.
引文
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