【作者】 陈龙祥；

【导师】 蔡国平；

【作者基本信息】 上海交通大学 ， 一般力学与力学基础， 2009， 博士

【摘要】 主动控制系统中不可避免的存在着时滞现象,它有时是控制系统本身所固有的,如传感器信号的采集和传输、控制器的计算、作动器的作动过程等,有时是人为引入进去的,如数字滤波器的使用等。时滞会使得最后作用于结构的控制力产生不同步,导致在系统不需要能量时作动器向系统输入能量,有可能引起控制效率的下降或控制系统失稳。另外,即使原动力学系统本身是线性的,在加入控制环节和考虑时滞后,系统也会呈现出非线性诸多复杂的动力学行为。因此,对控制系统中时滞问题的研究具有重要的理论意义和实际应用价值。时滞问题也是目前数学、控制、力学和结构工程等研究领域的热点前沿方向之一。时滞问题的研究大体可以分为两方面:时滞消除技术,时滞利用技术。时滞消除技术认为时滞是“坏”因素,应当在控制设计中消除它对系统性能所造成的负面影响,目前常采用的方法有泰勒技术展开法、移项技术、状态预估法等。时滞利用技术则是不考虑控制系统本身所固有的时滞量,而是人为地向系统中引入时滞量,将时滞作为一个设计参数和利用时滞进行控制反馈,通过调整时滞量的大小以取得满意的系统性能和控制效果,如时滞阻尼器、时滞滤波器、混沌时滞控制、利用时滞改善系统稳定性等。虽然目前人们关于时滞问题已经进行了大量研究,取得了许多成果,但是多数的研究是在理论上进行探讨,少有实验研究报道。另外,目前的研究多数考虑的是单时滞问题,多时滞问题的研究较少。本论文在国家自然科学基金(编号:10772112,10472065)、教育部重点项目(编号:107043)、教育部博士点专项基金(编号:20070248032)和上海市教育委员会科研重点项目(编号:09ZZ17)的资助下,开展了结构主动控制中多时滞问题的研究,并且进行了大量实验验证。主要研究内容和成果总结如下:(1)对离散形式的多时滞问题处理方法进行了研究。结构模型分别考虑了有限自由度系统(建筑结构)和分布参数系统(柔性梁、柔性板)。在时滞控制律设计中,通过一种特殊的状态变量增广,将包含有时滞项的时滞微分方程转换成形式上不包含有时滞项的标准差分状态方程形式,然后采用离散最优控制方法和离散变结构控制方法进行了时滞控制律的设计。论文中给出了时滞控制律的详细设计过程和各个变量详细的迭代计算格式,并且给出了时滞系统的稳定性判据。在所设计的时滞控制律的表达式中,不但包含有当前步的状态反馈,而且包含有前若干步控制项的线性组合。由于时滞控制律是直接通过时滞微分方程进行设计而得出,而且在设计过程中无需做任何近似和假设处理,因此这种时滞问题处理方法易于保证控制系统的稳定性,不但可以处理小时滞量问题,也能处理大时滞量问题。仿真结果显示出,该方法是可行的和有效的。另外,论文中还采用可控Gramian矩阵和粒子群优化算法对柔性板上压电作动器的优化位置进行了详细研究。(2)对连续形式的多时滞问题处理方法进行了研究。结构模型考虑了柔性机械臂系统,系统模型采用了一次近似模型,控制方法采用了最优跟踪控制方法,柔性机械臂上粘贴有压电作动器。在连续形式的多时滞控制律的设计中,通过一种特殊形式的积分变换,将系统的时滞微分方程转换成形式上不包含有时滞项的标准状态方程形式,系统维数保持不变,控制律的设计可以针对该标准状态方程进行设计而得出。论文中给出了连续形式多时滞控制律的设计过程,以及积分变换中的积分项的迭代计算格式。仿真中分别考虑了如下三种情况:(i)仅使用关节扭矩进行系统控制,关节扭矩存在时滞,(ii)使用关节扭矩和压电作动器同时进行系统控制,仅压电作动器存在时滞;(iii)使用关节扭矩和压电作动器同时进行系统控制,两者存在不同的时滞量。仿真结果显示,时滞控制律能够有效地保证机械臂系统在有限时间到达预定位置,并且机械臂的残余振动可以得到有效抑制。(3)基于DSP控制卡开展了柔性梁、柔性板和柔性机械臂系统的单时滞和多时滞的主动控制实验研究,进行了实验方案的设计和DSP程序的二次开发,解决了数据处理、差分电路、摩擦补偿等诸多实验中的问题,通过实验验证了以上离散和连续形式多时滞控制律的有效性。(4)对时滞动力学系统的时滞辨识问题进行了研究和探索。研究中,将时滞辨识转化为一个优化问题,以一段时间内系统的预估响应与真实响应之差的绝对值之和作为目标函数,采用粒子群算法作为优化算法,开展了单时滞和多时滞的辨识研究。仿真结果显示,所给时滞辨识方法能够有效地辨识出控制系统中的时滞量。时滞问题是一个具有挑战性的研究课题,许多方面还需要进一步深入研究与探讨,因此在论文的最后,对本文的研究工作和成果进行了全面总结,对未来的研究问题进行了展望。更多还原

【Abstract】 Time delay inevitably exists in active control systems. Sometimes it is inherent in control systems such as sensor signals gathering and conveying, controller calculating and process for actuator to build up the required control force; sometimes it is a voluntary introduction into the system such as the using of data filter. Time delay may result in non-synchronization of control force, making the actuator input energy into the controlled system when energy is not needed. This may cause the degradation of control efficiency or even the instability of the control system. Moreover, even original dynamic system is linear, the system may behave with many complex nonlinear dynamic behaviors when active control is applied and time delay is taken into account. Therefore, the research on time delay is of important theoretical significance and practical value. Today time delay is also one of the hot frontiers in mathematics, control mechanics and structural engineering etc.Generally speaking, study on time delay falls into two categories: elimination technology and utilization technology. Elimination technology takes time delay as a“bad”factor and, in control design, tries to eliminate its negative effect on system performance. General practices in elimination technology include the Taylor series expansion, phase shift technique and advance state estimation etc. While time-delay utilization technology not only ignores the inherent delay in the system but introduces a voluntary delay and takes it as a design parameter for control feedback and, by adjusting the magnitude of time delay, to get satisfying control performance and effectiveness. This technology includes time-delay resonator, time-delay filter, time-delay utilization for controlling chaotic motion and for improving system stability etc. Although up to now researches have been done much on the elimination and utilization of time delay, most work is theoretically based and little on the experiment. Furthermore, the work is more about single time-delay problems and little about multiple time-delays. This dissertation presents theoretical and experimental studies on multiple time delays in active control of flexible structures. The research was funded by the National Natural Science Foundation of China (Grant No.’s 10772112, 10472065), the Key Project of Ministry of Education of China (Grant No. 107043), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070248032), and the Key Scientific Project of Shanghai Municipal Education Commission (Grant No. 09ZZ17). Some achievements are obtained both in theory and application and a few highlights are as follows:(1)This dissertation studies the Discrete Processing Method for multiple time-delay problems, with the finite degree-of-freedom system (building structure) and the distributing parameter system (flexible beam and plate) being regarded as structure models. In design of the discrete time-delay controller, by a particular augmentation of state variables, the system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay, then the controller with time delays is designed using the discrete optimal control method and the discrete variable structure control method. The detailed design process of this controller, the iterative algorithm for all parameters and the stability criteria for the delay system are all provided. The designed time-delay controller contains not only the state feedback of current step but also the linear combination of some previous steps of control. Since the time-delay controller is designed directly from the time-delay differential equation and no approximation and hypothesis involved, it tends to guarantee the stability of control systems, and is suitable for both small time delay and large time delay. Simulation results have shown that this controller is feasible and effective in the vibration suppression of flexible structures. In addition, the location of piezoelectric (PZT) actuator on the flexible plate is optimized by using the controllable Gramian matrix and the particle swarm optimizer (PSO) algorithm.(2)This dissertation also probes the Continuous Processing Method for multiple time delays, with a manipulator system being the structural model; the first-order approximation equation being the dynamics model; the optimal tracking control method being the controller and a piezoelectric patch being the actuator adhered on the flexible arm. In design of continuous multiple-time-delay controller, by a particular integral transformation for state variables, the system state equation with multiple time delays is first transformed into a standard form without any explicit time delay and system dimensions stay unchanged, and then the active controller can be designed based on the standard state equation. The design process of continuous multiple-time-delay controller and the iterative algorithm of integral term in the integral transformation are both detailed in the paper. The following three cases are considered in the numerical simulations: (i) Only the joint torque is applied for system control and it has time delay; (ii) Both the joint torque and PZT actuator are applied for system control and only the PZT actuator has time delay; (iii) Both the joint torque and PZT actuator are applied for system control and they have different time delays. Simulation results indicate that the designed time-delay controller can make the manipulator system arrive at an expected position in a specified time and the vibration of flexible arm can also be suppressed.(3)Based on a DSP control board, the experimental study is conducted for active control of the flexible beam, plate and manipulator, in which single time delay and multiple time delays are both considered. Experimental scheme is programmed and secondary development of the DSP program is also implemented. All practical problems encountered in the experiment such as signal differential, circuit and friction compensation are effectively solved. Both the discrete and continuous time-delay processing methods prove effective in the experiment.(4)This dissertation explores the delay identification problem in the time-delay dynamic system as well. When doing this, delay identification is converted to an optimization problem, where the sum of absolute values of the difference between the predicted response and actual response of the controlled system in a period of time makes the objective function and the particle swarm optimizer makes the optimization algorithm. The identifications of single time delay and multiple time delays are both discussed. Simulation results indicate that the identification method presented is effective in determining the real delay in control systems.Time-delay problem is a challenging research topic, where many aspects need further study and more efforts. At conclusion, a summary of work done in this dissertation is given out and some problems of interest are also brought forward for future research.更多还原