结构振动噪声的鲁棒结构奇异值控制研究

以工程中普遍存在的封闭空间结构-声耦合系统为对象,基于鲁棒结构奇异值理论,建立了结构-声耦合系统鲁棒主动控制模型,提出了设计鲁棒μ-synthesis控制器的方法。通过引入虚拟的不确定块,将耦合系统响应性能的问题转化为广义系统的稳定鲁棒性问题求解,兼顾了系统的稳定鲁棒性和性能鲁棒性。封闭空间结构-声耦合系统的控制仿真表明,与鲁棒H_∞控制结果相比,μ-synthesis方法对模型不确定性具有良好的稳定鲁棒性和性能鲁棒性。     

带刚性基柔性附件振动鲁棒控制

研究了刚体基上柔性附件的振动鲁棒控制问题.介绍了结构奇异值μ理论,基于此理论设计鲁棒控制器,用压电材料作传感器和作动器(μ),用输出乘性不确定性结构来描述低阶标称模型与实际系统的误差,给出了系统μ控制器综合框架.以柔性梁附件为对象示例了分析过程.数值仿真结果表明μ控制器具有良好的鲁棒性能,用于振动控制是必要且可行的.     

论反标架方法对多变量系统鲁棒性设计的改进

Macfarlane等提出的反标架方法(Reversed-Frame-Nomalizing)是适用于多变量系统鲁 棒性CAD的频域方法,这一方法是基于矩阵赋值函数的奇异值分解.本文在介绍这一方法 的基础上,着重讨论反标架方法对系统鲁棒性设计的改进,并对该方法中分频段补偿器的设计 提出了改进建议.通过数值例子说明这一方法较逆奈氏阵列法与特征轨迹法对系统鲁棒稳定 性设计具有的优越性,也说明了这一方法在PC机上的可实现性.     

网络控制系统的μ鲁棒控制研究

基于结构奇异值理论,针对网络控制系统的延时问题,建立了网络控制系统的鲁棒主动控制模型,提出了μ鲁棒控制器的设计方法。通过引入虚拟不确定块将网络控制系统的鲁棒性问题转化为广义系统的鲁棒稳定性问题求解。仿真表明,μ综合方法对系统模型不确定性具有很好的稳定鲁棒性和性能鲁棒性。     

基于模型不确定性鲁棒结构奇异值控制研究

本文以工程中普遍存在的封闭空间结构-声耦合模型不确定性系统为对象,基于鲁棒结构奇异值理论,建立了结构-声耦合系统鲁捧主动控制模型,提出了设计鲁棒μ控制器的方法:通过引入虚拟的不确定块,将耦合系统响应性能的问题转化为广义系统的稳定鲁棒性问题求解,兼顾了系统的稳定鲁棒性和性能鲁捧性.封闭空间结构-声耦合系统的控制仿真表明,与鲁捧H∞控制结果相比,μ方法对模型不确定性具有良好的稳定鲁棒性和性能鲁棒性.     

多变量过程的鲁棒解耦

运用Doyle的结构奇异值理论,提出了不确定系统解耦控制器设计方法.该方法在保证 闭环系统稳定性和动态性能前提下,使解耦控制器对范数约束的不确定系统作最大限度地解 耦.仿真表明,这种鲁棒解耦控制器效果良好.     

基于结构奇异值μ综合的热轧带钢AGC鲁棒控制

基于鲁棒结构奇异值μ理论, 建立了热轧带钢AGC的鲁棒控制模型, 把AGC系统中分散的摄动集中成一个对角阵进行描述, 分析了μ综合控制在热轧带钢中的摄动抑制机理, 应用鲁棒稳定与鲁棒性能准则约束条件, 设计了热轧带钢AGC μ控制器．仿真结果表明μ综合控制能有效地抑制AGC系统中的摄动, 对模型不确定性具有很好的鲁棒性.     

具有非线性扰动的广义系统的鲁棒H∞控制

研究具有非线性结构扰动广义系统的鲁棒H∞控制和鲁棒H∞保性能控制问题,该不确定性为时间和状态的函数.且满足Lipschitz条件.目的是分别设计系统的鲁棒H∞控制器和鲁棒H∞保性能控制器.应用线性矩阵不等式方法,分别给出了系统的鲁棒H∞控制器和鲁棒H∞保性能控制器存在的充分条件.当这些条件可解时,分别给出了鲁棒H∞控制器和鲁棒H∞保性能控制器的表达式.最后通过一个仿真算例说明了所给出方法的应用.     

一类不确定性鲁棒LQR的奇异值特性分析

针对系统矩阵存在的范数有界不确定性,基于一种鲁棒线性二次调节器(LinearQuadratic Regulators,LQR)的设计,利用其鲁棒回差方程,详细推导了这种鲁棒LQR灵敏度函数的奇异值最大值与规范LQR灵敏度函数的奇异值最大值之间的关系,证明这种鲁棒LQR相对于规范LQR具有较小的灵敏度函数的最大奇异值,灵敏度函数的奇异值特性分析说明这种鲁棒LQR设计相对规范LQR有较好的控制性能。表明灵敏度函数的奇异值特性分析,是一种有效的控制系统性能分析方法。     

关于结构奇异值的一个注记

１引言Ｄｏｙｌｅ在１９８２年提出的结构奇异值（μ）方法是分析和综合结构式不确定系统的有力工具［１，２］．基于结构奇异值分析的小μ定理［２］给出了具有多个摄动块的线性动态系统鲁棒稳定的充要条件．而鲁棒性能定理［２］则进一步地将鲁棒稳定性问题和鲁棒性能问题统一成μ分析问题．然而．我们注意到，在所有研究结构奇异值的文献中，均要求块对角摄动矩阵中每个子摄动块是方的．这一要求无疑大大限制了μ方法的应用，因为非方摄动块在系统中是经常存在的．此时对Ｄｏｙｌｅ给出的结构奇异值的上界函数［１］必须进行修正．２非方…     

连续搅拌反应釜过程的闭环增益成形PID控制器设计

针对连续搅拌反应釜（CSTR）系统控制问题,设计了一种基于闭环增益成形算法的PID控制器,以提高PID控制器设计的简洁性和鲁棒性。首先假设期望闭环回路传递函数有一阶形式,同时将受控对象的一阶传递函数和PID控制器构成实际闭环回路传递函数。然后,比较期望闭环回路传递函数和实际闭环回路传递函数,即可确定PID参数。最后,以某CSTR系统为例,利用该方法设计了PID控制器,并通过仿真结果比较,检验了该方法所得PID控制器的良好鲁棒稳定性和动态品质。     

低阶时滞过程的伪预测PI／PID控制

基于单位反馈控制结构,根据期望的闭环传递函数设计得到了一种伪预测PI/PID(ADQPI/ADQPID)控制器。这种控制器只有一个可调参数,可调参数与系统动态响应性能和鲁棒稳定性之间存在直接关系,只需单调的调节控制器参数,便可实现系统的动态响应性能与鲁棒稳定性之间的最佳折衷。仿真实例表明,这种控制器在扰动和模型失配的情况下仍然具有良好的控制性能和鲁棒稳定性,是一种值得在实际工程中推广运用的新型控制器。     

A simple robust PI/PID controller design via numerical optimization approach

This paper presents a simple but effective method for designing robust PI or PID controller. The robust PI/PID controller design problem is solved by the maximization, on a finite interval, of the shortest distance from the Nyquist curve of the open loop transfer function to the critical point-1. Simulation studies are used to demonstrate the effectiveness of the proposed method.     

A two‐degree‐of‐freedom ℋ︁∞ control design method for robust model matching

We propose an ??_∞ controller design method which achieves a closed‐loop transfer function equal or otherwise sensibly close to a desired transfer function, viz. a model reference design. The proposed controller design method inherits the model reference feature of the internal model control design method and incorporates the weighting scheme of the ??_∞ loop‐shaping. It utilizes Youla–Kucera parameterization in a two‐degree‐of‐freedom scheme to achieve robust model reference and high performance design while ensuring a sensible robust stability margin, and can be readily applied to the generic class of LTI systems (SISO, MIMO, stable, unstable). Copyright © 2006 John Wiley & Sons, Ltd.     

一类非自衡对象的PID控制

本文讨论非自衡对象PID控制器设计问题.首先在鲁棒控制理论的基础上定义了 最优性能指标,然后针对控制系统性能传递函数的特点发展了两种设计方法,通过引入2型滤 波器使系统满足了渐近跟踪的要求,并解析地得到了PID控制器.控制器的特点是标称性能 可以定量地估计,鲁棒性可以方便地调节.     

Performance preserving controller reduction via additiveperturbation of the closed-loop transfer function

An H_∞ performance preserving controller order reduction method is proposed. Here performance preservation indicates that the H_∞ norm bound of the closed loop transfer function with reduced-order controller is not greater than the H_∞ norm bound of the closed loop transfer function with full order controller. We assume additive perturbations to the closed-loop transfer function and obtain a sufficient condition for performance preservation. Two kinds of useful weightings are derived, and the controller reduction problem is solved via a frequency weighted model reduction problem     

A closed-loop data based test for robust performance improvement in iterative identification and control redesigns

In robust iterative identification and control redesign techniques, a stabilizing controller connected in a closed loop is normally replaced by an alternative attractive stabilizing controller to improve robustness and performance of the closed-loop system. In this paper, novel test methods are proposed to check whether a new stabilizing controller improves performance or not when the existing controller is replaced by this new controller in the closed loop. The proposed tests are based on closed-loop data and no plant model, and can be used for both the SISO and MIMO linear time-invariant systems. For the proposed tests, the plant dynamics is assumed to be unknown whereas the existing and new controller transfer function matrices are known to the designer. These assumptions are common in iterative identification and control redesign techniques. The performance improvement test methods proposed in this paper build on the experimental set-up proposed in Dehghani, Lecchini, Lanzon, and Anderson (2009) which was used to only check whether controllers ensure internal stability of a feedback interconnection or not. In this paper, new test methods are proposed to ascertain robust performance improvement that cannot be obtained from test results of Dehghani et al. (2009). A numerical example is illustrated to show effectiveness of the proposed test methods.     

有效传递函数在多变量耦合系统中的应用

针对多变量系统具有多时滞、强铰链耦合的特点,提出了有效开环传递函数解耦策略。由于有效开环传递函数所描述的动力学行为的复杂性,首先采用模型降阶技术,将系统逼近一阶环节+延时(FOPDT)形式;然后运用IMC控制策略实现单位反馈控制。为得到传统PID控制器的典型表达形式,将IMC控制器进行麦克劳林级数展开,通过对相应项系数的比对得到了传统PID控制器。仿真分析表明了该方法能够提高系统动态响应速度、减小稳态误差,实现了多变量耦合系统的理想控制。     

Robust control of a distillation column by the method of inequalities

The method of inequalities is applied to design a robust PI controller for the control of distillate composition using the reflux flow as the manipulated variable. The controller design method takes into account wide variations in k,τ and τ_D of the first order plus the delay transfer function of the process. The performance of the controlled system is evaluated for different levels and changes in direction of set point changes on the linear and also on the original non-linear model equations. The performance of the proposed controller is compared with that of a controller with Zieglar-Nichols (Z-N) settings based on a nominal operating point. The closed loop system becomes unstable at other operating points for the Z-N method whereas the present controller gives good response for wide operating points.     

A Novel Application of Minimax LQG Control Technique for High‐speed Spiral Imaging

Over the last two decades, increasing the scanning speed of an atomic force microscopy (AFM) has been attempted either by applying novel controllers, using alternative scanning methods, or by modifying the hardware setup. This paper demonstrates, the first two approaches to achieve high‐speed AFM image scanning. A robust minimax linear quadratic Gaussian (LQG) controller is designed and spiral scanning is considered as an alternative scanning method rather than conventional raster scanning. The minimax LQG controller is designed based on an uncertain system model which is constructed by measuring the plant variations due to variations in sample mass and also modeling error between the measured and model frequency responses. This controller is also robust against uncertainties introduced as a result of variations of sample mass, spillover dynamics of the scanner at frequencies higher than the first resonance frequency of the scanner, and variation in plant transfer functions due to temperature and humidity. The designed controller is experimentally implemented on an AFM using a dSPACE ds‐1103 real‐time prototyping system and open‐loop and closed‐loop spiral imaging performances are evaluated. The proposed controller provides sufficient damping at the resonant modes to accurately track the sinusoidal reference signal and generate vibration free images. Also, creep, hysteresis, and cross‐coupling effects are significantly reduced. The experimental results show that the proposed scheme outperforms the open‐loop case and some other existing approaches.