有限频域线性重复过程的动态迭代学习控制

针对不同相对度的离散线性重复过程,研究有限频域范围的动态迭代学习控制问题.对于零相对度和高相对度的控制对象,结合二维(2D)系统理论,分别设计有限频域的动态迭代学习控制器;然后,运用广义Kalman-Yakubovich-Popov(KYP)引理,以线性矩阵不等式(LMI)的形式给出控制器存在的充分条件以及控制器的增益...     

广义系统的有限频域故障估计器设计

针对具有执行器故障和未知扰动的线性广义系统,提出一种新的故障估计器设计方法.所设计的故障估计器具有非奇异结构,便于实现.在故障频域范围有限的条件下,为了抑制未知扰动和有限频域故障对故障估计误差的影响,基于广义Kalman-Yakubovich-Popov（KYP）引理给出了故障估计器的鲁棒性设计条件,并将其转化为方便求解的线性矩阵不等式形式.最后,通过一个电路系统的仿真算例验证了所提出方法的有效性.     

有限频域约束下串联弹性驱动器的刚度控制

工程实际中的被控对象都具有明显的有限频域特性,但目前的物理人机交互研究大多是针对全频域性能指标来设计阻抗控制器,由此得到的控制器往往失之保守.本文针对绳牵引串联弹性驱动下的人机物理交互问题,采用有限频域性能约束方法来提升系统在设定频段的刚度控制性能.首先,分析绳牵引串联弹性驱动的刚度控制目标并将其转化成有限频域性能约束下的H∞控制问题.其次,根据广义Kalman-Yakubovich-Popov (KYP)引理,将有限频域性能约束转化成矩阵不等式条件,进而分解变换成有关全信息控制器和待求的静态输出反馈控制器的条件.然后,求解出一个满足条件的全信息控制器,并迭代优化得到输出反馈控制器.仿真和实验结果都表明,本文方法在设定频段取得了更加精确的刚度控制效果.     

二维FM系统的同时故障检测与控制

本文研究二维Fornasini-Marchesini (FM)系统的同时故障检测与控制问题.针对故障和干扰的有限频特性, 设计满足有限频性能指标的故障检测滤波器/控制器, 在实现故障检测目标的同时兼顾控制性能.借助于二维广义KYP引理, 将有限频性能指标转化为矩阵不等式条件.在此基础上, 采用构造切平面的方法以及两步算法解决设计过程中出现的非凸问题.最后, 将所提出的方法应用于带钢轧制过程以验证其有效性.     

基于广义KYP 引理方法的奇异摄动系统有限频段正实性能分析

基于广义KYP引理,研究了奇异摄动系统的有限频段正实性能.根据奇异摄动系统的双频标特性,即有低频和高频两种频域尺度,应用广义KYP引理,分别研究了奇异摄动系统的降阶子系统在其低频段和高频段的正实性,并以线性矩阵不等式形式给出了上述子系统在有限频段正实的充分必要条件.在此基础上,进一步证明了奇异摄动系统在一定条件下是部分频段正实的.     

离散线性系统有限频域基于观测器的迭代学习控制

针对一类离散线性系统,在有限频域范围内研究基于观测器的迭代学习控制问题.首先,结合二维系统理论,构建由基于观测器的状态反馈和PID型前馈学习项组成的控制器;然后,借助于广义Kalman-Yakubovich- Popov(KYP)引理,将闭环系统有限频域性能规范转换为相应的线性矩阵不等式(LMI),进而得到控制器和观测器存在的充分条件,同时,该条件也确保闭环控制系统的稳定性和跟踪误差单调收敛性;最后,通过桁架机器人系统的仿真,验证所提出设计方法的有效性.     

空间互联系统的有限频率范围迭代学习控制

针对一类包含多个节点的空间互联系统,提出一种有限频率范围内的迭代学习控制算法.首先基于提升技术沿空间节点分布方向将重复运行的多维空间互联系统转换为一类二维等效系统,然后设计迭代学习控制律将被控系统转化为线性重复过程,并根据输出期望轨迹跟踪信号的频谱范围,利用Kalman-Yakubovich-Popov (KYP)引理将系统的频域稳定性能分析和控制律设计问题转换成以相应的线性矩阵不等式(LMI)求解问题,同时保证输出跟踪误差在时域和频域范围内的单调收敛性.最后以有源梯形电路的控制仿真验证所提算法的有效性.     

线性时滞系统窗口H∞频域分析

在实际控制系统中,常常需要关注局部频段下的性能指标,而现有的频率加权方法缺乏针对性.由于时滞现象的普遍性及时滞条件下频域分析的复杂性,需要进一步给出时滞系统在局部频段下的H∞性能分析方法.为研究线性时滞系统在局部频段下的性能,基于广义Kalman-Yakubovich-Popov引理及窗口频域H∞范数的概念,给出了线性时滞系统的广义界实定理.针对不同频率范围,给出适用于不同频率条件的频域分析线性矩阵不等式判据.最后通过仿真实例,表明窗口频域分析比传统的全频段H∞分析具有针对性和有效性.     

离散重复过程的有限频率范围迭代学习容错控制

针对一类执行器故障不确定离散重复过程, 提出一种有限频率范围的迭代学习容错控制算法. 通过定义故障系数矩阵和输出跟踪系统的等价二维模型, 沿故障系统的时间轴和批次轴设计迭代学习被动容错控制器, 以线性矩阵不等式形式分别给出基于KYP 引理的全频、分频区域重复控制系统稳定的充分必要条件, 同时保证故障系统在时域和频域范围内的容错性能. 最后, 以重复注塑过程的注射速度控制仿真验证了所提出分频控制算法的有效性.

     

具有执行器容错的汽车主动悬架系统有限频率H∞控制

本文研究了一类具有执行器容错的主动悬架系统有限频率H_∞控制问题.运用广义的Kalman-Yakubovich-Popov(KYP)引理,设计了有限频率H_∞控制器.该控制器不仅能够最大程度地减少路面在4～8 Hz范围内对乘客的影响,还能够保证汽车的悬架行程和车轮的动静载之比在它们允许的范围内.因此所设计的有限频率H_∞控制器不仅能够保证汽车驾驶的舒适性还能够保证汽车驾驶的安全性.为了解决系统状态不完全可测的问题,本文采用了动态输出反馈控制器策略.除此之外,在控制器的设计过程中还考虑了主动悬架系统的参数不确定性以及执行器随机故障的现象.最后,本文基于四分之一汽车主动悬架系统验证了控制器的有效性.     

Experimentally verified generalized KYP Lemma based iterative learning control design

This paper considers iterative learning control law design for plants modeled by discrete linear dynamics using repetitive process stability theory. The resulting one step linear matrix inequality based design produces a stabilizing feedback controller in the time domain and a feedforward controller that guarantees convergence in the trial-to-trial domain. Additionally, application of the generalized Kalman–Yakubovich–Popov (KYP) lemma allows a direct treatment of differing finite frequency range performance specifications. The results are also extended to plants with relative degree greater than unity. To support the algorithm development, the results from an experimental implementation are given, where the performance requirements include specifications over various finite frequency ranges.     

Generalized KYP lemma: unified frequency domain inequalities with design applications

The celebrated Kalman-Yakubovic/spl caron/-Popov (KYP) lemma establishes the equivalence between a frequency domain inequality (FDI) and a linear matrix inequality, and has played one of the most fundamental roles in systems and control theory. This paper first develops a necessary and sufficient condition for an S-procedure to be lossless, and uses the result to generalize the KYP lemma in two aspects-the frequency range and the class of systems-and to unify various existing versions by a single theorem. In particular, our result covers FDIs in finite frequency intervals for both continuous/discrete-time settings as opposed to the standard infinite frequency range. The class of systems for which FDIs are considered is no longer constrained to be proper, and nonproper transfer functions including polynomials can also be treated. We study implications of this generalization, and develop a proper interface between the basic result and various engineering applications. Specifically, it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain/phase properties in several frequency ranges. The method is illustrated by numerical design examples of digital filters and proportional-integral-derivative controllers.     

Sum-of-Squares Decomposition via Generalized KYP Lemma

The Kalman–Yakubovich–Popov (KYP) lemma establishes the equivalence between a frequency domain inequality (FDI) of a proper rational function and a linear matrix inequality (LMI). A recent result generalized the KYP lemma to characterize an FDI of a possibly nonproper rational function on a portion of a curve on the complex plane. This note examines implications of the generalized KYP result to sum-of-squares (SOS) decompositions of matrix-valued nonnegative polynomials of a single complex variable on a curve in the complex plane. Our result generalizes and unifies some existing SOS results, and also establishes equivalences among FDI, LMI, and SOS.      

Finite frequency positive real control for singularly perturbed systems

In this paper, strictly positive real control for singularly perturbed systems in (semi)finite frequency ranges is studied. For the general linear systems, necessary and sufficient conditions for the existence of a stabilizing state feedback controller are given based on the generalized KYP lemma, and use the results to study singularly perturbed systems, a composite state feedback controller is constructed, which preserves the stability and positive real property.     

On Kalman-Yakubovich-Popov lemma for stabilizable systems

The Kalman-Yakubovich-Popov (KYP) lemma has been a cornerstone in system theory and network analysis and synthesis. It relates an analytic property of a square transfer matrix in the frequency domain to a set of algebraic equations involving parameters of a minimal realization in time domain. This note proves that the KYP lemma is also valid for realizations which are stabilizable and observable     

H∞ Output Feedback Control of Linear Time-invariant Fractional-order Systems over Finite Frequency Range

This paper focuses on the H_∞ output feedback control problem of linear time-invariant fractional-order systems over finite frequency range. Based on the generalized Kalman-Yakubovic-Popov (KYP) Lemma and a key projection lemma, a necessary and sufficient condition is established to ensure the existence of the H_∞ output feedback controller over finite frequency range, a desirable property in control engineering practice. By using the matrix congruence transformation, the feedback control gain matrix is decoupled and further parameterized by a scalar matrix. Two iterative linear matrix inequality algorithms are developed to solve this problem. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.