基于状态空间的稳定广义预测控制器

给出了稳定广义预测控制（ＳＧＰＣ）算法的状态空间表达形式，并讨论了基于状态空间表达式的ＳＧＰＣ和基于输入输出表达式的ＳＧＰＣ之间的等价性。最后给出了算法的仿真结果。     

零点配置与一类非线性广义系统的状态反馈控制

针对状态空间实现为非最小相位的非线性广义系统的控制问题,提出一种非线性广义系统的状态空间实现算法,构建了一个等价于原输出函数的综合输出函数,能任意配置状态空间实现的传输零点,使该状态空间实现为最小相位的.所构建的最小相位输出函数能直接用于构造状态反馈控制器,实现对非线性广义系统状态反馈控制.将所得结论应用于Logistic增长的SIR传染病模型,仿真结果表明了所提方法的有效性和可行性.     

基于子空间辨识的状态空间模型预测控制

针对无法从工业过程中获得准确状态空间模型的问题,提出一种基于子空间辨识的状态空间模型预测控制方法。利用子空间辨识方法得到的状态空间模型作为系统模型,给出约束条件下的预测控制算法。以CD播放器机械臂系统为例,通过状态空间模型预测控制方法实现对系统输出的跟踪控制,仿真结果表明,该方法控制效果良好。     

增广非最小状态空间法的稳定平台预测控制研究

针对传统的模型预测控制器鲁棒性较差及模糊PID控制系统比较复杂的问题,提出了利用增广非最小状态空间模型与模型预测控制相结合的稳定平台预测控制。建立了稳定平台广义被控对象的数学模型,以增广形式的非最小状态空间模型为基础,结合滚动时域控制原则和线性二次型最优控制,通过对稳定平台离散模型的非最小状态空间形式进行增广变换,给出了基于Laguerre函数的状态反馈增益矩阵算法,设计了增广非最小状态模型下的预测控制器,实现了对导向钻井稳定平台控制系统的仿真研究。仿真结果表明稳定平台预测控制系统可以很好地满足钻井工程对控制精度和动态特性的要求,而且对有时变性的盘阀摩擦干扰力矩及模型参数摄动具有较强的鲁棒性。     

基于状态反馈的预测二次稳定系统设计

基于广义预测的状态空间形式，提出了一种新的鲁棒预测控制设计方法—预测二次稳定控制器。利用Riccati方程给出了最优控制律，并在理论上给出了严格的证明。这种控制算法可以保证控制系统的稳定性。与广义预测控制方法进行比较，仿真结果表明该鲁棒预测控制方法是有效的，其控制性能明显优于常规的广义预测控制。     

网络控制系统补偿器设计及稳定性分析

为解决网络延时对网络化控制系统性能的影响, 从控制的角度提出基于系统模型的补偿器设计方案以解决网络延时问题. 通过对广义预测控制算法GPC状态空间形式的推导, 设计具有多步预测功能的网络控制器, 实现前向通道的延时补偿; 构造具有延时补偿功能的状态观测器以补偿反馈通道延时. 分析了使用上述延时补偿策略所构成的闭环网络控制系统的稳定性. 通过对不同网络延时补偿的仿真实验, 证实了该补偿算法能有效改善控制系统性能并保持系统的稳定.     

线性混杂自动机的非线性广义最小方差控制

研究线性混杂自动机(LHA) 模型. 线性混杂自动机在一定条件下可以转化成与之等价的状态依赖空间模型, 等价性是指两个系统所产生的轨迹是相同的. 采用非线性广义最小方差算法对状态依赖空间模型进行控制器的设计, 非线性广义最小方差控制器的设计则基于更为一般的非线性模型, 模型中可含有时滞项和外界干扰, 控制器的计算过程简单且易于实现. 仿真结果表明, 非线性广义最小方差控制算法能够有效地控制线性混杂自动机, 而且在系统存在延时、干扰以及噪声的情况下能够得到较为理想的控制效果.     

状态反馈预测控制的结构性能及应用实例

本文分析了状态反馈预测控制系统的结构与控制性能，基于状态空间模型，使用实 测状态变量反馈，状态反馈预测控制系统是状态变量动态反馈结构．对比动态矩阵控制（DM C）、广义预测控制（GPC）和内模控制（IMC）算法，由于使用可测状态变量动态反馈结构 ，提高了控制系统抑制不可测干扰能力，改善了控制系统的鲁棒性，预测模型可适用于较大 的操作范围．预测控制系统稳定时，对阶跃型给定值及干扰静态无偏差．给出了催化裂化装 置稳定吸收系统，稳定汽油饱和蒸汽压先进控制的应用实例，先进控制系统的设计功能全部 在DCS层实现，现场运行实测数据对比表明控制效果较好．     

基于输入状态稳定的离散广义系统预测控制

针对一类具有持续扰动和输入约束的离散广义系统, 研究其鲁棒预测控制器的设计问题. 将输入状态稳定的概念引入广义系统预测控制, 在quasi-min-max 性能指标下, 提出了广义系统双模鲁棒预测控制器的设计方法, 证明了基于双模鲁棒预测控制器的闭环广义系统输入状态稳定, 且具有正则、因果性. 数值仿真结果验证了所提出方法的有效性.

     

含未知输入的广义系统的状态与输入估计

研究了含未知输入的广义系统的输入解耦观测器设计问题. 在系统脉冲能控的条件下通过系统输入-状态对的非奇异变换, 把此问题等价地转化为正常状态空间系统的相应问题. 用大家熟知的方法设计正常状态空间系统的观测器, 从而得到广义系统的输入解耦观测器. 然后用广义系统的观测器状态和系统输出的线性组合渐近估计系统的状态与未知输入.     

Note on ‘ On the definition of transfer function ’

An algorithm for directly obtaining the canonical state-space model corresponding to the Cauer third form of continued fraction expansion (CFE) from a given general state-space model is presented. The algorithm can be used to determine the transfer function of linear time-invariant system from its state-space model as well as to obtain the reduced order models..Two new similarity matrices, one transforms a state-space equation from a general form to a Cauer third CFE canonical form, and the other transforms a state-space model in phase-variable form to a state-space model in a Cauer third CFE canonical form, are derived. Using these matrices an approximate relationship between the original state vector and the state-vector of reduced model obtained by the method of Cauer third CFE is established     

Data driven local coordinates for multivariable linear systems and their application to system identification

In this paper we introduce a new parametrization for state-space systems: data driven local coordinates (DDLC). The parametrization is obtained by restricting the full state-space parametrization, where all matrix entries are considered to be free, to an affine plane containing a given nominal state-space realization. This affine plane is chosen to be perpendicular to the tangent space to the manifold of observationally equivalent state-space systems at the nominal realization. The application of the parametrization to prediction error identification is exemplified. Simulations indicate that the proposed parametrization has numerical advantages as compared to e.g. the more commonly used observable canonical form.     

Fractional representations of linear systems

A fractional representation of an arbitrary linear system is obtained that can be viewed as a generalization of a classical fractional representation of a transfer function. Conversely, a state-space model, not necessarily observable or controllable, can be assigned to any such fractional model. It is then shown that the categories of state-space and fractional representations of a linear system are equivalent.     

A general algorithm for determining state-space representations

A new and direct procedure is presented for determining state-space representations of given, time-invariant systems whose dynamical behavior is expressed in a more general, differential operator form. The procedure employs some preliminary polynomial matrix operations, if necessary, in order to “reduce” the given system to an equivalent differential operator form which satisfies four specific conditions. An equivalent state-space representation is then determined in a most direct manner; i.e. the algorithm presented requires only a single matrix inversion. An explicit relationship between the partial state and input of the given system and the state of the equivalent state-space system is also obtained.     

On finding the transmittance between any two points in a composite system

The concept of a strong component in a digraph is generalized. A graphical method is evolved to search for the subsystems in a composite system which affect the transmittance between the input of any given subsystem and the output of any given subsystem. The transmittances may be in transfer-function form or state-space form. In the latter case, the state-space model obtained for a transmittance in the composite system is minimal in a graphical sense.     

广义系统的受限能控性

本文讨论广义系统在控制能量或幅值受限下的状态能控性,得到了充要条件。这一充要条件指出,广义系统在控制受限下的能控性不仅取决于它的慢子系统的能控性,并且还取决于慢子系统的特征根的分布。     

Equivalence of dynamical systems by bisimulation

A general notion of bisimulation is defined for linear input-state-output systems, using analogies with the theory of concurrent processes. A characterization of bisimulation and an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation is shown to be a notion which unifies the concepts of state-space equivalence and state-space reduction, and which allows to study equivalence of systems with nonminimal state-space dimension. The notion of bisimulation is especially powerful for "nondeterministic" dynamical systems, and leads in this case to a notion of equivalence which is finer than equality of external behavior. For abstractions of systems it is shown how the results specialize to previously obtained results by other authors. Extensions of the main results to the nonlinear case are provided.