具有给定闭环极点的最优控制系统的设计

文中给出了线性二次型性能指标函数中的加权系数矩阵 Q 和 R 与控制系统的闭环极点之间的关系.只要给定系统的最优闭环极点,就能方便地求得矩阵 Q 和 R.     

一种新的最优控制系统设计方法

本文采用LQ逆问题方法得到了一种新的最优控制系统设计方法，推导了线性二次型性能指标中的加权矩功Q与开环特征多项式，最优闭环特征多项式之间的关系。并研究LQ逆问题解的存在性和唯一性问题。只要给定期望的闭环极点，即可确定与之对应的加权矩阵Q，从而获得一个具有指定闭环极点的最优控制系统。     

确定线性调节器加权矩阵的简易方法

本文给出了线性二次型性能指标中加权矩阵与开环、最优闭环系统特征多项式系数之间的解析关系。只要给定一组期望的闭环极点,即可直接确定与之对应的加权矩阵。     

关于确定加权矩阵的两个定理

给定一线性连续或离散时间系统以及与其对应的二次型性能指标函数,文中证明了在系统的开、闭环特征多项式,系统的系数矩阵以及二次型性能指标函数中的加权矩阵之间存在一组确定的显式关系.根据这组关系,满足期望闭环特征值要求的加权矩阵的确定问题变为求解一组具有二次变量的非线性方程组.对于高阶系统,用数值方法求解该方程组也是十分方便的.     

一种新的最优极点配置方法

本文从LQ逆问题着眼提出了一种新的最优极点配置方法,推导了加权矩阵Q和R与开环特征多项式、最优闭环特征多项式之间的关系。只要给定一组期望的闭环极点,即可确定与之对应的加权矩阵Q和R,从而得到一个具有指定极点的最优控制系统。     

离散系统最优调节器的逆问题

本文证明了在闭环特征多项式的系数,以及二次型指标函数中的矩阵Q和系统的系数矩阵A,B之间所存在的一组关系,并对系统(A,B)的形式无特别要求。对于SiSO系统来说,如果给定开环系统以及所希望的闭环特征,通过这组关系,就能方便地求出矩阵Q。     

一种新的离散系统最优闭环极点配置方法

分析了LQ逆问题解的存在条件,以便合理选择期望的闭环极点,使之成为一组最优极点．提 出了一种以离散系统LQ逆问题分析为基础的新的最优控制系统设计方法,得到了开环、闭环 特征多项式系数与加权矩阵之间的解析关系,只要给定一组期望闭环极点,即可确定与 之对应的加权矩阵Q和R,从而得到一个具有指定极点的最优控制系统．     

离散系统LQ逆问题及其在最优闭环极点配置中的应用

本文采用离散系统LQ逆问题方法得到了最优闭环系统的两个必要条件,分析了单输入单输出系统权阵Q与开环特征多项式系数a_i、及闭环特征多项式系数b_i之间的关系,最后应用所得结论研究了离散系统逆问题方法在最优闭环极点配置中的应用。     

二次型最优离散系统的两个必要条件

本文给出了线性定常二次型最优离散系统的两个必要条件,得到了单输入单输出系统开环特征多项式系数a_i和最优闭环特征多项式系数b_i与权阵Q之间的直接关系,所得结论有益于设计一个具有指定闭环极点的最优控制系统。     

离散系统LQ逆问题及其在最优闭极点配置中的应用

本文采用离散系统LQ逆向问题方法得到了最优闭环系统的两个必要条件，分析了单输入单输出系统权阵Q与开环特征多项式系数ai，及闭环特征多项式系数bi之间的关系，最后应用所得结论研究了离散系统逆问题方法在最优闭环极点配置中的应用。     

线性定常系统的综合性最优控制问题

本文讨论了具有二次型性能指标的线性定常系统的降低性能指标灵敏度、降低轨迹灵敏 度和配置闭环极点的综合性最优控制问题,提出了新的综合性能指标,从而得到了易于计算 的结果;解决了多参数变化时降低轨迹灵敏度的综合性最优控制问题;推导了闭环特征值对 Q阵的梯度阵公式,提出了一种配置互异的全部闭环极点Q阵算法,并给出了算例.     

Linearity of the coefficients of the closed-loop characteristic polynomial

This note examines the condition given by Kolka for linearity of the coefficients of the closed-loop characteristic polynomial. An alternative necessary and sufficient condition is given for v coefficients of the characteristic polynomial to be linear in the elements of the output-feedback matrix. It is shown that this condition is applicable to a wider class of systems and provides more information about the system properties.     

线性二次型最优控制闭环系统极点的必要条件

本文推导了线性二次型(LQ)最优控制闭环系统极点应满足的必要条件,以及与加权阵Q和R的等式关系。     

随机系统的多模型直接自适应解耦控制器

针对多变量离散时间随机系统, 提出了一种采用广义最小方差性能指标的多模型直接自适应解耦控制器. 该多模型控制器由多个固定控制器和两个自适应控制器构成. 固定控制器用以覆盖系统参数的可能变化范围, 自适应控制器用以保证系统的稳定性和提高暂态性能. 该多模型控制器利用矩阵的伪交换性和拟Diophantine方程性质, 基于广义最小方差性能指标, 将随机系统辨识算法和最优控制器设计相结合, 直接辨识出控制器的参数, 通过广义最小方差性能指标中加权多项式的选取,不但实现了多变量系统的动态解耦控制, 而且消除了稳态误差、配置了闭环极点. 文末给出了全局收敛性分析. 仿真结果表明该方法明显优于常规自适应控制器.     

Relations between coefficients of the closed-loop characteristic polynomial and output-feedback gains

This paper deals with explicit analytical dependencies between all coefficients of the closed-loop characteristic polynomial and all entries of the output feedback matrix. First, a special kind of non-linear relation that occurs is explained. Next, computationally-efficient formulae are discussed that yield closed-loop characteristic polynomial coefficients with explicit feedback gain dependence. Then it is shown how the closed-loop characteristic polynomial is associated with the transfer function matrix of the open-loop system. Finally, the results obtained are interpreted graph-theoretically.     

LQ逆问题研究

本文研究了线性定常系统LQ逆问题解的存在性问题,给出了逆问题解的参数化公式,得 到了加权矩阵Q与开环、闭环特征多项式系数之间的解析关系.只要给定一组稳定的闭环极 点,即可确定与之对应的Q阵.     

The use of a quadratic performance index to design multivariable control systems

A quadratic performance index is considered as a generalized criterion for designing linear multivariable control systems. A method is developed for expressing the characteristic polynomial of the optimal system as an explicit function of the weighting matrix elements of the performance index. Since these elements are actually the design parameters it then becomes possible to obtain some general properties of the optimal systems as well as to select the weighting matrix elements, such that more conventional criteria on the system transient response are satisfied. The results are applied to the design of two multivariable systems; in one case, the plant is initially unstable and, in the second case, it is desired to have the system response follow that of a linear model.     

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

The well-known stabilizing property of linear quadratic state feedback (LQSF) design is used to obtain a quantitative measure of the robustness of LQSF designs in the presence of perturbations. Bounds are obtained for allowable nonlinear, time-varying perturbations such that the resulting closed-loop system remains stable. The special case of linear, time-invariant perturbations is also treated. The bounds are expressed in terms of the weighting matrices in a quadratic performance index and the corresponding positive definite solution of the algebraic matrix Riccati equation, and are easy to compute for any given LQSF design. A relationship is established between the perturbation bounds and the dominant eigenvalues of the closed-loop optimal system model. Some interesting asymptotic properties of the bounds are also discussed. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed, based on LQSF theory, and the results presented in this paper. The variation of the perturbation bounds to changes in the weighting matrices in the LQSF design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable bound for perturbations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.     

多变量加权多步预报控制*

对于线性多变量系统,本文给出了一种完全不同于以往的全状态反馈或观测器-控制器型的算法——多变量加权多步预报控制(MWLPC)算法。这种算法除引进了预测控制中的多步输出预报、滚动优化等机制外,最重要的是在二次型性能指标中引入了可调的多项式或有理分式矩阵权因子;适当选取这些权因子,便可按设计要求、仅用系统的输出信息反馈便能任意配置闭环系统的特征矩阵,从而保证闭环稳定性和其他优良性质。此外,该算法不改变原系统的零点,因而适用于非最小相位系统。