多变量H∞最优敏感性控制器的解耦设计方法*

本文提出了一种用H~∞控制理论设计多变量系统的最优敏感性控制器的方法。方法通过敏感性函数矩阵解耦,将多变量系统的H~∞最优敏感性设计问题化为若干个单交量的同样问题。文章证明了系统的解耦最优敏感性是唯一的;给出了在多变量情况下如何用真的次优控制器近似非真的最优控制器的方法;最后用算例说明了设计过程。     

广义系统的H∞最优控制

研究连续广义系统的标准H2最优控制器的设计问题.利用线性分式变换方法给出该 系统的所有稳定化控制器的参数化形式,从而借助于两个广义H2代数Riccati方程和两个广义 Lyapunov方程,分别给出该系统的一个标准H2最优控制器的设计及最优H2范数的计算.最 后用一个算例进一步说明设计方法.     

广义系统的H2最优控制

研究连续广义系统的标准H2最优控制器的设计问题.利用线性分式变换方法给出该系统的所有稳定化控制器的参数化形式,从而借助于两个广义H2代数Riccati方程和两个广义Lyapunov方程,分别给出该系统的一个标准H2最优控制器的设计及最优H2范数的计算.最后用一个算例进一步说明设计方法.     

指定极点区域的H-设计方法及实例研究

本文提出了一种综合考虑闭环动态性能,鲁棒性及控制器本身稳定性的指定极点区域的H~∝设计方法,给出了利用实参数寻优求解最优控制器的方法。并用这种方法设计了一个倒立摆平衡控制器。仿真研究结果表明,与LQ和常规H~∞设计方法相比,按本文所提出的设计方法得到的控制器具有鲁棒稳定能力强,闭环动态性能良好及控制器稳定等优点,具有很好的应用前景。     

l~1最优控制器物理不可实现时的修正方法

本文证明了对任意可实现的控制对象p,都存在内稳定p的物理可实现的控制器。并且,l~1优化设计问题的可行域限制在可实现的控制器集合上后,性能指标的下确界不变。对物理不可实现的l~1最优控制器给出了使之成为可实现的,同时又不明显降低最优性能指标的修正方法。方法简单清晰,并给出了算例。     

不确定系统混合H2/H∞鲁棒控制的直接迭代LMI方法

设计多胞型不确定系统的控制器时,引入附加变量能够减小设计保守性,但这会使线性矩阵不等式(LMI)的维数大大增加,控制器难以求解.本文阐述了一种基于直接迭代线性矩阵不等式(DILMI)方法的混合H2/H∞鲁棒控制方法.首先借助于仿射二次稳定理论将整个多胞型不确定集合的稳定性问题转化为该集合各顶点的稳定性问题.利用参数依赖Lyapunov方法,给出了一个保证系统鲁棒稳定,并满足混合H2/H∞性能指标的充分条件.随后采用DILMI算法实现了Lyapunov变量和控制增益的解耦,无需引入附加变量就能够求解充分条件中的非凸优化问题.最后,关于F-16多胞型模型的飞行仿真验证了该方法的有效性.     

具有完整性的状态反馈H2最优控制器设计

基于互质分解的状态空间描述方法,给出了状态反馈下对执行器失效具有完整性的 H2最优控制器的一种新的参数化形式,将具有完整性H2最优控制器设计转化为设计一严格 正则的稳定控制器同时镇定对应于k个故障状态的k个辅助对象.     

具有最优时域指标的有界控制器设计

针对SISO线性离散系统,运用线性规划的方法,在控制器输出幅值受约束的条件 下,设计最优控制器,使闭环系统获得最优动态性能.为方便计算,将求取最优解的线性规划 问题转化为一个关于有界变量的BVLP(有界变量线性规划)问题.     

多变量系统多指标最优设计

本文提出了多变量系统多指标最优设计法,此方法既能保证设计人员对所预计的最优极 点心中有数,又能使多变量系统的各子系统分别满足不同的最优性能指标和实现全系统的最 优控制.本设计法以一个配水系统的子系统为例,进行了数字仿真.仿真结果说明本设计法 具有灵活性、简易性和准确性.     

最优鲁棒容错控制新方法及其在飞行控制中的应用*

本文研究了一类参数不确定且传感器失效的多变量系统的容错控制问题，提出了一种基于模型参数的最优鲁棒容错控制器新的设计方法，该方法可用于解决部分传感器失效时的最优容错控制，并给出了某国产飞机纵向飞行控制的仿真结果。     

Robust maximum principle for multi-model LQ-problem

This paper presents the version of the robust maximum principle in the context of multi-model control formulated as the minimax Bolza problem. The cost function contains a terminal term as well as an integral one. A fixed horizon and terminal set are considered. The necessary conditions of the optimality are derived for the class of uncertain systems given by an ordinary differential equation with parameters from a given finite set. This problem consists in the control design providing a good behaviour for a given class of multi-model system. It is shown that the design of the minimax optimal controller is reduced to a finite-dimensional optimization problem given at the corresponding simplex set containing the weight parameters to be found. The robust optimal control may be interpreted as a mixture (with the optimal weights) of the controls which are optimal for each fixed parameter value. The proof is based on the recent results obtained for minimax Mayer problem (Boltyanski and Poznyak 1999a). The minimax linear quadratic control problem is considered in detail and the illustrative examples dealing with finite as well as infinite horizons conclude this paper.     

连铸方坯的二冷水控制问题

对连铸过程的二冷水控制问题进行了讨论;将二维凝固温度场的边界控制问题,用线性化方法将原问题等价地转化为在几个Ｒａｎｄｏｎ测试空间求最优测度的有限维线性优化问题,从而得到全局最优控制律。数值试验显示此方法是有效的。     

非最小相位不稳定对象的鲁棒最优模型匹配

研究了单输入单输出(SISO)线性时不变系统的鲁棒最优模型匹配问题.采用二自 由度的控制器,对于被控对象具有乘性摄动时,充分考虑控制器的自由参数,将问题转化成有 约束的H∞控制问题,使闭环系统既是H∞范数意义下的最优模型匹配,又具有更大的鲁棒稳 定性.最后,通过解两个H∞范数的最优内插问题,给出了一种新的设汁方法来确定控制器的 参数.该方法简单、直接,对非最小相位系统和不稳定系统均适用.     

Youla-Kučera design of decoupled control systems

A multivariable linear controller based upon pole placement design is developed from the family of all stabilizing controllers. In addition, decoupling behaviour is achieved. The decoupling conditions are established and guarantee the existence of a stabilizing controller that will give rise to a closed-loop transfer function matrix which is non-singular and diagonal. Further requirements may be imposed on the controller - here we discuss H 2 norm minimization.     

Rank-one LMI approach to simultaneous stabilization of linear systems

Following a polynomial approach to control design, the simultaneous stabilization by a controller of given fixed order of a family of SISO linear systems is interpreted as an NP-hard BMI feasibility problem. Upon formulating this BMI problem as an LMI problem with an additional non-convex rank constraint, two simultaneous stabilization methods are then proposed. The first method is a heuristic algorithm performing rank minimization by potential reduction. The second method hinges upon necessary conditions and sufficient conditions for simultaneous stabilization derived from geometric properties of the intersection of a set of ellipsoids. Both methods are then illustrated by numerical examples.     

The method of piecewise constant control of the solidification temperature field

In this paper, a boundary control problem for the solidification temperature field is discussed. The problem is modified into one consisting of the minimization of a linear form over a set of positive measures satisfying linear constraints; the minimization in the new problem is global and can be approximated by a finite-dimensional linear programming problem. A nearly optimal control is constructed. An example is given to illustrate the procedure.     

A parameter optimization approach to robust PI-controller design for systems with interval plants

The purpose of this paper is to develop an analytic way for designing optimal PI-controllers for the interval plant family. Optimality means that the coefficient intervals of the plant stabilized by a PI-controller is maximized. It will be shown that the optimization problem can be formulated in terms of an eigenvalue minimization problem of matrix pairs of the form （H（h0, g0）, H（δ1,k, δ2,k））, where k= 1, 2, 3, 4 and both H（h0, g0） and H（δ1,k,δ2,k） are frequency independent Hurwitz-like matrices. A numerical example is provided to illustrate that optimal controller parameters can be successfully obtained by a two-dimensional search.     

全局最优鲁棒控制器设计

研究了一类时变不确定系统,证明了求解全局最优鲁棒性能问题的一线线性矩阵不等式（LMI）,给出了相应的全局最优鲁棒控制器的具体设计方法,并通过算例对控制器的设计作了进一步的说明。     

Optimal static output feedback simultaneous regional pole placement.

The problem of optimal simultaneous regional pole placement for a collection of linear time-invariant systems via a single static output feedback controller is considered. The cost function to be minimized is a weighted sum of quadratic performance indices of the systems. The constrained region for each system can be the intersection of several open half-planes and/or open disks. This problem cannot be solved by the linear matrix inequality (LMI) approach since it is a nonconvex optimization problem. Based on the barrier method, we instead solve an auxiliary minimization problem to obtain an approximate solution to the original constrained optimization problem. Moreover, solution algorithms are provided for finding the optimal solution. Furthermore, a necessary and sufficient condition for the existence of admissible solutions to the simultaneous regional pole placement problem is derived. Finally, two examples are given for illustration.