采用D–K–D迭代算法设计导弹增益调度自动驾驶仪

导弹增益调度自动驾驶仪除具有对时变参数的自适应调节能力外, 还应具有对不可测量不确定性的抑制能力. 为此, 将导弹自动驾驶仪设计问题描述为一类含有不可测量不确定性的线性参数时变(LPV)系统的鲁棒增益调度问题, 构造了模型匹配自动驾驶仪设计结构, 并通过D–K–D迭代算法综合运用LPV控制方法和μ综合方法设计了导弹鲁棒增益调度自动驾驶仪. 设计的自动驾驶仪不仅能够随导弹飞行马赫数和高度的变化自动进行参数调节, 还能够有效抑制量测噪声、量测误差及建模误差等不可测量不确定性. 仿真结果验证了设计方法的有效性和可行性.     

采用D-K-D迭代算法设计导弹增益调度自动驾驶仪

导弹增益调度自动驾驶仪除具有对时变参数的自适应调节能力外,还应具有对不可测量不确定性的抑制能力.为此,将导弹自动驾驶仪设计问题描述为一类含有不可测量不确定性的线性参数时变(LPV)系统的鲁棒增益调度问题,构造了模型匹配自动驾驶仪设计结构,并通过D-K-D迭代算法综合运用LPV控制方法和μ综合方法设计了导弹鲁棒增益调度自动驾驶仪.设计的自动驾驶仪不仅能够随导弹飞行马赫数和高度的变化自动进行参数调节,还能够有效抑制量测噪声、量测误差及建模误差等不可测量不确定性.仿真结果验证了设计方法的有效性和可行性.     

BTT导弹H∞鲁棒自动驾驶仪的6DOF数学仿真

该文Ｈ∞对控制方法设计的ＢＴＴ导弹自动驾驶仪进行六自由度（６ＤＯＦ）数学仿真，与传统的逐段切换自动驾驶仪增益以控制导弹沿全弹道飞行方法相比，本仿真仅用对标准弹道上上某特征设计的一个Ｈ∞鲁棒自动驾驶仪控制导弹的全弹道飞行，仿真结果表明，设计的Ｈ∞鲁棒自动驾驶仪控制导弹在大域内稳定，准确地飞行，在满足一定的性能指标要求的前提下系统有很强的鲁棒稳定性。     

基于μ分析的导弹自动驾驶仪稳定裕度评估

介绍了一种关于导弹自动驾驶仪稳定裕度评估的新方法;利用结构奇异值理论对存在不确定性参数的导弹自动驾驶仪性能进行分析,并确定“最坏情况”时不确定性参数的组合;首先,针对存在不确定性参数的导弹系统,建立线性分式变换(LFT)形式的模型;然后,将系统稳定裕度要求看作虚拟的非结构不确定性并引入模型;最后,使用结构奇异值理论对模型进行分析.分析证明自动驾驶仪满足性能要求,并且得到了最坏情况的不确定参数组合:结果表明这是一种比传统方法更加高效和准确的评估方法.     

导弹的LPV建模与混合H2/Hinf自动驾驶仪设计

导弹在飞行过程中,高度、速度、攻角、动压等变量变化剧烈,如何在其大范围变化情况下设计满足要求的自动驾驶仪是研究的重点所在.论文利用线性参数时变方法对导弹动态系统完成建模过程,并采用线性分式变换将控制器设计问题转换为设计名义主控制器与根据飞行状态实时调整的参数控制器的过程,同时以混合H2/Hinf为性能指标,利用线性矩阵不等式对上述问题完成求解.最后以导弹自动驾驶仪设计为例对文中算法进行仿真验证,经验证表明此算法可以满足跟踪指令输入并具有较好的鲁棒稳定性.     

基于前馈—反馈控制导弹自动驾驶仪鲁棒稳定性分析

针对一类前馈—反馈的气动力/直接力复合控制导弹自动驾驶仪结构特点,基于对直接力喷流装置放大因子与攻角的对应关系和直接力寄生回路的耦合机理的分析,完成了气动力/直接力复合控制系统的非线性建模,并采用Lyapunov非线性稳定性理论,对复合控制导弹自动驾驶仪的鲁棒稳定性问题进行了证明,给出了采用气动力/直接力复合控制导弹自动驾驶仪的稳定域,具有较好的工程参考价值。     

导弹非零给定点LQR自动驾驶仪设计

静不稳定控制技术是提高空空导弹机动性能的有效手段.针对静不稳定导弹的控制问题,基于非零给定点线性二次型调节器(LQR)理论设计了纵向两回路自动驾驶仪.首先给出一种基于英美弹体坐标系的静不稳定导弹状态空间模型,引入加速度计到质心的距离参量;然后使用非零给定点输出调节器理论,推导了针对一般状态空间表达式描述的系统的最优控制问题,求得了通用解和自动驾驶仪的结构和参数表达式;最后根据经典控制理论对权重系数的选择进行理论研究和仿真分析,并对所设计自动驾驶仪的鲁棒性能以及引入加速度计到质心的距离变量对控制效果的影响进行仿真分析.结果表明所设计的自动驾驶仪有较强的鲁棒性,对静不稳定导弹起到了较好的控制作用.     

具有结构不确定性的输出反馈性系统的鲁棒稳定性分析

基于向量的幂变换方法，对具有结构不确定性的输出反馈线性系统的鲁棒稳定性问题作了分析。单参数摄动时给出了闭环系统鲁棒稳定的充要条件，多参数摄动时得到了保证系统鲁棒稳定的充分条件，导出了闭环系统鲁棒稳定区域的一种代数表达形式。最后给出了实例。     

基于准线性化模型设计导弹H∞增益调度自动驾驶仪

实现针对系统快变量攻角的自适应参数调节是导弹鲁棒增益调度自动驾驶仪设计的一个难点. 为解决此问题, 提出采用由状态替换方法建立的导弹准线性化模型作为设计模型, 基于线性参数时变(LPV)/μ控制技术构造自动驾驶仪设计结构, 并通过D-K-D迭代算法设计导弹H_∞增益调度自动驾驶仪. 所设计的自动驾驶仪不仅能够实现对马赫数和高度两个系统慢变量的自适应参数调节, 还能实现对系统快变量攻角的自适应参数调节. 非线性仿真结果验证了所提出方法的有效性.     

空空导弹增益调度鲁棒H_∞控制自动驾驶仪设计

为了满足空空导弹大空域、高机动飞行的技术指标要求,提出了BTT导弹的增益调度鲁棒H∞自动驾驶仪设计方法;建立了BTT导弹线性变参数(LPV)系统数学模型;提出了LPV系统增益调度鲁棒H∞控制设计方法和设计过程;通过把BTT导弹自动驾驶仪分为俯仰、偏航/滚转通道分别进行设计,并以俯仰通道为例进行了仿真验证;仿真结果表明该控制算法具有良好的控制性能,从而,验证了增益调度鲁棒H∞控制算法的正确性和有效性。     

Robust Stability of a Class of Uncertain Markov Jump Nonlinear Systems

This note addresses the problem of robust stability analysis for a class of Markov jump nonlinear systems subject to polytopic-type parameter uncertainty. A condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed. An estimate of a robust domain of attraction of the origin is also provided. The approach is based on a stochastic Lyapunov function with polynomial dependence on the system state and uncertain parameters. A numerical example illustrates the proposed result     

LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions

The robust stability of uncertain linear systems in polytopic domains is investigated in this paper. The main contribution is to provide a systematic procedure for generating sufficient robust stability linear matrix inequality conditions based on homogeneous polynomially parameter-dependent Lyapunov matrix functions of arbitrary degree on the uncertain parameters. The conditions exploit the positivity of the uncertain parameters, being constructed in such a way that: as the degree of the polynomial increases, the number of linear matrix inequalities and free variables increases and the test becomes less conservative; if a feasible solution exists for a certain degree, the conditions will also be verified for larger degrees. For any given degree, the feasibility of a set of linear matrix inequalities defined at the vertices of the polytope assures the robust stability. Both continuous and discrete-time uncertain systems are addressed, as illustrated by numerical examples.     

Computation of nonconservative stability perturbation bounds forsystems with nonlinearly correlated uncertainties

Consideration is given to the problem of robust stability analysis of linear dynamic systems with uncertain physical parameters entering as polynomials in the state equation matrices. A method is proposed giving necessary and sufficient conditions for computing the uncertain system stability margin in parameter space, which provides a measure of maximal parameter perturbations preserving stability of the perturbed system around a known, stable, nominal system. A globally convergent optimization algorithm that enables solutions to the problem to be obtained is presented. Using the polynomial structure of the problem, the algorithm generates a convergent sequence of interval estimates of the global extremum. These intervals provide a measure of the accuracy of the approximating solution achieved at each step of the iterative procedure. Some numerical examples are reported, showing attractive features of the algorithm from the point of view of computational burden and convergence behavior     

Generalization of the Nyquist robust stability margin and its application to systems with real affine parametric uncertainties

The critical direction theory for analysing the robust stability of uncertain feedback systems is generalized to include the case of non‐convex critical value sets, hence making the approach applicable for a much larger class of relevant systems. A redefinition of the critical perturbation radius is introduced, leading to the formulation of a Nyquist robust stability measure that preserves all the properties of the previous theory. The generalized theory is applied to the case of rational systems with an affine uncertainty structure where the uncertain parameters belong to a real rectangular polytope. Necessary and sufficient conditions for robust stability are developed in terms of the feasibility of a tractable linear‐equality problem subject to a set of linear inequalities, leading ultimately to a computable Nyquist robust stability margin. A systematic and numerically tractable algorithm is proposed for computing the critical perturbation radius needed for the calculation of the stability margin, and the approach is illustrated via examples. Copyright © 2001 John Wiley & Sons, Ltd.     

Robust analysis of LFR systems through homogeneous polynomial Lyapunov functions

In this note, the use of homogeneous polynomial Lyapunov functions (HPLFs) for robust stability analysis of linear systems subject to time-varying parametric uncertainty, affecting rationally the state space matrix, is investigated. Sufficient conditions based on linear matrix inequalities feasibility tests are derived for the existence of HPLFs, which ensure robust stability when the uncertain parameter vector is restricted to lie in a convex polytope. It is shown that HPLFs lead to results which are less conservative than those obtainable via quadratic Lyapunov functions.     

Enhancement of robust performance for fuzzy parametric uncertain time‐delay systems using differential evolution algorithm

This paper proposes a systematic methodology for the enhancement of robust stability and performance of a fuzzy parametric uncertain time‐delay system. A fuzzy parametric uncertain time‐delay system is an example for a linear time‐invariant uncertain time‐delay system with fuzzy coefficients. By using the nearest approximation, these fuzzy coefficients are approximated into crisp sets called intervals to get an interval system. The proposed approach develops the necessary and sufficient stability conditions of interval polynomials for determining the robust stability. Then, by using these developed stability conditions, a set of inequalities in terms of controller parameters are obtained from the closed‐loop characteristic polynomial of fuzzy parametric uncertain time‐delay system. Finally, these inequalities are solved to obtain robust controller with the help of a differential evolution algorithm for an unstable fuzzy parametric uncertain time‐delay system. Consequently, a lead‐lag compensator is constructed based on the frequency domain approach to improve the performance of the fuzzy parametric uncertain time‐delay system. The proposed method has the advantage of less computational complexity and easy to implement on a digital computer. The viability of the proposed methodology is illustrated through a numerical example for its successful implementation. The efficacy of the proposed methodology is also evaluated against the available approach in the literature and the simulation results are successfully implemented for robust stability and performance of fuzzy parametric uncertain time‐delay systems.     

参数不确定性广义周期时变系统的鲁棒稳定性分析

基于广义周期时变系统允许的充分必要条件，提出了参数不确定性广义周期时交系统鲁棒稳定的概念,并得到了该类系统鲁棒稳定的充分必要条件．研究在状态反馈控制下保证闭环系统鲁棒稳定的条件，给出了一族状态反馈鲁棒稳定器的设计方法．引入广义周期时变系统二次稳定的概念，讨论了二次稳定性与鲁棒稳定性的关系．最后通过数值算例说明了所得的主要结果，     

Guaranteed cost control of uncertain nonlinear systems via polynomial lyapunov functions

In this paper, we consider the problem of guaranteed cost control for a class of uncertain nonlinear systems. We derive linear matrix inequality conditions for the regional robust stability and performance problems based on Lyapunov functions which are polynomial functions of the state and uncertain parameters. The performance index is calculated over a set of initial conditions. Also, we discuss the synthesis problem for a class of affine control systems. Numerical examples illustrate our method.     

Robust H∞ performance using lifted polynomial parameter-dependent Lyapunov functions

This paper investigates the robust H _∞ performance of time-invariant linear uncertain systems where the uncertainty is in polytopic domains. Robust H _∞ is checked by constructing a quadratic parameter-dependent Lyapunov function. The matrix associated with this quadratic Lyapunov function is a polynomial function of the uncertain parameters, expressed as a particular polynomial matrix involving κ powers of the dynamic matrix of the system and one symmetric matrix to be determined. The degree of this polynomial matrix function is arbitrary. Finsler's Lemma is used to lift the obtained stability conditions into a larger space in which sufficient stability tests can be developed in the form of linear matrix inequalities. As κ increases, less conservative H _∞ evaluations are obtained. Both continuous and discrete-time systems are investigated. Numerical examples illustrate the method and compare the present results with similar works in the literature.