基于多环QFT的飞行仿真转台鲁棒控制

阐述了定量反馈理论(QFT)的基本原理及设计方法,并给出了某型飞行仿真转台的QFT控制器设计实例。为了有效地抑制高频测量噪声对系统的干扰,以及避免系统的高频不确定性,在单环QFT控制的基础上,引入了基于多环QFT的鲁棒控制。理论分析和仿真实验表明,这种多环QFT控制可以明显地缩减控制器的带宽,使系统具有很强的抗高频测量噪声的性能,达到了理想的控制效果。该方法在转台的控制上取得了成功的应用,具有广泛的应用价值。     

基于Matlab语言定量反馈控制器的分析与设计

对定量反馈理论（QFT）的基本原理进行了介绍和利用Matlab语言工具箱进行设计的基本方法，Matlab通用QFT工具箱为用户进行QFT控制器的设计提供了有利的工具，文章就以典型二阶系统为例进行QFT控制器的设计，仿真的结果表明定量反馈理论在不确定系统设计中有着经典控制理论无法替代的性能。     

基于多环QFT的高超声速飞行器鲁棒控制

阐述了定量反馈理论(QFT)的基本原理和设计方法,针对超燃冲压发动机不同工作状态时高超声速飞行器不确定性模型,应用多环QFT设计了高超声速飞行器纵向飞行控制系统;仿真结果表明,运用QFT方法设计的控制系统不仅具有良好的跟踪性能和抗干扰性能,而且能够很好地解决飞行控制系统由于模型参数具有不确定性而造成的控制系统鲁棒性设计问题,并从工程应用角度为高超飞行器纵向飞行控制系统提供了一种鲁棒控制设计方案。     

QFT与神经网络并行控制研究

阐述了定量反馈理论(Quantitative Feedback Theory，简称QFT)的基本原理及设计步骤，并给出了设计实例。在QFT的基础上，提出了一种QFT和神经网络并行控制的方案，以QFT为主控制器，神经网络进行动态误差补偿。QFT控制能克服对象的参数不确定性，保障系统的鲁棒性；神经网络可以进一步提高系统的跟踪精度。仿真表明，这种方法实现了QFT控制和神经网络控制的完美结合，很适合高精度伺服系统的鲁棒控制。     

定量反馈理论在重构飞行器控制中的应用

定量反馈理论(quantitative feedback theory,QFT)作为一种频率域鲁棒控制技术,综合考虑了对象的不确定性范围和对系统的性能指标要求,以定量方式在Nichols图上展开分析与设计,从而保证了设计结果具有稳定鲁棒性;而当某处喷管失效时,作用在飞行器上的控制力矩所受的影响可看作是不确定对象鲁棒性问题的扩展,因此,考虑喷管故障时的重构飞行控制也可用QFT方法进行分析与设计;在讨论QFT原理与应用的基础上,以某飞行器的飞行控制设计为例,对鲁棒和重构飞行控制进行了分析、研究与设计,获得了满意的设计结果。     

基于QFT和ZPETC的高精度鲁棒跟踪控制器设计

阐述了定量反馈理论(QFT)和零相差跟踪控制器(ZOETC)的基本原理及设计方法，并给出了设计实例。在QFT和ZPETC的基础上，提出了一种是实现高精度鲁棒跟踪控制的方案，采用QFT控制保证系统的鲁棒性，通过ZPETC提高系统的跟踪精度。仿真表明，这种方法实现了QFT和ZPETC的完美结合，很适合高精度跟踪系统的鲁棒控制。     

定量反馈理论发展综述

定量反馈理论是一种基于频域的鲁棒控制理论,可以用于具有高度不确定性的单变量线性/非线性系统、多变量线性/非线性系统控制器设计.本文概述了定量反馈理论的基本原理、设计过程以及特点.总结了近年来QFT在提高系统性能、鲁棒稳定性、自动设计以及应用等方面的最新研究进展,并且给出了一些已有的理论应用成果.最后讨论了进一步的研究方向.     

一种基于QFT的锅炉水位鲁棒控制及分析

在工业实际应用中,锅炉汽包水位在系统动态特性发生较大变化并且受到各种干扰因素影响时,模型的参数将发生变化,成为一个不确定系统.基于此种情况,本文应用定量反馈理论(QFT),提出了基于QFT的锅炉水位鲁棒控制方案,即内回路采用小积分常数比例积分控制器快速消除给水扰动,外回路应用QFT理论设计出主控制器并对主控制器的PID参数进行了整定,以保证水位无静态偏差,仿真结果表明,此种控制方法能够达到比较满意的效果.     

基于灵敏度理论的μ/QFT鲁棒飞行控制器设计

针对具有大的不确定性和非线性特性的对象,研究了一种综合μ方法和定量反馈理论(QFT)的鲁棒控制器的设计方法,使闭环系统具有良好的鲁棒性;该方法在利用μ理论设计初始控制器的基础上,采用QFT方法进行优化整形;其中,为便于μ方法权函数的选择和QFT边界曲线的计算,引进鲁棒控制中的灵敏度设计方法进行分析;最后,通过对一个实例的仿真分析验证了该方法的有效性和可行性。     

基于QFT的无人机纵向飞行控制系统设计

介绍了定量反馈理论(QFT)的基本原理和设计步骤;定量反馈理论作为一种新颖的频率域鲁棒控制技术,综合考虑了对象的不确定性范围和系统的性能指标要求,以定量方式进行分析设计,从而保证了设计结果具有稳定鲁棒性和性能鲁棒性;无人机飞行过程中具有较强的不确定性,气动参数会不断发生变化,运用QFT对无人机纵向飞行控制系统进行设计,可以很好解决飞行控制系统中的不确定性问题;仿真结果显示,QFT设计的控制器能够很好地满足无人机鲁棒稳定性指标和跟踪性能,符合纵向控制的要求。     

Stability of quantitative feedback designs and the existence of robust QFT controllers

Quantitative feedback theory (QFT) has received much criticism for a lack of clearly stated mathematical results to support its claims. Considered in this paper are two important fundamental questions: (i) whether or not a QFT design is robustly stable, and (ii) does a robust stabilizer exist. Both these are precursors for synthesizing controllers for performance robustness. Necessary and sufficient conditions are given to resolve unambiguously the question of robust stability in SISO systems, which in fact confirms that a properly executed QFT design is automatically robustly stable. This Nyquist-type stability result is based on the so-called zero exclusion condition and is applicable to a large class of problems under some simple continuity assumptions. In particular, the class of uncertain plants include those in which there are no right-half plane pole-zero cancellations over all plant uncertainties. A sufficiency condition for a robust stabilizer to exist is derived from the well-known Nevanlinna-Pick theory in classical analysis. Essentially the same condition may be used to answer the question of existence of a QFT controller for the general robust performance problem. These existence results are based on an upper bound on the nominal sensitivity function. Also considered is QFT design for a special class of interval plants in which only the poles and the DC gain are assumed uncertain. The latter problem lends itself to certain explicit computations that considerably simplify the QFT design problem.     

Some results in nonlinear QFT

Nonlinear QFT (quantitative feedback theory) is a technique for solving the problem of robust control of an uncertain nonlinear plant by replacing the uncertain nonlinear plant with an ‘equivalent’ family of linear plants. The problem is then finding a linear QFT controller for this family of linear plants. While this approach is clearly limited, it follows in a long tradition of linearization approaches to nonlinear control (describing functions, extended linearization, etc.) which have been found to be quite effective in a wide range of applications. In recent work, the authors have developed an alternative function space method for the derivation and validation of nonlinear QFT that has clarified and simplified several important features of this approach. In particular, single validation conditions are identified for evaluating the linear equivalent family, and as a result, the nonlinear QFT problem is reduced to a linear equivalent problem decoupled from the linear QFT formalism. In this paper, we review this earlier work and use it in the development of (1) new results on the existence of nonlinear QFT solutions to robust control problems, and (2) new techniques for the circumvention of problems encountered in the application of this approach. Copyright © 2001 John Wiley & Sons, Ltd.     

On characterizing sensitivity-based and traditional formulations for quantitative feedback theory

Recent developments in quantitative feedback theory include the 'new formulation' approach in which a robust performance and robust stability problem, similar to Horowitz's traditional QFT formulation, is developed in terms of sensitivity function bounds. The motivation for this approach was to provide the basis for a more rigorous treatment of nonminimum phase systems and/or plants characterized by mixed parametric and non-parametric uncertainty models. However, it has been found in practice that the sensitivity-based formulation exhibits some unique behaviour, i.e. in terms of the open loop design bounds obtained for various choices of nominal plant. Experience has shown that these bounds will dominate (i.e. are more conservative than) the corresponding traditional QFT bounds for the same problem; it has also been observed that the degree to which this occurs varies with choice of the nominal plant. Further, it has been found that the choice of nominal, in certain cases, can lead to a problem which is infeasible with respect to Bode sensitivity (i.e. requiring S(jomega) < 1 as omega infinity), while the traditional QFT problem remains feasible. Heretofore, this behaviour has not been fully explained. In this paper, these issues are characterized in the simplest possible setting, focusing primarily on the behaviour at zero phase angle. A 'modified' sensitivity-based QFT formulation is proposed here in which limitations on the choice of nominal plant are clearly delineated; this formulation results in open loop design bounds which are equivalent to the traditional QFT problem at zero phase angle, while over-bounding them elsewhere. The modified formulation is also shown to meet the same necessary condition for Bode feasibility as traditional QFT. In conclusion, these issues are demonstrated by means of a basic example.     

An interactive approach to template generation in quantitative feedback theory methodology

The calculation of templates associated with plant uncertainty at some frequencies is one of the first steps in the design of robust controllers using the quantitative feedback theory (QFT) methodology. If the QFT designer does not calculate the templates correctly, the design will be unnecessarily conservative, or even erroneous. This paper describes the main features of Template Interactive Generator (TIG), a new, free software tool that calculates the templates of plants with special parameter dependences, such as interval plants and plants with affine parametric uncertainty. The paper also includes two examples that illustrate the ease of use and the high level of interactivity of TIG. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A combined QFT/H ∞ design technique for TDOF uncertain feedback systems

A new way of incorporating QFT principles into H X -control design techniques for solving the two-degrees of freedom feedback problem with highly uncertain plants is developed. The proposed practical design approach consists of two stages. In the first stage, the robustness problem, due to plant uncertainties, is solved by H X -norm optimization. In this stage, the controller inside the loop (the first degree of freedom) is designed, with the ultimate goal of minimizing the cost of feedback. Minimization of the sensor white noise amplification at the input to the plant is also performed using QFT principles. In the second stage of the design, the prefilter outside the loop (the second degree of freedom), is used to achieve the tracking specifications by conventional classical control theory, as practiced by the QFT design procedure. The combined QFT/H X design procedure for single input-single output (SISO) feedback systems is directly applicable to multi input-multi output (MIMO) feedback uncertain systems. The efficiency of the proposed technique is demonstrated with SISO and MIMO design examples for higly uncertain plants.     

Generation of QFT bounds for robust tracking specifications for plants with affinely dependent uncertainties

This paper presents an efficient algorithm for the generation of QFT bounds for robust tracking specifications for plants with affinely dependent uncertainties. For a plant with m affinely dependent uncertainties, it is shown that whether a point in the Nichols chart lies in the QFT bound for a robust tracking specification at a given frequency can be easily tested by computing the maxima and minima of m2^m?1 univariate functions corresponding to the edges of the parameter domain box. This test procedure is then utilized along with a pivoting procedure to trace out the boundary of the QFT bound with a prescribed accuracy or resolution. The developed algorithm has the advantages that (1) it is efficient in the sense that it requires less floating point operations than other existing algorithms in the literature; (2) it can avoid the unfavorable trade‐off between the computational burden and the accuracy of the computed QFT bounds that has arisen in the application of many existing QFT‐bound generation algorithms; (3) the maximum allowable error of the computed QFT bound can be prespecified; and (4) it can compute QFT bounds with multi‐valued boundaries. Numerical examples are given to illustrate the proposed algorithm and its computational superiority. Copyright © 2010 John Wiley & Sons, Ltd.     

QFT design for uncertain non-minimum phase and unstable plants revisited

Design method for uncertain non-minimum phase and unstable plants in the quantitative feedback theory (QFT) developed by Horowitz and Sidi is revisited in this paper. It is illustrated that the existing method may not work since some design rules have not been clearly specified by several examples including non-minimum phase plants and unstable plants. Then stability of a new nominal plant is carefully examined and analysed, and an improved design method is presented. The result in this paper provides mathematical justification of the QFT design procedure for nonminimum phase and unstable plants in Horowitz and Sidi (1978) and Horowitz (1992).     

Robust multiple model adaptive control: Modified using ν‐gap metric

A new robust adaptive control method is proposed, which removes the deficiencies of the classic robust multiple model adaptive control (RMMAC) using benefits of the ν‐gap metric. First, the classic RMMAC design procedure cannot be used for systematic design for unstable plants because it uses the Baram Proximity Measure, which cannot be calculated for open‐loop unstable plants. Next, the %FNARC method which is used as a systematic approach for subdividing the uncertainty set makes the RMMAC structure being always companion with the µ‐synthesis design method. Then in case of two or more uncertain parameters, the model set definition in the classic RMMAC is based on cumbersome ad hoc methods. Several methods based on ν‐gap metric for working out the mentioned problems are presented in this paper. To demonstrate the benefits of the proposed RMMAC method, two benchmark problems subject to unmodeled dynamics, stochastic disturbance input and sensor noise are considered as case studies. The first case‐study is a non‐minimum‐phase (NMP) system, which has an uncertain NMP zero; the second case‐study is a mass‐spring‐dashpot system that has three uncertain real parameters. In the first case‐study, five robust controller design methods (H₂, H_∞, QFT, H_∞ loop‐shaping and µ‐synthesis) are implemented and it is shown via extensive simulations that RMMAC/ν/QFT method improves disturbance‐rejection, when compared with the classic RMMAC. In the second case‐study, two robust controller design methods (QFT and mixed µ‐synthesis) are applied and it is shown that the RMMAC/ν/QFT method improves disturbance‐rejection, when compared with RMMAC/ν/mixed?µ. Copyright © 2010 John Wiley & Sons, Ltd.     

GENERATION OF EXACT QFT BOUNDS FOR PLANTS WITH AFFINELY DEPENDENT UNCERTAINTIES

This paper presents an efficient method for the generation of exact QFT bounds for robust sensitivity reduction and gain‐phase margin specifications for plants with affinely dependent uncertainties. It is shown that, for a plant with m affinely dependent uncertainties, the exact QFT bounds for robust sensitivity reduction and gain‐phase margin specifications at a given frequency and controller phase can be computed by solving m^2m‐1 bivariate polynomial inequalities corresponding to the edges of the parameter domain box. Moreover, the solution set for each bivariate polynomial inequality can be computed by solving for the real roots of one fourth‐order and six second‐order polynomials. This avoids the unfavorable trade‐off between the computational burden and the accuracy of QFT bounds that has arisen in the application of many existing QFT bound generation algorithms. Numerical examples are given to illustrate the proposed method and its computational superiority.     

Quantitative feedback design for sampled-data systems

In quantitative feedback theory (QFT) the plant uncertainty is defined by a set P = {P} ofpossible plants. The problem is to guarantee that the system response is in a specified acceptable set A, for all P in P. QFT has been developed for large classes of plants imbedded in continuous feedback structures. This paper extends QFT to sampled-data structures. A central problem is to find the minimum sampling frequency (ω_s)_min needed. The greater the plant uncertainty and the narrower the performance tolerances, the larger must ( ω_s)_min be. The detailed design procedure parallels very closely that for continuous systems, by using the complex variable w, which maps the unit circle in the z-domain to the imaginary axis in the w-domain.