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.     

融合GPC和QFT对不确定性系统的鲁棒控制

针对广义预测控制(GPC)与定量反馈理论(QFT)的特点,提出了把两种算法融合的鲁棒控制算法。该方法是在对QFT进行修改的基础上,采用双回路控制。内回路采用QFT控制器实现对系统不确定性的控制;外回路采用GPC控制器,实现对系统的各种性能要求并且提高鲁棒性。该方法可以充分利用两种控制理论的优点。最后的仿真结果显示,融合的算法比单独采用其中的任何一种控制算法所取得的控制效果都好。     

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。     

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。     

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.     

The input amplitude saturation problem in QFT: A survey

In this work the input amplitude saturation problem is analysed in the Quantitative Feedback Theory (QFT) framework. This paper reviews previous works in the literature dealing with the input amplitude saturation problem in the presence of an uncertain plant in the frequency domain using QFT. The objective of this paper is to compare the different available approaches and summarize the design process for each case so that this paper can be used as a tutorial; there are six main approaches to this problem. Two of these approaches use the classical two degrees of freedom control scheme for QFT; in both of these, the design constraints of a linear QFT compensator are added in the loop shaping stage: they are added in the first approach to avoid excitation of the actuator saturation and in the second one to guarantee global stability. The other three techniques are considered as anti-windup (AW) approaches. Starting from a base design in QFT with two degrees of freedom, the first AW approach introduces a third degree of freedom that guarantees the stability of the system, allowing for base designs for high performance. The other two AW approaches also introduce a third degree of freedom, but they take simple stability considerations into account and focus on the performance of the system. The last solution consists of using a reference governor technique, which guarantees the computation of a reference signal for an inner control loop that is shaped using QFT in such a way that robust stability will be guaranteed. The reference governor technique is a time domain approach that implies the resolution of an optimization problem. The rest of the approaches are frequency domain techniques based on a loop shaping method in the traditional QFT sense.     

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。     

Interactive parameter space design for robust performance of MISO control systems

This paper presents a method for the design of nonconservative low-order controllers achieving robust performance in the case of multi-input single-output parallel structure plants subject to unstructured uncertainty. The first step is the analytical generation of gain-phase controller bounds, as in quantitative feedback theory (QFT). Then, to avoid the difficult step of QFT loop shaping, which often produces high-order controllers, these bounds are translated into the controller parameter space where the iterative design of low fixed order controllers takes place. This, as well as the design transparency offered by this technique, constitutes appreciable advantages over the other popular robust performance design method of /spl mu/-synthesis. Other important features are the fact that no extra conservatism is introduced by the method presented and the fact that the method is directly compatible with a sequential loop closing strategy. Finally, the direct search optimization of any additional secondary criteria is possible.     

基于INA—QFT的高超声速飞行器鲁棒控制器设计

针对高超声速飞行器数学模型的不确定性,提出基于逆奈氏阵列法设计预补偿器和定量反馈理论设计控制器相结合的方法。该方法首先对相互关联的飞行器三通道进行预补偿,使开环前向通道的逆传递函数矩阵成为对角优势阵。然后根据某型号飞行器俯仰通道多个模型参数变化范围,利用定量反馈理论进行鲁棒控制器设计。线性和非线性仿真结果表明,该方法跟踪效果良好,具有较强的工程应用价值。     

Feedback design for robust tracking and robust stiffness in flight control actuators using a modified QFT technique

The problem of dynamic stiffness of hydraulic servomechanisms has often been recognized as a significant performance issue in a variety of applications, the most notable of which includes flight control actuation. When a hydraulic actuator such as this is operated in position control, an aerodynamic flutter load on the control surface manifests itself as a force disturbance on the system. Although this would appear to be a standard disturbance rejection problem, the disturbance does not enter the system as in the classical sense (i.e. at the plant output) and hence, this problem must be considered in a modified formulation. A hydraulic servomechanism is said to be 'stiff' if it exhibits acceptable rejection of force disturbances within the control bandwidth. In this paper, an approach to feedback design for robust tracking and robust disturbance rejection is developed via the quantitative feedback theory (QFT) technique. As a result, it is shown that reasonable tracking and disturbance rejection specifications can be met by means of a fixed (i.e. non-adaptive), single loop controller. The methodology employed in this development is the sensitivity-based QFT formulation. As a result, robust tracking and robust disturbance rejection specifications are mapped into equivalent bounds on the (parametrically uncertain) sensitivity function; hence, the frequency ranges in which tracking or disturbance rejection specifications dominate become immediately obvious. In this paper, a realistic non-linear differential equation model of the hydraulic servomechanism is developed, the linear parametric frequency response properties of the open loop system are analysed, and the aforementioned QFT design procedure is carried out. Analysis of the closed loop system characteristics shows that the tracking and disturbance rejection specifications are indeed met.     

基于EA／QFT的飞行控制律设计及其稳定性评估

提出特征结构配置和定量反馈理论相结合的鲁俸控制设计方法,并应用该方法对某型飞机横侧向进行控制律设计,然后通过μ分忻对控制律进行稳定性评估。仿真结果表明：该方法使某飞机不仅具有良好解耦效果和动态响应,而且具有较强的鲁棒性。     

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。     

Electrohydraulic force control design of a hardware-in-the-loop load emulator using a nonlinear QFT technique

This paper presents the design of a robust force control system for an electrohydraulic load emulator utilized as part of a hardware-in-the-loop flight simulation experiment. In this application, the force controlled hydraulic actuator is used to artificially recreate in-service loads upon a second hydraulic flight actuator operated in closed-loop position control. Electrohydraulic force control is more difficult than electrohydraulic position tracking because the load dynamics influence the force transfer function in a way that makes it challenging to develop an accurate force tracking system using simple feedback control. Nonlinear quantitative feedback theory (QFT) is applied in this paper to address this issue. First, an effective and robust feedback controller is designed by nonlinear QFT to desensitize the force control loop to nonlinear servovalve flow/pressure effects and typical system uncertainties. A secondary compensator is also designed within the QFT framework to extend the force tracking bandwidth with respect to the load motion. Experiments demonstrate acceptable force tracking performance within the scope of a representative flight-simulation experiment.     

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.     

Automated synthesis of multivariable QFT controller using interval constraint satisfaction technique

Robust controller synthesis of Multi-Input–Multi-Output (MIMO) systems is of great practical interest and their automation is a key concern in control system design. The synthesis problem consists of obtaining a controller that ensures stability and meets a given set of performance specifications, in spite of the disturbance and model uncertainties. In addition to perform the above tasks, a MIMO controller also has to perform the difficult task of minimizing the interaction between the various control loops.Unlike existing manual or convex optimization based Quantitative Feedback Theory (QFT) design approaches, the proposed method gives a controller which meets all performance requirements in QFT, without going through the conservative and sequential design stages for each of the multivariable sub-systems. In this paper, a new, simple, and reliable automated MIMO QFT controllers design methodology is proposed. A fixed structure MIMO QFT controller has been synthesized by solving QFT quadratic inequalities of robust stability and tracking specifications. The quadratic inequalities (constraints) are posed as Interval Constraint Satisfaction Problem (ICSP). The constraints are solved by constraint solver — RealPaver. The main feature of this method is that the algorithm finds all the solutions to within the user-specified accuracy. The designed MIMO QFT controllers are tested on the experimental setup designed by Educational Control Product (ECP) Magnetic Levitation Setup ECP 730. From the experimental results presented, it is observed that, the designed controller satisfies the desired performance specifications. It is also observed that, the interactions between the loops are within the specified limits. The robustness of the designed controllers are verified by putting extra weights on the magnets.     

On quantitative feedback design for robust position control of hydraulic actuators

This paper discusses several practical issues related to the design of robust position controllers for hydraulic actuators by quantitative feedback theory (QFT). Important properties of the hydraulic actuator behavior, for control system design, are identified by calculating a family of equivalent frequency responses from acceptable nonlinear input–output data. The role of this modeling approach towards reducing over-design by decreasing the sizes of the QFT plant templates is described. The relationship between the geometry of the QFT bounds and the complexity of the robust feedback law is examined through the development of two low-order controllers having characteristics suitable for different applications. Experimental test results demonstrate the extent that each QFT controller is able to maintain robustness against variations in the hydraulic system dynamics that occur due to changing load conditions as well as uncertainties in the hydraulic supply pressure, valve spool gain, and actuator damping.     

H∞ multiple objective robust controllers forinfinite-horizon single measurement single control input problems

A graphical method is introduced that solves the robust infinite horizon H_∞ multiple-objective control problem for single measurement, single control input systems. The solution is obtained by describing boundaries on the Nichols chart. Each boundary defines the set of all admissible gain and phase values for the loop transmission at a given frequency. These boundaries are obtained by using the well-known parameterization of all the solutions for a single objective H_∞ control problem. The new method links between the theories of H_∞ and quantitative feedback theory (QFT). It can be used to design robust H_∞ controllers with almost no overdesign, and it provides a convenient solution of H_∞ multiple-objective problems that are difficult to solve by the standard four-block setting. It also extends the methods of SISO QFT to deal with a vector of disturbances. The latter may affect the controlled plant through any input coupling matrix and not necessarily through the controller input, or the measurement output     

Self-tuning of quantitative feedback theory for force control of an electro-hydraulic test machine

The aim of this paper is to design and fabricate an electro-hydraulic test machine (EHTM) for conducting performance and stability test of force and/or position control in the bench system and to propose a robust adaptive controller—the self-tuning quantitative feedback theory (STQFT)—in order to improve the force control performance of electro-hydraulic actuators (EHAs). By using the gradient descent method to adjust the QFT parameters, the novel STQFT controller is able to adapt to a wide range of working conditions. Experiments were carried out to evaluate the effectiveness of the proposed control method applied to the EHTM.     

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。