An improved non‐sequential multi‐input multi‐output quantitative feedback theory design methodology

This paper presents an improved non‐sequential multi‐input multi‐output (MIMO) Quantitative Feedback Theory (QFT) design methodology for uncertain systems. A non‐sequential MIMO QFT stability theorem is derived that serves as the basis for an improvement of the design methodology, whereby it can be successfully applied to non‐minimum phase systems, albeit with a degree of conservatism partially inherent in independent and decentralized design methodologies. The results reduce the conservatism in a non‐sequential MIMO QFT design and provide insight into the plant cases for which the methodology can be successfully applied. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

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.     

Analytical formulation to compute QFT bounds: The envelope method

This paper describes an analytical formulation to compute quantitative feedback theory (QFT) bounds in one‐degree‐of‐freedom feedback control problems. The new approach is based on envelope curves and shows that a QFT control specification can be expressed as a family of circumferences. Then, the controller bound is defined by the envelope curve of this family and can be obtained as an analytical function. This offers the possibility of studying the QFT bounds in an analytical way with several useful properties. Gridding methods are avoided, resulting in a lower computational effort procedure. The new formulation improves the accuracy of previous methods and allows the designer to calculate multivalued bounds. Copyright © 2009 John Wiley & Sons, Ltd.     

Multi-input/single-output computer-aided control design using the quantitative feedback theory

The quantitative feedback theory is an engineering design technique of uncertain feedback systems having robust stability and robust performance specifications. The crux of the quantitative feedback theory is a transformation of robust stability and robust performance specifications into domains in the complex plane, referred to as bounds, where a nominal loop transmission should lie within. To date, a quantitative feedback theory design is being carried out using manual (i.e. graphical) procedures or search algorithms. This paper shows that there exists a formal map from the uncertain plant and each closed-loop specification to these bounds. In particular, it is shown that each map has a closed form consisting of a quadratic inequality. These maps greatly simplify the computational aspects of the quantitative feedback theory in design of single-loop feedback systems. Based on this new development, a simple-to-implement, efficient computer algorithm is outlined.     

Simultaneous meeting of robust control specifications in QFT

Simultaneous meeting of different‐nature feedback control specifications requires special attention, particularly in the presence of uncertainties. This paper introduces some ideas to obtain a feasible set of QFT bounds, analysing the compatibility of the desired control specifications and the model uncertainty. It studies general robust feedback requirements and their mapping on QFT bounds through quadratic inequalities. Analysing them, it is possible to infer the bound typology with dependence on the model of each particular specification and the uncertainty size. Two bound typologies (amongst three categories: upper, outer and lower bounds) are possible for each type of control objective. On this basis, some general hints are established to guarantee compatible bounds at each frequency, before designing the controller. Copyright © 2003 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。     

An optimal approach to output‐feedback robust model predictive control of LPV systems with disturbances

An observer‐based output feedback predictive control approach is proposed for linear parameter varying systems with norm‐bounded external disturbances. Sufficient and necessary robust positively invariant set conditions of the state estimation error are developed to determine the minimal ellipsoidal robust positively invariant set and observer gain through offline computation. The quadratic upper bound of state estimation error is updated and included in an ‐type cost function of predictive control to optimize transient output feedback control performance. Recursive feasibility of the dynamic convex optimization problem is guaranteed in the proposed predictive control strategy. With the input‐to‐state stable observer, the closed‐loop control system states are steered into a bounded set. Simulation results are given to demonstrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Construction of linear time‐invariant equivalent plants for nonlinear continuous‐time and sampled‐data systems

In this paper, a technique is presented for constructing the so‐called linear time‐invariant equivalent (LTIE) plants used in the nonlinear quantitative feed back theory (QFT) approach. The proposed technique is applicable equally well to both continuous‐time and sampled‐data nonlinear plants described by nonlinear integro‐differential equation and nonlinear autoregressive moving average with exogenous inputs (NARMAX) models, respectively. The technique uses inclusion function and interval integration tools of interval analysis. A nonlinear chemical reactor example is used to illustrate the procedure for both nonlinear continuous‐time and sampled‐data systems, and found to yield satisfactory results in both cases. Copyright © 2003 John Wiley & Sons, Ltd.     

A QFT SUBSONIC ENVELOPE FLIGHT CONTROL SYSTEM DESIGN

An aircraft's response to control inputs varies widely throughout its full flight envelope. Furthermore, the aircraft configuration impacts control response through variations in centre of gravity and moments of inertia. Quantitative feedback theory (QFT) is a robust control system design method which provides a full-envelope flight control system design and gives the engineer direct control over compensator order and gain. A full subsonic flight envelope FCS is designed for using QFT for four representative aircraft configurations. Flying qualities are embedded in the longitudinal design by using a control variable which varies with the aircraft's energy state throughout the flight envelope. Linear simulations with realistically large control inputs are used to validate the design. © 1997 by John Wiley & Sons, Ltd. This paper was prepared under the auspices of the US Government and it is therefore not subject to copyright in the US.     

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。     

Quantitative feedback theory with applications in welding

Two different control systems were developed using quantitative feedback theory for weld quality improvement. The first application to be discussed was designed for the resistance pinch welding process and uses electrode displacement and force as feedback parameters. A correlation between weld quality and electrode displacement is established for constant electrode force. The system is capable of producing repeatable welds of consistent quality, with wide variations in weld parameters. This is the first time feedback control has been successfully applied to pinch welding. The second example presented in this paper was developed for penetration control of the gas-tungsten-arc welding process. The feedback signal is obtained by measuring the amount of light emitted from the back side of the weld. Welds of constant penetration have been demonstrated in tests with travel speeds varying from 1.5 to 6 inches per minute and with 200 per cent changes in part thickness.     

Robust control of water quality in intensive aquaculture using multi-variable quantitative feedback theory: From an Indian context

This paper addresses the problem of controlling turbidity, dissolved oxygen, ammonium-ion concentration, and water-temperature to maintain the desired water quality in an intensive aquaculture plant. The research is carried out to fit into the present scenario of intensive aquaculture in India. The plant model along with uncertain parameters are derived using physical laws and the data acquired from an aquaculture pond in Assam, India. A pre-compensated multi-variable quantitative feedback theory (QFT)-based fully populated robust matrix controller is proposed to mitigate the control challenge. A novel method is used to design the pre-compensator to enhance the diagonal dominance of plant transfer function matrix. The desired robust stability, reference tracking, and sensitivity specifications are fulfilled by the proposed QFT-based robust controller despite the parametric uncertainty. The effectiveness of the proposed method is validated through numerical simulation. A comparative study against a $H_{\infty }$ controller shows that the proposed controller strategy gives a satisfactory performance compared to it.     

A robust synthesis methodology for neutrally stable uncertain SISO plants under input amplitude saturation

In this article, a control system design methodology for neutrally stable, uncertain, single-input single-output plants under input amplitude saturation is presented. Based on Horowitz's original three degree of freedom design and extensions developed afterwards, this approach concentrates on neutrally stable, higher type, uncertain plants. A three degree of freedom non-interfering loop structure is used for the synthesis, along with the structure of the additional, independent loop transmission around the saturating element proposed for designing the third degree of freedom H(s). Robust stability and performance are established. The circle criterion, the describing function and non-overshooting conditions are utilised to obtain design constraints. Finally, all these design constraints are expressed in frequency domain bounds and synthesis follows from loop shaping methods such as quantitative feedback theory.     

A model reference quantitative feedback design theory with application to turbomachinery

A new decentralized robust control design framework, model reference quantitative feedback design (MRQFD), is developed for the design of the MIMO parametric uncertain control systems. An internal model reference loop is proposed to obtain the achievement of generalized diagonal dominance (GDD) and the reduction of uncertainty in the resultant compensated internal loop system. Based on nonnegative matrix theory, a useful design guide is derived to achieve the GDD condition for the internal model reference loop. Then a sensitivity-based quantitative feedback design (QFD) method is developed and used to solve the resulting series of single-loop QFD problems. The MIMO quantitative specifications are guaranteed to be satisfied by the proposed design framework for largely uncertain systems. A successful application to the design of a robust multivariable controller for the Allison PD-514 aircraft turbine engine is presented to demonstrate the effectiveness of the methodology developed here.     

Computation of QFT bounds for robust tracking specifications

An algorithm is proposed for generation of QFT controller bounds to achieve robust tracking specifications. The proposed algorithm uses quadratic constraints and interval plant templates to compute the bounds, and presents several improvements over existing QFT tracking bound generation algorithms. The proposed algorithm (1) guarantees robustness against template inaccuracies, (2) guarantees robustness against phase discretization, (3) provides a posteriori error estimates, (4) is computationally efficient, achieving a reduction in flops and execution time, typically by 1-2 orders of magnitude. The algorithm is demonstrated on an aircraft example having five uncertain parameters.     

基于LMI的输出反馈鲁棒完整性控制器设计

完整性是容错控制的一个重要研究方向,不确定系统的鲁棒完整性研究具有很强的实际意义.本文基于[0,σ]故障模型和线性矩阵不等式(LMI)方法,提出了参数不确定系统的输出反馈鲁棒完整性控制器存在的充分条件,通过求解两个矩阵不等式获得控制器,使闭环系统在传感器发生故障时仍然保持二次稳定,并对参数不确定性具有鲁棒性.数值示例说明了该方法的有效性.     

基于定量反馈理论的时滞系统自抗扰控制参数整定

工业过程对象普遍存在时滞、模型参数不确定性和外部扰动多等特点,传统Smith预估控制方法难以设计出满足期望性能的鲁棒控制器.针对模型参数不确定性和外部扰动,本文采用自抗扰控制技术进行估计和补偿.针对系统存在时滞的特点,本文提出改进Smith预估器结构,提升扩张状态观测器对于扰动估计的实时性.在此基础上,本文以一阶时滞系统为例提出了控制器参数整定方法.首先根据最优参数选取准则确定预估器模型,然后在等效模型框架下采用定量反馈理论整定自抗扰控制器参数,确保控制系统达到预期性能指标.在仿真实验中,将所提出方法与几种常见时滞系统控制方法进行比较,通过设定值跟踪、抗扰及蒙特卡罗实验验证了所提出方法具有良好抗扰能力与鲁棒性.     

弹性飞机的QFT控制器设计

以某弹性飞机纵向模型为例,考虑模型的不确定性及外部扰动,应用定量反馈理论设计了其俯仰姿态保持系统.仿真结果表明,利用该理论方法设计的控制器能很好地抑制弹性飞机的结构弹性变形,具有良好的鲁棒性,并取得了满意的控制效果,证明了该方法在弹性飞机控制律设计中的有效性和实用性.