Non‐diagonal MIMO QFT controller design reformulation

This paper presents a reformulation of the full‐matrix quantitative feedback theory (QFT) robust control methodology for multiple‐input–multiple‐output (MIMO) plants with uncertainty. The new methodology includes a generalization of previous non‐diagonal MIMO QFT techniques; avoiding former hypotheses of diagonal dominance; simplifying the calculations for the off‐diagonal elements, and then the method itself; reformulating the classical matrix definition of MIMO specifications by designing a new set of loop‐by‐loop QFT bounds on the Nichols Chart, which establish necessary and sufficient conditions; giving explicit expressions to share the load among the loops of the MIMO system to achieve the matrix specifications; and all for stability, reference tracking, disturbance rejection at plant input and output, and noise attenuation problems. The new methodology is applied to the design of a MIMO controller for a spacecraft flying in formation in a low Earth orbit. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Simultaneous automated design of structured QFT controller and prefilter using nonlinear programming

This paper describes a nonlinear programming‐based robust design methodology for controllers and prefilters of a predefined structure for the linear time‐invariant systems involved in the quantitative feedback theory. This controller and prefilter synthesis problem is formulated as a single optimization problem with a given performance optimization objective and constraints enforcing stability and various specifications usually enforced in the quantitative feedback theory. The focus is set on providing constraints expression that can be used in standard nonlinear programming solvers. The nonlinear solver then computes in a single‐step controller and prefilter design parameters that satisfy the prescribed constraints and maximizes the performance optimization objective. The effectiveness of the proposed approach is demonstrated through a variety of difficult design cases like resonant plants, open‐loop unstable plants, and plants with variation in the time delay. Copyright © 2016 John Wiley & Sons, Ltd.     

Quantitative feedback control for multivariable model matching and disturbance rejection

This article extends two recent contributions in the field of quantitative feedback theory to the multivariable case. They concern the model matching and the measured disturbance rejection problems. The model matching problem is a tracking control problem with specifications given as acceptable deviations from an ideal response. The measured disturbance rejection problem balances feedback and feedforward actions to reject disturbances. Both perspectives present advantages over classical quantitative feedback theory techniques in certain situations. This paper develops the necessary tools to solve both control problems in the case of multi‐input multi‐output plants. In particular, it shows how to derive nonconservative controller bounds for each of the single‐input single‐output control problems in which the overall multivariable problem is divided. The result is a systematic controller design methodology for multi‐input multi‐output plants with structured uncertainty. The application of the technique to the well‐known quadruple‐tank process illustrates the benefits of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

Decentralised controller design based on structured singular values

In this study, structured singular values are used in a different way from those commonly used in the robust control literature. It is shown that subject to conditions based on structured singular values, each local area controller can be designed independently. A MATLAB? program is developed to plot inverse structured singular values of multi input multi output (MIMO) system relative error matrix. This plot can be used to predict the stability of the global system with decentralised controller. Therefore decentralised controller design problem can be translated into an equivalent problem of decentralized controller design for a MIMO control system.     

Multiple Fuzzy Relation and Its Application to Coupled Fuzzy Control

Using semi‐tensor product (STP) of matrix, this paper investigates the fuzzy relation of multiple fuzzy and uses this to design coupled fuzzy control is designed. First of all, under the assumption that the universe of discourse is finite, a fuzzy logical variable can be expressed as a vector, which unifies the expression of elements, subsets, and fuzzy subsets of a universe of discourse. Then, the matrix expression of set mappings is naturally extended to fuzzy sets. Second, based on STP, logic‐based matrix addition and product are proposed. These are particulary useful for the calculation of compounded fuzzy relations. Third, a dual fuzzy structure is introduced, which assures the finiteness of the universe of discourse, and is used for fuzzification and defuzzification. Finally, using the results obtained, a new technique is developed to design a coupled fuzzy controller for multi‐input multi‐output (MIMO) systems with coupled multiple fuzzy relations.     

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.     

Quantitative non‐diagonal controller design for multivariable systems with uncertainty

The loop coupling reduction of multivariable systems under the presence of plant uncertainty is currently a most discussed topic. Following the ideas suggested by Horowitz, in this paper the role played by the non‐diagonal controller elements is analysed in order to state a design methodology. Thus, the definition of a coupling matrix and a quality function of the non‐diagonal elements come into use to quantify the amount of loop interaction and to design the controllers, respectively. This yields a criterion that makes possible to propose a sequential design methodology of the fully populated matrix controller, in the quantitative feedback theory (QFT) robust control frame. Finally, a real example with the heat exchanger of a pasteurization plant is included to show the practical use of this technique. Copyright © 2002 John Wiley & Sons, Ltd.     

非匹配不确定系统的显式反步变结构控制

研究非线性多输入多输出不确定系统在非匹配条件下的鲁棒输出跟踪问题.基于相对阶的假设,给出了多输入多输出不确定系统的标准型;进而结合反步设计方法和变结构控制方法,提出一种非匹配条件下非线性不确定系统鲁棒输出跟踪问题的显式反步变结构控制器设计方法.所给跟踪算法不仅只由不确定性的变化范围直接确定,而且有效地克服了现有反步设计算法因隐式递推关系和复杂偏导数计算给实时控制带来的困难.     

FAULT TOLERANT CONTROL OF FLEXIBLE SMART STRUCTURES USING ROBUST DECENTRALIZED FAST OUTPUT SAMPLING FEEDBACK TECHNIQUE

This paper presents the modeling, design and simulation of a Robust Decentralized Fast Output Sampling (RDFOS) feedback controller for the vibration control of a smart structure (flexible cantilever beam) when there is actuator failure. The beam is divided into 8 finite elements and the sensors / actuators are placed at finite element positions 2, 4, 6, and 8 as collocated pairs. The smart structure is modeled using the concepts of piezoelectric theory, Euler‐Bernoulli beam theory, Finite Element Method (FEM) techniques and the state space techniques. Four multi‐variable state‐space models of the smart structure plant are obtained when there is a failure of one of the four actuators to function. The effect of failure of one of the piezo actuators to function during the vibration of the beam is observed. The tip displacements, open and closed loop responses with and without the controller are observed. For all of these models, a common stabilizing state feedback gain F is obtained. A robust decentralized fast output sampling feedback gain L which realizes this state feedback gain is obtained using the LMI approach. In this designed control law, the control inputs to each actuator of the multi‐model representation of the smart structure is a function of the output of that corresponding sensor only and the gain matrix has got all off‐diagonal terms zero and this makes the control design a robust decentralized one. Then, the performance of the designed smart system is evaluated for Active Vibration Control (AVC). The robust decentralized FOS controller obtained by the designed method requires only constant gains and hence may be easier to implement in real time.     

Quantitative design method for MIMO uncertain plants to achieve prescribed diagonal dominant closed-loop minimum-phase tolerances

A quantitative design method for multi-input multi-output linear time-invariant feedback systems for plants with large uncertainty has been presented by Horowitz ( 1982), and by Yaniv and Horowitz ( 1986). This design method is developed here to guarantee minimum-phase closed-loop diagonal elements for systems with basically non-interacting (Horowitz and Loecher 1981) off-diagonal closed-loop tolerances. The advantage of this design is that with minimum-phase transfer functions, a very important class of time-domain specifications can be translated to the frequency domain, as shown by Krishman and Cruickshanks ( 1977) and by Horowitz ( 1976). The attractive properties of this design method are: (a) the problem is reduced to a successive single-loop design with no interaction between the loops, and no iterations are necessary; (b) the technique can be applied to all n × n plants P with P^?1 having no poles in the right-half plane, and satisfying some conditions described in § 5; (c) the procedure is interactive with n steps for an n × n MIMO plant, and in each step, one of the elements of the diagonal feedback compensation and one row of the prefilter matrix are designed.     

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     

MIMO网络控制系统的控制器设计

研究了长时延有界的情况下,多输入多输出网络控制系统发生传感器故障时的控制器设计问题。首先,利用容错控制的思想建立了多输入多输出网络控制系统发生传感器故障时的模型。在此基础上,借助切换系统的理论,分析了闭环网络控制系统的稳定性,用线性矩阵不等式（LMI）形式给出了多输入多输出网络控制系统渐近稳定的充分条件和控制器的设计形式。仿真结果表明,该方法可以对多输入多输出网络控制系统中传感器故障问题进行有效的容错控制。     

Input/Output Decoupling of Square Linear Systems by Dynamic Two‐Parameter Stabilizing Control

Analytical expressions of the free parameters of a two‐parameter stabilizing control (TPSC), solving an input/output (I/O) decoupling problem, are presented, and stability conditions are given. Multi‐input‐multi‐output (MIMO), proper, lumped and linear time invariant (LTI) systems are considered. These systems have stabilizable and detectable realizations. The separation principle is applied to design a dynamic output control in a controller‐observer feedback configuration. The I/O relation of the overall system is equivalent to a subsystem, in which the I/O decoupling problem has a solution. Also, if the state dimension of the plant is even, and is double the input dimension of the plant, then coprime factorizations of the plant used for the stabilizing controllers are proposed. The results are illustrated through an example.     

Stabilization of an unstable tubular reactor by nonlinear passive output feedback control

The multiple–input multiple–output (MIMO) output feedback (OF) control problem of an exothermic multi-jacket tubular open-loop unstable reactor is addressed. Over its axial length, the reactor has several equally sized cooling jackets. The controller must adjust the jacket temperatures on the basis of per jacket temperature measurements so that the closed-loop system is robustly stable. The problem is solved within a constructive framework, by combining notions and tools from chemical reactor engineering and partial differential equations (PDEs) control systems theory. The result is a MIMO nonlinear OF dynamic control design with (i) a decentralized MIMO passive state feedback (SF) controller implemented with a pointwise observer (PWO), (ii) closed-loop stability conditions in terms of sensor set and control gains, and (iii) efficient late lumping-based on-line implementation. The design is put in perspective with industrial PI and inventory control, and applied to a representative example through numerical simulation with favorable comparison against adaptive controllers.     

QFT prefilter design for multivariable systems using interval constraint satisfaction technique

In this paper, a computationally efficient method is proposed for automated design of the prefilters for multivariable systems. In quantitative feedback theory （QFT） method, proposed by Horowitz, the prefilter is designed to achieve the desired tracking specifications. In the proposed approach, we pose the prefilter design problem as an interval constraint satisfaction problem and solve it using the well-established interval constraint satisfaction techniques. The proposed method finds optimal values of the parameters of fixed structure prefilter within the initial search domain. An approach based on prefilter synthesis for single-input single-output is already developed. The purpose of this paper is to extend this approach to QFT prefilter design for general multivariable systems. To validate the above design approach, we applied the method to a laboratory setup of magnetic levitation system.     

MIMO网络控制系统的指数稳定性

研究具有时延和数据包丢失的多输入多输出网络控制系统的指数稳定性和控制器设计问题.对在传感器与控制器、控制器与执行器间皆有时延和数据包丢失的网络控制系统结构进行了简化,建立了动态输出反馈网络控制系统模型.基于异步动态系统理论、Lyapunov稳定性原理和线性矩阵不等式方法导出网络控制系统指数稳定的半负定矩阵条件和动态输出反馈控制律设计方法.数值算例说明结果是可行的.     

Distributed event‐triggered containment control for dynamical multiagent networks

This paper studies the event‐triggered containment control problem for dynamical multiagent networks of general MIMO linear agents. An event‐triggered containment control strategy is provided, which consists of a control law based on a relative‐state feedback and a distributed triggering rule based on both the relative‐state information and a time‐dependent threshold function. Compared to the previous related works, our main contribution is that the triggering rule depends only on local information of communication networks. It is proved that under the proposed event‐based controller, the containment errors are uniformly ultimately bounded and the Zeno behavior can be excluded. Moreover, when the derivation constant in the threshold function is equal to zero, the containment control problem can be solved. Then, the results are extended to the event‐triggered observer‐based containment controller design.     

Multiclass AQM on a TCP/IP router: A control theory approach

Active queue management (AQM) is a well‐known technique to improve routing performance under congested traffic conditions. It is often deployed to regulate queue sizes, thus aiming for constant transmission delay. This work addresses AQM using an approach based on control theory ideas. Compared with previous results in the literature, the novelty is the consideration of heterogeneous traffic, ie, multiclass traffic. Thus, each traffic class may have different discarding policies, queue sizes, and bandwidth share. This feature brings the proposal nearer to real network management demands than previous approaches in the literature. The proposed technique assumes that each class already has a simple controller, designed a priori, and focuses on designing a static state‐feedback controller for the multiclass system, where the design is based on using LMIs for the calculations. For this, optimization problems with LMI constraints are proposed to compute the state‐feedback gains that ensure stability for a large set of admissible initial conditions. These conditions ensure not only closed‐loop stability but also some level of performance. As far as we know, this is the first control theory based approach for the AQM problem on TCP/IP routers that allows a multiclass AQM while also considering time‐varying delays and input saturation. This is an important step to frame AQM in a more formal, yet realistic context, enabling it to address important service level agreement (SLA) directives. The proposal is tested on a simulated system at the end of this paper, showing the feasibility and performance of the approach in the presence of multiclass traffic.