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.     

Multivariable quantitative feedback design for tracking error specifications

The use of tracking error specifications in quantitative feedback theory (QFT) design is discussed for multi-input, multi-output (MIMO) systems. These specifications bound the closed loop transfer function within a disk around some nominal (model) performance while preserving the QFT approach that allows treatment of highly structured (and unstructured) uncertainty. Because the specifications capture phase information, the level of over-design in certain MIMO QFT designs is reduced. The method presented allows independent, two-degree-of-freedom design.     

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.     

A quantitative feedback solution to the multivariable tracking error problem

This paper introduces a novel solution for the multi‐input multi‐output (MIMO) quantitative feedback theory control design problem with tracking error specifications. Looking for a minimum controller overdesign, the technique finds new controller quantitative feedback theory bounds based on necessary and sufficient conditions for the existence of suitable associated prefilter matrix elements. It improves previous approaches to the subject and includes (i) the possibility of a free selection of the nominal plant, (ii) a less conservative application of the Schwartz inequality to decisively reduce the potential controller overdesign, (iii) a methodology to design independently the elements of the prefilter matrix, and (iv) a scope of application to both sequential and nonsequential MIMO controller design methods. The benefits of the new control design technique are illustrated by means of two examples. The first one, a standard 2 × 2 MIMO problem, is provided for comparison purposes with previous approaches. The second example, included as a major control challenge, deals with a well‐known demanding distillation column benchmark problem. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Lyapunov Design of Multivariable MRAC via Generalized Passivation

A Lyapunov design of multiple input, multiple output (MIMO) model‐reference adaptive control (MRAC) systems is proposed using new generalized passivity concepts based on WSPR and WASPR properties. The new design avoids control overparameterization and leads to the simplest unnormalized gradient algorithm by means of a passivating multiplier. To this end, a necessary and sufficient condition on the high frequency gain matrix to achieve the WASPR property is established. This condition is referred to as Positive Diagonal Jordan (PDJ) form. Based on the robustness WSPR and WASPR properties, a systematic determination of a robust passivating matrix multiplier is then presented. The advantages of the new design are illustrated by numerical simulation including a robotics adaptive visual servoing problem and a 4‐input‐4‐output dynamic system. © 2014 Chinese Automatic Control Society and Wiley Publishing Asia Pty Ltd     

多变量动态矩阵控制系统的闭环稳定性

定量分析了无约束多输入多输出（MIMO）动态矩阵控制系统的闭环稳定条件,首先基于脉冲响应模型重新描述了动态矩阵控制（DMC）算法;在此基础上,推导得到了MIMODMC系统的闭环稳定条件,以便于预测控制系统的分析与设计。     

ROBUST LTV FEEDBACK SYNTHESIS FOR SISO NON-LINEAR PLANTS

Given a feedback system with uncertain nonlinear plant, it is required that the plant's output, to a set of command inputs, will satisfy certain specifications, i.e., will be bounded between a maximum response β(t) and a minimum response α(t). A rigorous synthesis technique to solve this problem using an LTV controller is developed. A design example is included, and it is shown that the LTV design has much lower bandwidth as compared to LTI designs. All design steps utilize the well-established QFT technique for LTI SISO uncertain systems. The methodology also suits rejection of disturbances at the plant's input or output, and for output specifications for nonzero initial conditions. © 1997 by John Wiley & Sons, Ltd.     

Multiband multiple‐input multiple‐output antenna with high isolation for future 5G smartphone applications

A multiband high‐isolation multiple‐input multiple‐output (MIMO) antenna using balanced mode and coupled neutralization line (NL) is presented in this article. The balanced modes of dipole and loop antennas, which leads to good isolation intrinsically are used for the 8 × 8 MIMO in the LTE bands 42 (3400‐3600 MHz)/Chinese 5G band (3300‐3400 and 3400‐3600 MHz). The unbalanced mode of loop antennas, which optimized by decoupling structure are designed for the 4 × 4 MIMO in the LTE band 40 (2300‐2400 MHz). Therefore, the eight‐antenna array is formed by four dipole elements and four loop elements. The simulated and measured results show that the proposed antenna can cover 2300 to 2400 and 3300 to 3600 MHz, with reflection coefficient better than ?6 dB and isolation higher than 15 dB. Good radiation performance and low envelope correlation coefficient can also be obtained. Specific absorption rate of user's hand is also discussed in this article.     

Disturbance observer–based adaptive boundary layer sliding mode controller for a type of nonlinear multiple‐input multiple‐output system

In this paper, a disturbance observer–based adaptive boundary layer sliding mode controller (ABLSMC) is proposed to compensate external disturbance and system uncertainty for a class of output coupled multiple‐input multiple‐output (MIMO) nonlinear systems. To show the effectiveness of the proposed ABLMSC, a traditional adaptive sliding mode controller (ASMC) is also designed. The stability of the closed‐loop system is examined by using the Lyapunov stability approach. The proposed control approach is implemented for a class of nonlinear output coupled MIMO systems. For real‐time validation, a coupled tank system is considered for study. Finally, simulation and real‐time results show that the proposed ABLMSC gives better performance such as reduced chattering and energy efficiency than that of the ASMC and some reported works in the literature.     

Identification and robust control for systems with ellipsoidal parametric uncertainty by convex optimization

In this paper, sufficient conditions for robust output feedback controller design for systems with ellipsoidal parametric uncertainty are given in terms of solutions to a set of linear matrix inequalities (LMIs) Performance specifications are in terms of combined pole placement with sensitivity function shaping in the H₂ or H_∞ norm. Furthermore, an optimal input design technique for parameter estimation that is integrated into the robust control design is employed in this paper. This means that performance specifications on the closed‐loop transfer functions are translated into the requirements on the input signal spectrum. The simulation results show the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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。     

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.     

Small‐size four‐element antenna system for 2 × 2 LTE LB and 4 × 4 LTE M/HB MIMO operations in 5G mobile terminals

A small‐size four‐element antenna system for 2 × 2 LTE low band (LB, 698‐960 MHz) and 4 × 4 LTE middle/high band (M/HB, 1710‐2690 MHz) multiple‐input multiple‐output (MIMO) operations in 5G (fifth‐generation) mobile terminals is presented. The proposed antenna system is formed by two identical tunable loop antennas and two identical coupled‐fed IFA (Inverted‐F Antenna) antennas. By loading a RF switch with four output states as tunable component, the proposed loop antenna can not only operate in the M/HB, but also achieve improved bandwidth coverage in the LB. Each coupled‐fed IFA element operating in the M/HB with compact volume. The four antennas are placed on the both short side‐edge of the mobile terminal with small ground clearance of 4.2 mm. The simulated S‐parameters show that the proposed MIMO system can cover 698 to 960 MHz and 1710 to 2690 MHz with reflection coefficients less than ?6 dB and isolations are all more than 12 dB. Good MIMO performances such as radiation efficiencies, envelope correlation coefficient (less than 0.4 within the entire operation bands) and channel capacity are also obtained. The effects of user's hand(s) on performances for the proposed antenna system are also discussed. This four‐element antenna system prototype is fabricated and measured.     

Simultaneous Achievement of Open and Closed Loop Diagonal Dominance Through Constant Feedback

This paper proposes a new and low complexity technique for the simultaneous achievement of open and closed loop diagonal dominance for uncertain plants. The method is based on the introduction of a static high gain inner feedback which modifies the plant to attain a diagonal dominant open loop compensated plant. The sufficient, easy to use, conditions derived for the open loop diagonal dominance also assure the simultaneous achievement of closed loop diagonal dominance under soft assumptions on the diagonal elements of the decoupled controller robustly stabilizing the plant. These assumptions agree with the usual closed‐loop performance specifications, so that closed‐loop diagonal dominance is achieved without any extra complication on the controller design procedure. The main merits of the present method are: applicability to uncertain plants, ease of implementation and low computational cost. Three examples taken from the relevant literature, are given to show the effectiveness of the proposed approach.     

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