Non‐diagonal controllers in MIMO quantitative feedback design

This paper discusses multivariable quantitative feedback design through the use of controllers with off‐diagonal elements. Controller design for multivariable plants with significant uncertainty is simpler and potentially less conservative if some sort of dominance is achieved (by reducing the interaction effect of off‐diagonal plant elements) before a diagonal (decentralized) controller design is attempted. Traditional approaches for achieving dominance are not applicable when plant uncertainty must be considered. This paper discusses parallel and series implementations and for the latter, a pseudo‐Gauss elimination approach to the design has been developed. The interaction is measured using the Perron–Frobenius root of an interaction matrix. In some applications, it is possible to trade off individual plant cases against each other in order to reduce to the worst‐case interaction over the entire plant set. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

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.     

Diagonal dominance for multivariable nyquist array methods using function minimization

A new method of achieving diagonal dominance for Nyquist array design methods is presented. The technique utilizes a conjugate direction function minimization algorithm to obtain dominance over a specified frequency range by minimizing the ratio of the moduli of the off-diagonal terms to the moduli of the diagonal terms of the appropriate open loop transfer matrix. The new dominance algorithm is easily implemented in either a batch or interactive computer mode and will yield dominant compensators when alternative methods fail. Several concepts new to the Nyquist array methods are also presented. The proposed method is applied to the control system design for a sixteenth order state model of the Pratt-Whitney F-100 turbofan engine with three inputs.     

LMI optimization approach to robust decentralized controller design

A new approach for design of robust decentralized controllers for continuous linear time‐invariant systems is proposed using linear matrix inequalities (LMIs). The proposed method is based on closed‐loop diagonal dominance. Sufficient conditions for closed‐loop stability and closed‐loop block‐diagonal dominance are obtained. Satisfying the obtained conditions is formulated as an optimization problem with a system of LMI constraints. By adding an extra LMI constraint to the system of LMI constraints in the optimization problem, the robust control is addressed as well. Accordingly, the decentralized robust control problem for a multivariable system is reduced to an optimization problem for a system of LMI constraints to be feasible. An example is given to show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

鲁棒逆奈奎斯特方法中鲁棒Gershgorin带的近似估计

针对多输入多输出线性系统的鲁棒逆奈奎斯特阵列分析，提出一种保守性较小的鲁棒Gershgorin带近似估计方法．首先给出一个保守性较小的鲁棒对角优势性引理，基于此引理，对具有参数不确定性的传递函数矩阵，推导了鲁棒Gershgorin带的近似估计方法，降低了估计结果的保守性．最后给出了仿真验证．     

一种新的六自由度并联机器人分散控制方法

结合六自由度并联机器人机构的特点.提出一种新的分散控制方法.首先依据机构特点指出了关节空间内惯性矩阵块对角占优特性,从而将耦合强烈的邻近支路加以整体考虑,即分散控制3个两输入两输出子系统;然后将惯性矩阵的逆分解为块对角矩阵与耦合矩阵之和,从而得到每个子系统的动力学方程;最后针对子系统负载随机构运动而变化的特点引入线性变参数(LPV)控制方法,降低了使用线性定常控制器的保守性.仿真结果表明了所提出方法的有效性.     

New dominance concepts for multivariable control systems design

This paper sets out a revised view of the classical diagonal dominance method for multivariable feedback systems. The various types of dominance measure are unified by using one fundamental dominance theorem (FD)l. It is shown that the fundamental dominance condition yields the smallest dominance measure when compared with all the known classical diagonal dominance measures. In addition it is shown that the dominance measures such as row/column, generalized dominance and a few new ones are special cases and can be derived from this same FD theorem. This improved dominance criterion also provides the sufficient condition for a system to be approximated by a nominal one in the sense that the stabilization of this nominal system will assure the stability of the original one. Finally, a new type of dominance measure named L-dominance is presented. It has been shown that this new approach yields an even smaller dominance measure, and that when it is applied to matrices with non-positive off-diagonal elements, the L-dominant condition and the M-matrix condition are equivalent, but the testing of the former is easier and can be achieved via simple Gaussian eliminations     

利用常数补偿器实现鲁棒对角优势

本文研究了利用常数补偿器实现鲁棒对角优势的问题。首先给出了系统在某一点处实现鲁棒对角优势的条件。然后研究了系统在某一频段内鲁棒对角优势的实现问题。最后通过一个算例说明了该方法的有效性。     

对角优势的常数阵实现

本文考虑Nyquist阵列法中的对角优势问题,讨论了由常数阵实现对角优势的条件与算法。 符号约定: G(s):系统的过程传递函数阵G(s)∈C~(mxm) Q(s):包括补偿器在内的开环传递函数阵Q(s)∈C~(mxm) K:前置补偿器阵,在本文中 K∈R~(mxm) q_(?),k_(?)分别为Q(s),K阵的第j列向量 ‖·‖_s向量的欧氏范数 〔·〕~T:矩阵或向量的转置 λ(·):矩阵(·)的特征值     

Diagonal dominance design by Bode plots and root loci†

Bode plots and root loci are used for design of two-by-two systems based on diagonal dominance. The method provides insight into the effect of compensation, including minor loop feedback, on dominance characteristics which extends beyond this class.     

结构不确定线性系统鲁棒对角优势的实现

讨论了结构不确定性线性系统传递函数矩阵的鲁棒对角优势问题．在传统的伪对角化方法的基础上，提出了鲁棒的伪对角化方法，并研究了系统鲁棒对角优势的实现条件．最后，通过一个实例说明了该方法的有效性     

基于PSO的BTT飞行器鲁棒解耦控制设计

提出BTT飞行器的一种鲁棒解耦控制方法。针对飞行器具有非线性、强耦合、多输入多输出（MIM0）等特点,从飞行器数学模型分析通道间耦合产生的原因,并采用Gershgorin圆的方式,定量的分析系统的对角优势度;然后利用粒子群优化算法（PSO）得到小偏差线性模型的鲁棒解耦矩阵,使得系统满足对角优势的性质;最后设计鲁棒控制器,经仿真结果验证表明,该解耦方式的控制效果良好,并具有较强的工程应用价值。     

逆Nyquist阵列设计中的小增益递推原理与实现

本文通过在逆Ｎｙｑｕｉｓｔ阵列设计中引入小增益递推原理，提出了一种改进的ＩＮＡ（ＲＩＮＡ）设计方法，该方法既保持了传统的ＩＮＡ（ＲＩＮＡ）设计方法的优点，又解决了当系统的传递函数矩阵的对角优势（鲁棒对角优势）遭到破坏时，系统的稳定性（鲁棒稳定性）问题。     

Design of decentralized PI control systems based on Nyquist stability analysis

This paper presents a simple, but effective, design method for decentralized PI control systems with guaranteed closed-loop stability. Nyquist stability conditions are used to derive the stability region for each PI controller in terms of the controller parameters. A detuning factor for each loop is specified based on a diagonal dominance index. Then appropriate controller settings are determined using this index and the stability region. Simulation results for a variety of 2 × 2, 3 × 3, and 4 × 4 systems demonstrate that the proposed design method guarantees closed-loop stability and provides good set-point and load responses.     

鲁棒稳定性和鲁棒对角优势的关系

本文研究了多输入多输出系统的鲁棒稳定性和鲁棒对角优势的关系.不仅给出了使系统 鲁棒对角优势所需的鲁棒稳定性条件,而且还得出了系统鲁棒对角优势一定保证系统鲁棒稳 定这个一般性的结论.并可根据本文所给的结果,对允许摄动的最大边界进行估计,包括非结 构摄动的范数上界和结构性摄动的摄动矩阵的各元素的模的估计.本文得出的鲁棒对角优势 保证鲁棒稳定的结果是较少保守性的.     

Decentralized state feedback robust H ∞ control using a differential evolution algorithm

This paper presents a new method to synthesize a decentralized state feedback robust H ^∞ controller for a class of large‐scale linear uncertain systems satisfying integral quadratic constraints. The decentralized controller is constructed by taking only block‐diagonal elements of a nondecentralized state feedback controller and treating neglected off‐diagonal blocks as uncertainties. A solution to this controller synthesis problem is given in terms of a stabilizing solution to a parametrized algebraic Riccati equation where the parameters are obtained using a differential evolution algorithm.Copyright © 2012 John Wiley & Sons, Ltd.     

On multivariable stability in the gain space

General existence conditions under which the stability of the individual loops of a multivariable system in a given compact and bounded gain space imply the global asymptotic stability of the multivariable system in the same space are very useful in practice and essentially indicate when in principle it is possible to obtain stable closed-loop performance of a multivariable system by tuning every loop separately. Such conditions are particularly useful for fault tolerant control of multivariable systems. This paper gives the required necessary and sufficient conditions and effectively unifies all previous work on diagonal stabilizability which includes as special cases: the diagonal dominance, the H matrix, the GKK matrix and the decentralized integral controllability (DIC) conditions reported previously in the literature. Some application examples are included.     

鲁棒对角优势及在多变量系统鲁棒设计中应用

本文基于多变量系统奈氏阵列设计方法和鲁棒对角优势保证系统鲁棒稳定的结论,提出一种多变量系统鲁棒设计方法,该方法设计的鲁棒预补偿器使广义对象在一定摄动范围内严格符合鲁棒对角优势定义,因而系统一定是鲁棒稳定的,该方法具有保守性小,设计的控制器简单,易于工程实现等优点,用该方法对一参数不确定性工业对象进行了鲁棒系统设计,结果令人满意。