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。     

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 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.     

Closed‐loop performance metrics for fault detection and isolation filter and controller interaction

Fault detection and isolation (FDI) filters are typically synthesized for open‐loop or closed‐loop systems. The controller affects the FDI filter performance in the closed‐loop system. FDI filter performance and closed‐loop controller–filter interaction in the presence of uncertain dynamics were investigated as was the role of controller robustness on the FDI filter performance. The NASA Generic Transport Model aircraft was considered as a motivating application. Multiple example scenarios were presented to highlight the utility of FDI filter performance metrics. For example, comparing fault detection performance of different filters under identical uncertain plant dynamics and controller, the effect of different controllers on the FDI filter performance, and the effect of model uncertainty on filter performance. The Generic Transport Model aircraft FDI filter results are validated using worst‐case analysis and linear simulations. Copyright © 2011 John Wiley & Sons, Ltd.     

Closed‐Loop Identification for Control of Linear Parameter Varying Systems

This paper deals with system identification for control of linear parameter varying systems. In practical applications, it is often important to be able to identify small plant changes in an incremental manner without shutting down the system and/or disconnecting the controller; unfortunately, closed‐loop system identification is more difficult than open‐loop identification. In this paper we prove that the so‐called Hansen scheme, a technique known from linear time‐invariant systems theory for transforming closed‐loop system identification problems into open‐loop‐like problems, can be extended to accommodate linear parameter varying systems as well. We investigate the identified subsystem's parameter dependency and observe that, under mild assumptions, the identified subsystem is affine in the parameter vector. Various identification methods are compared in direct and Hansen Scheme setups in simulation studies, and the application of the Hansen Scheme is seen to improve the identification performance.     

A Measurement‐Based Approach for Designing Fixed‐Order Controllers for Unknown Closed‐Loop Architecture

This paper presents a new technique to design fixed‐structure controllers for linear unknown systems using a set of measurements. In model‐based approaches, the measured data are used to identify a model of the plant for which a suitable controller can be designed. Due to the fact that real processes cannot be described perfectly by mathematical models, designing controllers using such models to guarantee some desired closed‐loop performance is a challenging task. Hence, a possible alternative to model‐based methods is to directly utilize the measured data in the design process. We propose an approach to designing structured controllers using a set of closed‐loop frequency‐domain data. The principle of such an approach is based on computing the parameters of a fixed‐order controller for which the closed‐loop frequency response fits a desired frequency response that describes some desired performance indices. This problem is formulated as an error minimization problem, which can be solved to find suitable values of the controller parameters. The main feature of the proposed control methodology is that it can be applied to stable and unstable plants. Additionally, the design process depends on a pre‐selected controller structure, which allows for the selection of low‐order controllers. An application of the proposed method to a DC servomotor system is presented to experimentally validate and demonstrate its efficacy.     

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．     

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     

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.     

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。     

多变量系统鲁棒稳定性

本文用复变函数理论，证明了摄动系统为鲁棒对角优势，则系统一定是鲁棒稳定这个一般性结论该结合保守性小，与奈氏阵列法联系密切，可用于工业对象鲁棒控制系统设计。     

DIRECT ADAPTIVE FEEDBACK DESIGN FOR LINEAR DISCRETE‐TIME UNCERTAIN SYSTEMS

In this paper, we develope a direct adaptive control framework for linear discrete‐time uncertain MIMO systems, based on assumptions that the system is controllable and the difference of the unknown system matrix from the stable solution is bounded by a given value. The proposed framework is Lyapunov‐based, and the controller guarantees adaptive stabilization. In addition, the adaptive laws are characterized by means of Kronecker calculus. Furthermore, the results can easily be extended to time‐varying cases, where the deviation from the stable solution is bounded, and the controllability assumption holds. The controller not only tolerates plant deviation, but also guarantees asymptotical stability of the closed‐loop system. Two numerical examples are provided to demonstrate the performance of the controller.     

A Novel Application of Minimax LQG Control Technique for High‐speed Spiral Imaging

Over the last two decades, increasing the scanning speed of an atomic force microscopy (AFM) has been attempted either by applying novel controllers, using alternative scanning methods, or by modifying the hardware setup. This paper demonstrates, the first two approaches to achieve high‐speed AFM image scanning. A robust minimax linear quadratic Gaussian (LQG) controller is designed and spiral scanning is considered as an alternative scanning method rather than conventional raster scanning. The minimax LQG controller is designed based on an uncertain system model which is constructed by measuring the plant variations due to variations in sample mass and also modeling error between the measured and model frequency responses. This controller is also robust against uncertainties introduced as a result of variations of sample mass, spillover dynamics of the scanner at frequencies higher than the first resonance frequency of the scanner, and variation in plant transfer functions due to temperature and humidity. The designed controller is experimentally implemented on an AFM using a dSPACE ds‐1103 real‐time prototyping system and open‐loop and closed‐loop spiral imaging performances are evaluated. The proposed controller provides sufficient damping at the resonant modes to accurately track the sinusoidal reference signal and generate vibration free images. Also, creep, hysteresis, and cross‐coupling effects are significantly reduced. The experimental results show that the proposed scheme outperforms the open‐loop case and some other existing approaches.     

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。     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

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.     

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.     

A virtual closed loop method for closed loop identification

Indirect methods for the identification of linear plant models on the basis of closed loop data are based on the use of (reconstructed) input signals that are uncorrelated with the noise. This generally requires exact (linear) controller knowledge. On the other hand, direct identification requires exact plant and noise modelling (system in the model set) in order to achieve accurate results, although the controller can be non-linear. In this paper, a generalized approach to closed loop identification is presented that includes both methods as special cases and which allows novel combined methods to be generated. Besides providing robustness with respect to inexact controller knowledge, the method does not rely on linearity of the controller nor on exact noise modelling. The generalization is obtained by balancing input-noise decorrelation against noise whitening in a user-chosen flexible fashion. To this end, a user-chosen virtual controller is used to parametrize the plant model, thereby generalizing the dual-Youla method to cases where knowledge of the controller is inexact. Asymptotic bias and variance results are presented for the method. Also, the benefits of the approach are demonstrated via simulation studies.