239 research outputs found
Stability analysis for class of switched nonlinear systems
No full textStability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. The results are illustrated by numerical examples
Generalized Cross-Gramian for Linear Systems
No full textThe cross-gramian is a well-known matrix withembedded controllability and observability information. Thecross-gramian is related to the Hankel operator and the Hankelsingular values of a linear square system and it has severalinteresting properties. These properties make the cross-gramianpopular in several applications including model reduction, controlconfiguration selection and sensitivity analysis. The ordinarycross-gramian which has been defined in the literature is thesolution of a Sylvester equation. This Sylvester equation is notalways solvable and therefore for some linear square symmetricsystems, the ordinary cross-gramian does not exist. To cope withthis problem, a new generalized cross-gramian is introducedin this paper. In contrast to the ordinary cross-gramian, thegeneralized cross-gramian can be easily obtained for generallinear systems and therefore can be used in the applicationsinstead of the ordinary cross-gramian
Frequency-interval interaction measure for control configuration selection for multivariable processes
No full textIn many applications one is interested in control and analysis within a bounded frequency-interval. For such applications, the input-output interactions within the desired frequency-interval need to be quantified rather than the interactions within the whole frequency range. However, the interaction measures, which have been proposed so far, either quantify the input-output interactions for a single frequency or the whole frequency range. Motivated by this, a new interaction measure is proposed in this paper. The proposed interaction measure uses frequency-interval gramians and it can be used for control configuration selection of MIMO processes. Compared with other counterparts, the proposed gramian-based interaction measure can encode more information on the input-output interactions over a desired frequency-interval. This interaction measure in addition to decentralized control can be used to propose a richer sparse or block diagonal controller structure for distributed and partially decentralized control of multivariable systems. The method is illustrated with the help of a numerical example.</p
Fault Recoverability Analysis via Cross-Gramian
No full textEngineering systems are vulnerable to different kinds of faults. Faults may compromise safety, cause sub-optimal operation and decline in performance if not preventing the whole system from functioning. Fault tolerant control (FTC) methods ensure that the system performance maintains within an acceptable level at the occurrence of the faults. These techniques cannot be successful if the necessary redundancy does not exist in the system. Fault recoverability which is also known as control reconfigurability is a mathematical measure which quantifies the level of redundancy in connection with feedback control. Fault recoverability provides important and useful information which could be used in analysis and design. However, computing fault recoverability is numerically expensive. In this paper, a new approach for computation of fault recoverability for bilinear systems is proposed. This approach uses cross-gramian and reduces the computations significantly. The contribution of this paper is twofold. Firstly the concept of cross-gramian is extended to support discrete-time bilinear systems and an iterative algorithm for cross-gramian computation is proposed. Secondly a cross-gramian based approach for computation of fault recoverability is proposed which reduces the computational burden significantly. The proposed results are used for an electro-hydraulic drive to reveal the redundant actuating capabilities in the system
A brief note on the generalized singular perturbation approximation
No full textThe generalized singular perturbation approximation is a method for approximation of dynamical systems which has been presented in the literature on model reduction over the past two decades. In this note, the generalized singular perturbation approximation is studied and it is shown that this order reduction method is not always true and may leads to inaccurate results and is therefore erroneous. This conclusion holds for the extended methods such as the parametric generalized singular perturbation approximation or the recently presented dissipativity-preserving model reduction based on generalized singular perturbation.</p
Control configuration selection for multivariable switched dynamical systems and processes
No full textThe decentralized and partially decentralized control strategies have gained in a lot of popularity in industrial practices, and they are becoming even more in demand with the increasing complexity of large-scale processes and plants. A decentralized or partially decentralized control strategy cannot be successful unless proper input-output pairs are selected for the controller synthesis. Selecting proper control structure is therefore very important in practice. In this paper the issue of selecting proper control structures will be investigated for multivariable switched systems and processes. To the best of our knowledge, the reported results in this context, do not support switched systems and processes. However, in a lot of applications the underlying models for the systems and processes are of hybrid and switched nature. It is therefore necessary to define a measure which is capable of quantifying the interaction between different input-output pairs for such systems. The main contribution of this paper is to propose such measure based on the concept of gramians and to describe how to use this measure to select proper configuration for controllers for switched systems and processes. A numerical example explains the results in more details.</p
Generalized Time-Limited Balanced Reduction Method
No full textIn this paper, a new method for model reduction of bilinear systems is presented. The proposed technique is from the family of gramian-based model reduction methods. The method uses time-interval generalized gramians in the reduction procedure rather than the ordinary generalized gramians and in such a way it improves the accuracy of the approximation within the time-interval which the method is applied. The time-interval generalized gramians are the solutions to the generalized time-interval Lyapunov equations. The conditions for these equations to be solvable are derived and an algorithm is proposed to solve these equations iteratively. The method is further illustrated with the help of an example. The numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians
Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians
No full textA general method for model-order reduction of switched linear dynamical systems is presented. The proposed technique uses convex generalized gramian which is a convex combination of the generalized gramians. It is shown that different classical reduction methods can be developed into the generalized gramian framework for model reduction of linear systems and further for the reduction of switched systems by construction of the convex generalized gramian. Balanced reduction within specified frequency bound is taken as an example which is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, convex generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the method preserves the stability of the original switched system at least for stabilizing switching signal and it is also less conservative than the method which is based on the common generalized gramian. Some discussions on the coefficient of the vertices of the convex variables are presented. The performance of the proposed method is illustrated by numerical examples
Control Reconfigurability of Bilinear Hydraulic Drive Systems
No full textThe objective of the methods within the framework of the plug and play process control and particularly fault tolerant control is to establish control techniques which guarantee a certain performance through control reconfiguration at the occurrence of the faults or changes. These methods cannot be effective if sufficient redundancy does not exist in the process. A measure for control reconfigurability which reveals the level of redundancy in connection with feedback control is proposed in this paper for bilinear systems. The proposed control reconfigurability measure is the extension of its gramian-based analogous counterpart, which has been previously proposed for the linear processes. The control reconfigurability is calculated for the bilinear models of an electro-hydraulic drive to show its relevance to redundant actuating capabilities in the models
Generalized Gramian Framework for Model/Controller Order Reduction of Switched Systems
No full textIn this article, a general method for model/controller order reduction of switched linear dynamical systemsis presented. The proposed technique is based on the generalised gramian framework for model reduction. It isshown that different classical reduction methods can be developed into a generalised gramian framework.Balanced reduction within a specified frequency bound is developed within this framework. In order to avoidnumerical instability and also to increase the numerical efficiency, generalised gramian-based Petrov–Galerkinprojection is constructed instead of the similarity transform approach for reduction. The framework is developedfor switched controller reduction. To the best of our knowledge, there is no other reported result on switchedcontroller reduction in the literature. The method preserves the stability under an arbitrary switching signal forboth model and controller reduction. Furthermore, it is applicable to both continuous and discrete time systemsfor different classical gramian-based reduction methods. The performance of the proposed method is illustratedby numerical examples
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