Near-optimal kalman filters for multiparameter singularly perturbed linear systems

In this brief, we study the near-optimal Kalman filtering problem for multiparameter singularly perturbed system (MSPS). The attention is focused on the design of the near-optimal Kalman filters. It is shown that the resulting filters in fact remove ill-conditioning of the original full-order singularly perturbed Kalman filters. In addition the resulting filters can be used compared with the previously proposed result even if the fast state matrices are singular

A new design approach for solving linear quadratic Nash games of multiparameter singularly perturbed systems

In this paper, the linear quadratic Nash games for infinite horizon nonstandard multiparameter singularly perturbed systems (MSPS) without the nonsingularity assumption that is needed for the existing result are discussed. The new strategies are obtained by solving the generalized cross-coupled multiparameter algebraic Riccati equations (GCMARE). Firstly, the asymptotic expansions for the GCMARE are newly established. The main result in this paper is that the proposed algorithm which is based on the Newton's method for solving the GCMARE guarantees the quadratic convergence. In fact, the simulation results show that the proposed algorithm succeed in improving the convergence rate dramatically compared with the previous results. It is also shown that the resulting controller achieves O(∥μ∥2n) approximation of the optimal cost

Multimodeling Control via System Balancing

A new approach in multimodeling strategy is proposed. Multimodel strategies in which control agents use different simplified models of the same system are being developed using balancing transformation and the corresponding order reduction concepts. Traditionally, the multimodeling concept was studied using the ideas of multitime scales (singular perturbations) and weak subsystem coupling. For all reduced-order models obtained, a Linear Quadratic Gaussian (LQG) control problem was solved. Different order reduction techniques were compared based on the values of the optimized criteria for the closed-loop case where the full-order balanced model utilizes regulators calculated to be the optimal for various reduced-order models. The results obtained were demonstrated on a real-world example: a multiarea power system consisting of two identical areas, that is, two identical power plants

H2 and H∞ Filtering for Nonlinear Singular Systems

RÉSUMÉ Dans les dernières années, les systèmes singuliers des équations différentielles ont carrément explosé puisqu’on les trouve dans plusieurs champs d’applications allant des systèmes électromécaniques en passant par des circuits électroniques, réacteurs chimiques et/ou biologiques ainsi que les systèmes d’écoulement des fluides. Dans cette thèse, deux classes des systèmes singuliers non linéaires seront considérer, en l’occurrence : (i) systèmes singuliers perturbés, (ii) systèmes généralisés ou systèmes algébro-différentielles. Les techniques H2 et H∞ pour l’estimation de l’état de ces classes seront développés ainsi que des conditions suffisantes pour la résolution des problèmes en termes des équations d’Hamilton-Jacobi seront présentés. Deux systèmes, temps-continu et discrets, seront considérés et, pour plus de viabilité des résultats, des exemples pratiques seront présentés et résolus.----------ABSTRACT Singular systems of differential equations arise in many areas of science and technology, including electro-mechanical systems, electronic circuits, chemical and biological reactors, and fluid flow systems. In this thesis, two classes of singular nonlinear systems are considered; namely, (i) singularly perturbed systems, and (ii) generalized systems, or descriptor, or differential-algebraic systems. H2 and H∞ techniques for state estimation of these classes of systems are developed, and sufficient conditions for the solvability of the problems in terms of Hamilton-Jacobi equations are presented. Both continuous-time and discrete-time systems are considered, and examples are presented to show the usefulness of the results

Application of robust order reduction in modeling and control of real systems and objects in mechanical engineering

Дисертација „Примена робусне редукције реда система у моделовању и управљању реалним објектима у машинству“ је посвећена техникама и методама за редукцију реда линеарних модела, представљених у простору стања, као и условима и ограничењима за њихову примену. Приказан је концепт сингуларних пертурбација и његова примена у редукцији сложености модела система. Размотрене су различите карактеризације линеарних модела великог реда, чије репрезентације моделима у простору стања имају различите временске скале или и мали параметар (имају матрице великих димензија са пуно нула-елемената или са елементима, чији се редови величине веома разликују). Представљени су: сингуларно пертурбовани слабо повезани системи, слабо повезани системи, сингуларно пертурбовани системи, квази сингуларно пертурбовани системи и квази слабо повезани системи. Свака од ових класа представљена је одговарајућим моделом у простору стања неког реалног система. Детаљније је изложен прорачун регулатора за линеаран сингуларно пертурбован систем. Описана је метода балансирања, као и технике за редукцију реда линеарних модела, познате из литературе, које захтевају примену трансформације балансирања: балансирано одсецање, балансирана резидуализација, генералисана балансирана резидуализација, кориговано балансирано одсецање, метода заснована на брзом подсистему уз одбацивање спорог, модификована генералисана балансирана резидуализација, као и реверзна техника резидуализације. Свака од ових техника даје по један модел редукованог реда, полазећи од балансираног модела пуног реда. Технике изложене у овој тези, примењене су на редуковање реда четири модела реалних система. Први је модел бинарне дестилационе колоне са прегревачем и девет подова. Други је модел у простору стања борбене летелице L-1011. Трећи је математички модел каталитички контролисане реакције, из процесне технике. Четврти је математички модел дела електроенергетског система Србије, сачињен од две машине. Изложена је и редукција реда модела нестабилних линеарних система, на основу изабране литературе...The dissertation Application of Robust Order Reduction for Modeling and Control of Real Systems in Mechanical Engineering is dealing with techniques and methods of order reduction for linear models in the state space representation, as well as with conditions and limitations of their applicability. Well known concept of singular perturbations is described with its application in reduction of complexity of the system’s model. Different characterizations of large scale linear models are overviewed, having state space representations who exhibit different time scales or small parameter, too. These models have matrices of large dimensions with many zero-elements or elements with different size order, some very large and others very small. The singularly perturbed and weakly coupled systems, the weakly coupled systems, the singularly perturbed systems, the quasy singularly perturbed systems and the quasy weakly coupled systems are listed and represented here. Each class of these is represented with corresponding state space model of one real system. The design of the regulator for the linear singularly perturbed system is described in detail. The balancing method is analyzed, as well as techniques for the order reduction of linear model’s, known from the literature. These require application of the balancing transformation: the balancing truncation, the balancing residualization, the generalized balancing residualization, the corrected balancing truncation, the method based on the fast subsystem with rejection of the slow subsystem, the modified generalized balancing residualization, as well as the reversed residualization technique. Each of these techniques mentioned gives one model of reduced order, starting from the balanced full order model. Techniques represented in this thesis are applied on order reduction of four real system’s models. The first is the state space model of binary distillation column, with condenser, reboiler and nine plates. The second is the state space model of L-1011 fighter aircraft. The third is a mathematical model of the controlled catalytic reaction, from process engineering. The fourth part is a mathematical model of the part of electric power system of Serbia, consisting of two machines. Described here is the order reduction for models of unstable linear systems as well, based on the chosen references..

SPS flexible system control assessment analysis

Active control of the Satellite Power System (SPS0, a large mechanically flexible aerospace structure is addressed. The control algorithm is the principle component in the feedback link from sensors to actuators. An analysis of the interaction of the SPS structure and its active control system is presented

Flight Mechanics/Estimation Theory Symposium, 1991

Twenty-six papers and abstracts are presented. A wide range of issues related to orbit attitude prediction, orbit determination, and orbit control are examined including attitude sensor calibration, attitude dynamics, and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers