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EN
The linear parameter varying (LPV) approach has proved to be suitable for controlling many non-linear systems. However, for those which are highly non-linear and complex, the number of scheduling variables increases rapidly. This fact makes the LPV controller implementation not feasible for many real systems due to memory constraints and computational burden. This paper considers the problem of reducing the total number of LPV controller gains by determining a heuristic methodology that combines two vertices of a polytopic LPV model such that the same gain can be used in both vertices. The proposed algorithm, based on the use of the Gershgorin circles, provides a combinability ranking for the different vertex pairs, which helps in solving the reduction problem in fewer attempts. Simulation examples are provided in order to illustrate the main characteristics of the proposed approach.
EN
In this paper, a control framework including active fault-tolerant control (FTC) and reference redesign is developed subject to actuator stuck failures under input saturations. FTC synthesis and reference redesign approaches are proposed to guarantee post-fault system safety and reference reachability. Then, these features are analyzed under both actuator stuck failures and constraints before fault-tolerant controller switches. As the main contribution, actuator stuck failures and constraints are unified so that they can be easily considered simultaneously. By means of transforming stuck failures into actuator constraints, the post-fault system can be regarded as an equivalent system with only asymmetrical actuator constraints. Thus, methods against actuator saturations can be used to guarantee regional stability and produce the stability region. Based on this region, stuck compensation is analyzed. Specifically, an unstable open-loop system is considered, which is more challenging. Furthermore, the method is extended to a set-point tracking problem where the reachability of the original reference can be evaluated. Then, a new optimal reference will be computed for the post-fault system if the original one is unreachable. Finally, simulation examples are shown to illustrate the theoretical results.
PL
W pracy rozpatrzono zagadnienie syntezy obserwatora pełnego rzędu dla układów liniowych dyskretnych singularnych niecałkowitego rzędu. Sformułowano analityczne kryteria istnienia obserwatora i podano sposób wyznaczania macierzy wzmocnień obserwatora. Rozważania teoretyczne, do których wykorzystano liniowe nierówności macierzowe (LMI) zilustrowano przykładem liczbowym.
EN
The paper is devoted to observer synthesis for linear singular discrete-time fractional systems. The problem of finding a nonnegative gain matrix of the observer such that the observer is asymptotically stable is formulated and solved by the use of linear matrix inequality (LMI) method. The proposed approach to the observer synthesis is illustrated by theoretical example.
EN
This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.
EN
This paper is concerned with the problem of designing a robust modified repetitive-control system with a dynamic output feedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that accurately describes the features of repetitive control. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. The singular-value decomposition of the output matrix and Lyapunov stability theory are used to derive an asymptotic stability condition based on a Linear Matrix Inequality (LMI). Two tuning parameters in the LMI manipulate the preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.
EN
In this paper, the stabilization problem of a autonomous linear time invariant fractional order (LTI-FO) switched system with different derivative order in subsystems is outlined. First, necessary and sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems based on the convex analysis and linear matrix inequality (LMI) for two subsystems is presented and proved. Also, sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems for more than two subsystems is proved. Then a sliding sector is designed for each subsystem of the LTI-FO switched system. Finally, a switching control law is designed to switch the LTI-FO switched system among subsystems to ensure the decrease of the norm of the switched system. Simulation results are given to show the effectiveness of the proposed variable structure controller.
EN
The paper deals with the problem of full order fuzzy observer design for the class of continuous-time nonlinear systems, represented by Takagi-Sugeno models containing vestigial nonlinear terms. On the basis of the Lyapunov stability criterion and the incremental quadratic inequalities, two design conditions for this kind of system model are outlined in the terms of linear matrix inequalities. A numerical example is given to illustrate the procedure and to validate the performances of the proposed approach.
EN
The paper is devoted to observer synthesis for linear discrete-time positive fractional systems with different fractional orders. The problem of finding a nonnegative gain matrix of the observer such that the observer is positive and asymptotically stable is formulated and solved by the use of linear programming (LP) and linear matrix inequality (LMI) methods. The proposed approach to the observer synthesis is illustrated by theoretical example. Numerical calculations and simulations have been performed in the MATLAB/Simulink program environment.
PL
W pracy rozpatrzono problem syntezy obserwatorów dla dodatnich układów dyskretnych różnych niecałkowitych rzędów w równaniu stanu. Wykorzystując podejście oparte na typowym zadaniu programowania liniowego (LP) oraz zadaniu sformułowanym w ramach liniowych nierówności macierzowych (LMI) pokazano, że jest możliwe uzyskanie dodatniego asymptotycznie stabilnego obserwatora. Są to warunki dostateczne, alternatywne w stosunku do podanych w [5, 18] dla układów niedodatnich. Zaprojektowany obserwator poprawnie estymuje (odtwarza) zmienne stanu przyjętego do rozważań dyskretnego układu niecałkowitego rzędu. Wyniki obliczeniowe uzyskano w środowisku programowym MATLAB z wykorzystaniem biblioteki Optimization oraz pakietów SeDuMi i YALMIP. Rezultaty symulacyjne uzyskano przy wykorzystaniu dodatkowej biblioteki Fractional States Space Toolkit.
EN
This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1 ≤ α < 2 and 0 < α ≤1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.
EN
The robust H∞ state feedback control problem for both continuous- and discrete-time singular systems with polytopic-type uncertainties is revisited via a parameter-dependent approach. Attention is focused on the design of a parameter-dependent state feedback controller, such that the closed-loop system is admissible with prescribed H∞ noise attenuation level for all parameter uncertainties. Without using decomposition technique to the singular model, sufficient condition for the existence of an H∞ state feedback controller is expressed in terms of strict linear matrix inequalities (LMIs). In case that the LMI conditions are feasible, a suitable state feedback control law is explicitly given. The proposed approach is expected to be less conservative compared with previous results. Numerical examples are also provided to show the effectiveness of the approach.
PL
Analizowany jest odporny system sterowania ze sprzężeniem zwrotnym H∞ dla przypadku systemu dyskretnego i ciągłego i z niepewnościami typu polytopic. Do analizy wykorzystuje się metod. zależności parametrycznych. Sterownik opisany jest liniową macierzą nierowności LMI. (Odporne sterowanie ze sprzężeniem zwrotnym H∞ - metoda zależności parametrycznych)
EN
This paper explains the basics of the Linear Matrix Inequalities (LMI), with examples of simulations and calculations created in Matlab/Simulink programming environment where the controlled plant is the “Blue Lady” ship model. First chapter of this paper gives a short overview of publications describing the use of Linear Matrix Inequalities method. Second chapter contains basic definitions and equations for the LMI method. Chapter three presents the use of LMI method for ship control by describing controller synthesis for the “Blue Lady”. Chapter four compares the operation of two controllers, the first one consisting of three independent proper adjusted PID controllers and the second one being a multivariable LMI controller. Finally conclusions from the above comparison are drawn.
EN
This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed \alfa-convergence rate. The design of an observer based output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.
EN
This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.
EN
In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discrete-time systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task. The principle, when compared with previously published results, indicates that the proposed method outper forms the existing approaches, guarantees feasibility, and improves the steady-state accuracy of the control. Furthermore, better performance is achieved with essentially reduced design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated using one state equality constraint.
EN
In this paper, a Fault Tolerant Control (FTC) strategy for Linear Parameter Varying (LPV) systems that can be used in the case of actuator faults is proposed. The idea of this FTC method is to adapt the faulty plant instead of adapting the controller to the faulty plant. This approach can be seen as a kind of virtual actuator. An integrated FTC design procedure for the fault identification and fault-tolerant control schemes using LPV techniques is provided as well. Fault identification is based on the use of an Unknown Input Observer (UIO). The FTC controller is implemented as a state feedback controller and designed using polytopic LPV techniques and Linear Matrix Inequality (LMI) regions in such a way as to guarantee the closed-loop behavior in terms of several LMI constraints. To assess the performance of the proposed approach, a two degree of freedom helicopter is used.
EN
The concept of combining robust fault estimation within a controller system to achieve active Fault Tolerant Control (FTC) has been the subject of considerable interest in the recent literature. The current study is motivated by the need to develop model-based FTC schemes for systems that have no unique equilibria and are therefore difficult to linearise. Linear Parameter Varying (LPV) strategies are well suited to model-based control and fault estimation for such systems. This contribution involves pole-placement within suitable LMI regions, guaranteeing both stability and performance of a multi-fault LPV estimator employed within an FTC structure. The proposed design strategy is illustrated using a nonlinear two-link manipulator system with friction forces acting simultaneously at each joint. The friction forces, regarded as a special case of actuator faults, are estimated and their effect is compensated within a polytope controller system, yielding a robust form of active FTC that is easy to apply to real robot systems.
EN
The paper concerns the problem of stabilization of continuous-time linear systems with distributed time delays. Using extended form of the Lyapunov-Krasovskii functional candidate, the controller design conditions are derived and formulated with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. The result give sufficient condition for stabilization of the system with distributed time delays. It is illustrated with a numerical example to note reduced conservatism in the system structure.
EN
This paper is concerned with the problem of stochastic stability and generalized H2 control for discrete-time fuzzy largescale stochastic systems with time-varying and infinite-distributed delays. Large-scale interconnected systems consist of a number of discrete-time interconnected Takagi-Sugeno (T-S) subsystems. First, a novel Delay-Dependent Piecewise Lyapunov-Krasovskii Functional (DDPLKF0 is proposed, in which both the upper and the lower bound of delays are considered. Then, two improved delay-dependent stability conditions are established based on this DDPLKF in terms of Linear Matrix Inequalities (LMIs). The merit of the proposed conditions lies in its reduced conservatism, which is achieved by circumventing the utilization of some bounding inequalities for cross products of two vectors and by considering the interactions among the fuzzy subsystems in each subregion. A decentralized generalized H2 state feedback fuzzy controller is designed for each subsystem. It is shown that the mean-square stability for discrete T-S fuzzy large-scale stochastic systems can be established if a DDPLKF can be constructed and a decentralized controller can be obtained by solving a set of LMIs. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.
19
Content available Pairwise control principle in large-scale systems
EN
The purpose of the paper is present an algorithm of partially decentralized control design for one type of large-scale linear dynamical system. The pairwise autonomous principle is preferred where design conditions are derived in the bounded real lemma form, and global system stability is reproven to formulate potential application principle in fault tolerant control. The validity of the proposed method is demonstrated by the numerical example.
EN
This paper presents a linear matrix inequality (LMI) method for the design of the wide-area time-delay damping (WATDD) controller of static synchronous series compensator (SSSC)-type flexible ac transmission system (FACTS) device to enhance the power stability of the interconnected power systems. Firstly, in order to reveal the single-input multi-output (SIMO) characteristic of the open-loop power system with SSSC-type FACTS device, the prediction error estimation (PEE) algorithm based system identification method is applied to fit a special SIMO linear model. Then, based on the robust control theory and LMI method, the identified linear model is formulated as the standard control problem with the time-delay of the input signals of the WATDD controller, and combined with the designed state observer for the input state variables of the WATDD controller, the control parameters are optimized by the LMI iterative solution algorithm. Finally, the nonlinear simulation on the typical 2-area 4-machine system installed with SSSC-type WATDD controller is performed to verify the LMI-based design method and the proposed SSSC-type WATDD controller.
PL
W artykule przedstawiono metodę nierówności matrycy liniowej (LMI) do projektowania kontrolera z opóźnieniem kompensatora szeregowego synchronicznego (SSSC) elastycznego systemu przesyłowego prądu przemiennego (FACTS) w celu zwiększenia stabilności wzajemnie połączonych systemów zasilania. Po pierwsze, dopasowano specjalny model liniowy SIMO do charakterystyki otwartego systemu z urządzeniem SSSC-FACTS. Następnie, w oparciu o odporną teorię sterowania i metodę LMI, opisano zidentyfikowany model jako standardowy problem sterowania z opóźnieniem czasowym sygnałów wejściowych kontrolera WATDD i połączono go z utworzonym obserwatorem stanu wielkości wejściowych kontrolera WATDD - parametry sterowania są optymalizowane iteracyjnie za pomocą algorytmu LMI. W końcu, przeprowadzono symulację nieliniową typowego systemu (2-area 4-machine system) z kontrolerem SSSC typu WATDD w celu weryfikacji zaproponowanej metody.
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