Diagonal dominance via eigenstructure assignment

1989

Eigenstructure assignment for linear systems is basically an inverse eigenvalue problem. Two possible solutions to this problem are presented here that have been implemented on the Ctrl-C@ Commercial Design Package. Both algorithms use singular-value decomposition and produce robust (well-conditioned) answers to the statefeedback pole-assignment problem. An cxample is included to assess the relative strengths of the two techniques.

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. Two examples taken from the relevant literature, are given to show the effectiveness of the proposed approach.

Recent Advances in Robust Control - Novel Approaches and Design Methods

numerical examples are given to illustrate the feasibility and properties of different equivalent BRL representations. 2. Basic preliminaries 2.1 System model The class of the systems considering in this section can be formed as followṡ q(t)=Aq(t)+Bu(t) (1) y(t)=Cq(t)+Du(t) (2) where q(t) ∈ I R n , u(t) ∈ I R r ,a n dy(t) ∈ I R m are vectors of the state, input and measurable output variables, respectively, nominal system matrices A ∈ I R n×n , B ∈ I R n×r , C ∈ I R m×n and D ∈ I R m×r are real matrices.

IFAC Proceedings Volumes, 2004

This paper proposes the decentralization of interconnected descriptor system with disturbance under the light constraints. First, the interconnected descriptor system is stabilized by feedback control low and then the system is decomposed to slow-mode system and fast-mode system. In slow-mode system, the interacting term can be derived from its steady-state response. Moreover, the term of fast-mode system can be obtained from the derived interacting term of slow-mode system. Unfortunately, the derived two terms is not directly applied to the decentralization, owing to needing the information of global disturbance. This difficulty may be solved by allowing t.he least interconnection of states which a.re much influenced from disturbance.

1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, 1980

The design of stabilizing feedback controls for Large-Scale Systems often requires the general concepts of d e c e n t r a l i z a t i o n. I n t h i s p a p e r , we present a s t r u c t u r a l framework f o r t h e m u l t i l e v e l s t a b i l i z a t i o n problem of Large-Scale Systems. I n t h i s c o n t e x t , ve a d d r e s s t h e s t a b i l i z a t i o n of f i x e d m d e s v i a l o c a l and global feedback controls and develop a Dynamical Bierarchical approach to stabilization.

Lecture Notes in Control and Information Sciences, 2007

IEE Proceedings - Control Theory and Applications, 1999

A systematic optimisation approach to robust eigenstructure assignment for control systems with output feedback is presented. The proposed scheme assigns the maximum allowable number of closed-loop eigenvalues to desired locations, and determines the corresponding closedloop eigenvectors as close to desired ones as possible. Additionally, the stability of the remaining closed-loop eigenvalues is guaranteed by the satisfaction of an appropriate Lyapunov equation. The overall design is robust with respect to time-varying parameter perturbations. The approach is applied to a literature example, where it is shown to capture the shape of the desired transient response.

IEE Proceedings - Control Theory and Applications, 1994

A new method is described for the assignment of eigenvalues of closed-loop plants in linear time-invariant multivariable systems. The parameterisation of controllers is based on the derivation of zero eigenvalue assignment by implementation of vector companion forms. This method is computationally very attractive and can be used for optimisation of the feedback matrix which assigns the closed-loop eigenvalues (from the set of real, complex conjugates or even those of the open-loop system) to the desired locations. A numerical example is presented to illustrate some advantages of this new explicit parameterisation of the controller gain matrix. Paper 1157D (C8), first received Zlst lune 1993 and in revised form 8th

Citeseer

An optimization approach to control recon guration, based on eigenstructure assignment, for control systems with output feedback is presented. The emphasis is on the recovery of the nominal closed-loop performance, which is determined by the closed-loop eigenvalues and eigenvectors. The proposed scheme preserves the max(r; q) most dominant eigenvalues of the nominal closed-loop system and determines their associated closedloop eigenvectors as close to the corresponding eigenvectors of the nominal closed-loop system as possible. Additionally, the stability of the remaining closed-loop eigenvalues is guaranteed by the satisfaction of an appropriate Lyapunov equation. The overall design is robust with respect to uncertainties in the state-space matrices of the recon gured system. The cases of state feedback and dymanic output feedback are also studied. The approach is applied to two aircraft control examples, where it is shown to not only preserve the shape of the transient response but recover much of the characteristics of the steady-state response as well.

Electronics

This research paper addresses the challenge of designing a decentralized controller for a discrete-time uncertain polytopic system with a linear large-scale (LSS) structure. Specifically, we investigate this problem in cases where the subsystem’s output matrix lacks a decentralized structure. Firstly, the proposed novel procedure of a decentralized controller design transforms the LSS model to have a fully decentralized structure (both input and output matrices are block-diagonal). Then, the robust stability boundary parameter is calculated for the open-loop system. This stability boundary parameter is considered in robust decentralized controller design where an appropriate controller design method is used. The entire process of designing a robust decentralized controller takes place at the subsystem level, and the influence of interaction is considered through the robust stability boundary parameter. Lastly, we present an example of a five-order system comprising two subsystems to...