What is the minimum function observer order
01 May 1998-Journal of The Franklin Institute-engineering and Applied Mathematics (Pergamon)-Vol. 335, Iss: 4, pp 623-628
TL;DR: In this article, the design of a minimal order observer which can estimate the state feedback control signal with arbitrarily given observer poles and K, has been worked on for many years, with the prevailing conclusion that it is an unsolved problem.
Abstract: The design of a minimal order observer which can estimate the state feedback control signal K x( t ) with arbitrarily given observer poles and K , has been worked on for many years, with the prevailing conclusion that it is an unsolved problem. This paper asserts for the first time that this design problem has been simplified to a set of linear equations K = K z diag{c 1 ,…,c r } D , where D is fully determined and other parameters are completely free, and where r is the observer order. This paper also asserts that only this set of linear equations can provide the unified upper bound of r , min { n , v 1 + … + v p } and min { n − m ,( v 1 − 1) + … + ( v p − 1)}, for strictly proper and proper observers, respectively, where n , m , p and v i ( i = 1,…, p ) are the plant order, number of outputs, number of inputs, and the descending order observability indexes, respectively. This general upper bound is lower than all other existing ones and is the lowest possible general upper bound.
Citations
More filters
TL;DR: A constructive procedure to design a single linear functional observer for a time-invariant linear system with stable observers or fixed poles observers problems considered for minimality.
52 citations
TL;DR: By resorting to the gradient flow method, an optimization algorithm is proposed to reduce the influence of the environmental noises and the effectiveness of the obtained results is shown.
Abstract: This paper studies the consensus problem of the multi-agent systems with parallel Luenberger observers First, the structure of the cooperative system is established, where the output of the built-in Luenberger observer for each agent is used as its local control input and the cooperative control input combining with the cooperative measurement output is utilized as the input of the observers Based on the structure of the closed-loop system, the consensus problem is then analyzed In addition, two methods for designing the controller gains are provided By virtue of the proposed structure, it is pointed out that the design of the controller gains and the observer parameters can be carried out separately Finally, by resorting to the gradient flow method, an optimization algorithm is proposed to reduce the influence of the environmental noises The effectiveness of the obtained results is shown through a numerical example
40 citations
TL;DR: With the help of the Kronecker maps, general explicit solutions of the Sylvester-polynomial matrix equations are established when the polynomial matrices possess F-primeness.
Abstract: The concepts of Kronecker maps and Sylvester-polynomial matrix equations are proposed. Some properties of the Kronecker maps are deduced. It is shown that many kinds of matrix equations can be formulated into the so-called Sylvester-polynomial matrix equations. With the help of the Kronecker maps, general explicit solutions of the Sylvester-polynomial matrix equations are established when the polynomial matrices possess F-primeness. For the nonsquare case, the proposed solutions can offer all the degrees of freedom represented by a free parameter matrix
37 citations
TL;DR: Constructive procedures for the design of such a linear functional observer are deduced from the existence conditions in the case where the order of the observer is equal to the number of observed variables.
Abstract: The technical note deals with existence conditions of a functional observer for linear time-varying systems in the case where the order of the observer is equal to the number of observed variables. Constructive procedures for the design of such a linear functional observer are deduced from the existence conditions. As a specific feature, the proposed procedures do not require the solution of a differential Sylvester equation. Some examples illustrate the presented results.
37 citations
TL;DR: In this paper, a minimal-order observer-based control method is proposed for small power utility connected photovoltaic (PV) systems, where the PV power is controlled according to load variation to minimize the frequency deviation.
Abstract: In this paper, a minimal-order observer-based control method is proposed for small power utility connected photovoltaic (PV) systems. In the proposed method, the PV power is controlled according to load variation to minimize the frequency deviation. Load power and diesel power are estimated successfully by a minimal-order observer. From the estimated load power, load variation index is calculated. A second-order low-pass filter is used to produce PV base power from available maximum PV power. Then, the PV base power is added with the load variation index to generate the command PV power. The proposed method is compared with the method where maximum power point tracking control is used to produce the command PV power. From simulation results, it has been found that the proposed method is effective to reduce the frequency deviation of the utility and also delivers PV power near maximum PV power.
36 citations
References
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TL;DR: In this paper, the identity observer, a reduced-order observer, linear functional observers, stability properties, and dual observers are discussed, along with the special topics of identity observer and reduced order observer.
Abstract: Observers which approximately reconstruct missing state-variable information necessary for control are presented in an introductory manner. The special topics of the identity observer, a reduced-order observer, linear functional observers, stability properties, and dual observers are discussed.
2,544 citations
Book•
11 Feb 1983
TL;DR: The aim of this monograph is to remedy this omission by presenting a comprehensive and unified theory of observers for continuous-time and discrete -time linear systems.
Abstract: My aim, in writing this monograph, has been to remedy this omission by presenting a comprehensive and unified theory of observers for continuous-time and discrete -time linear systems. The book is intended for post-graduate students and researchers specializing in control systems, now a core subject in a number of disciplines. Forming, as it does, a self-contained volume it should also be of service to control engineers primarily interested in applications, and to mathematicians with some exposure to control problems.
506 citations
TL;DR: This paper presents an approach to the design of linear time-invariant control systems that does not involve computing complicated canonical forms, and at the same time generalizes easily to multi-input-output systems.
Abstract: The control of linear time-invariant systems is one of the most basic problems of modern automatic control theory. Although “optimal controllers” which minimize certain costs associated with control can be determined, in most applications “simple controllers” suffice, and are often more desirable. The criteria by which these simple controllers are designed are closely related to the problem of assigning the eigenvalues of the fundamental matrix (i.e., the poles of the system) to arbitrary but specified locations. This paper presents an approach to the design of such control systems. Our approach does not involve computing complicated canonical forms, as do some previous methods, and at the same time generalizes easily to multi-input-output systems. A simple solution of the problem of designing feedback control systems with a minimum number of dynamic elements is also presented.
290 citations
TL;DR: In this paper, a new recursive algorithm was proposed to construct a reduced-order observer with prescribed spectrum for a given observable system. The method is based on the staircase form and implicitly gives a new proof for the existence of such reduced order observers.
82 citations