Optimal Observer Design With Specified Eigenvalues for Time-Invariant Linear System

Abstract

The elements of the observer matrix are determined to meet the specified eigenvalues, distinct and multiple, and at the same time, the measure of quadratic estimate error expressed in block pulse functions is minimized. It is relatively simple as compared to other design methods for optimal observers.

Design of Full‐Order Observers for Systems with Unknown Inputs by Using the Eigenstructure Assignment

“…In other words, h i and v i depend of f i , thus J 1 depends on f i . The minimization of the function J 1 is known in the specialty literature as the eigenvalue sensitivity reduction; this problem is equivalent with the minimization of the condition numbers associated to a matrix eigenvalues (the reciprocals of the cosines of the angles between the left and right eigenvectors); for solving this problem, the algorithms proposed in can be used. J 2 will be minimized with respect to matrix S , which, according to and , also depends on the row vectors .…”

Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization

“…Although the asymptotic principle can be applied to improve the convergence of the estimated states by choosing the eigenvalues of the observer with a sufficiently negative real part, the design result is not satisfactory due to the fact that a large estimation error may occur during the transient period of observation. [13][14][15] Several previous studies have been devoted to coping with the design issue of reducing the large estimation error occurring during the transient period of observation. [12][13][14][15][16][17] The reduced-order observer reduces the order of the observer by using the sensed outputs.…”

“…[13][14][15] Several previous studies have been devoted to coping with the design issue of reducing the large estimation error occurring during the transient period of observation. [12][13][14][15][16][17] The reduced-order observer reduces the order of the observer by using the sensed outputs. To the authors' best knowledge, to date, only Kung and Yeh 13 as well as Horng and Chou 14,15 have studied the problem of transient estimation performance improvement for "reduced-order observers.…”

“…18,19 One design method requires the dynamical equation in an observable form, while the other design approach does not require so. Based on the dynamical system in an observable form, Kung and Yeh 13 as well as Horng and Chou 14,15 studied the problem of transient estimation performance improvement for the "reduced-order observer of an Observable-Form-Based dynamical system (OFB-reduced-order observer)." However, the methods proposed by Kung and Yeh 13 as well as Horng and Chou 14,15 cannot be applied to deal with the design issue of the "reduced-order observer of a Non-Observable-Form-Based dynamical system (NOFB-reduced-order observer)."…”

“…Therefore, many researchers have proposed various methods for observer design. 1–23 In order for the estimated states to be close and quickly converge to the actual states of the observed system, the primary consideration is that the real parts of the eigenvalues of the observer should be chosen to be more negative than those of the observed system. 7 As such, many researchers design observers in terms of the asymptotic sense.…”