Discrete-Time Well-Conditioned State Observer Design and Evaluation

2001 ◽  
Vol 123 (4) ◽  
pp. 615-622 ◽  
Author(s):  
Kunsoo Huh ◽  
Jongchul Jung ◽  
Jeffrey L. Stein
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Poor Performance ◽  
State Observer ◽  
Observer Design ◽  
False Alarms ◽  
Conditioning Factors ◽  
Estimation Performance ◽  
Filter Performance ◽  
Ill Conditioning

Model-based monitoring systems based on state observer theory often have poor performance with respect to accuracy, bandwidth, reliability (false alarms), and robustness. The above limitations are closely related to the ill-conditioning factors such as transient characteristics due to unknown initial values and round-off errors, and steady-state accuracy due to plant perturbations and sensor bias. In this paper, by minimizing the effects of the ill-conditioning factors, a well-conditioned observer is proposed for the discrete-time systems. A performance index is determined to represent the quantitative effects of the ill-conditioning factors and two design methods are described for the well-conditioned observers. The estimation performance of the well-conditioned observers is verified in simulations where transient as well as steady-state error robustness to perturbations is shown to be better than or equal to Kalman filter performance depending on the nature of modeling errors. The estimation performance is also demonstrated on an experimental setup designed and built for this purpose.

A Quantitative Performance Index for Observer-Based Monitoring Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 487-497 ◽  
Author(s):  
Kunsoo Huh ◽  
Jeffrey L. Stein
Keyword(s):  
Error Bounds ◽  
Estimation Error ◽  
State Observer ◽  
Observer Design ◽  
Observer Performance ◽  
Condition Numbers ◽  
Monitoring Systems ◽  
False Alarms ◽  
Machine Monitoring ◽  
L2 Norm

Model-based monitoring systems based on state observer theory are attractive for machine monitoring because practical, inexpensive, and reliable sensors can be located remote to the signal(s) of interest. Then, a model of the machine plus an estimation algorithm are utilized to convert the output of the remote sensors to signals representing the desired local behavior. While this type of monitoring system has shown much promise in the laboratory, it has not been widely accepted by industry because, in practice, these systems often have poor performance with respect to accuracy, bandwidth, reliability (false alarms), and robustness. In this paper, the limitations of the deterministic state observer are investigated quantitatively from the machine monitoring viewpoint. The limitations in the transient and steady-state observer performance are quantified based on the estimation error bounds, and from these error bounds, performance indices are selected. Then, based on the relationships between the indices, a main index is determined in order to represent the overall observer performance. The index is the condition number of the observer eigenvectors in L2 norm. It is shown that observers with small condition numbers are guaranteed to have small error bounds. This index can be utilized as a quality condition for any linear observer regardless of how it is designed as well as form the basis for an observer design methodology for high performance observer-based monitoring systems.

scholarly journals An LMI-Based H ∞ Discrete-Time Nonlinear State Observer Design for an Anaerobic Digestion Model

2017 ◽  
Vol 50 (1) ◽  
pp. 11547-11552
Author(s):  
K. Chaib Draa ◽  
H. Voos ◽  
M. Alma ◽  
A. Zemouche ◽  
M. Darouach
Keyword(s):  
Anaerobic Digestion ◽  
Discrete Time ◽  
State Observer ◽  
Observer Design ◽  
Nonlinear State

State observer design for a class of Takagi-Sugeno discrete-time descriptor systems

2015 ◽  
Vol 9 ◽  
pp. 5871-5885
Author(s):  
Ilham Hmaiddouch ◽  
Boutayna Bentahra ◽  
Abdellatif El Assoudi ◽  
Jalal Soulami ◽  
El Hassane El Yaagoubi
Keyword(s):  
Discrete Time ◽  
State Observer ◽  
Observer Design ◽  
Descriptor Systems ◽  
Takagi Sugeno

scholarly journals Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 88
Author(s):  
Andreas Rauh ◽  
Auguste Bourgois ◽  
Luc Jaulin
Keyword(s):  
Discrete Time ◽  
State Observer ◽  
Observer Design ◽  
State Variables ◽  
Computationally Efficient ◽  
True Solution ◽  
Bounded Error ◽  
Quasi Linear System ◽  
Outer Bounds ◽  
Predictor Corrector

Thick ellipsoids were recently introduced by the authors to represent uncertainty in state variables of dynamic systems, not only in terms of guaranteed outer bounds but also in terms of an inner enclosure that belongs to the true solution set with certainty. Because previous work has focused on the definition and computationally efficient implementation of arithmetic operations and extensions of nonlinear standard functions, where all arguments are replaced by thick ellipsoids, this paper introduces novel operators for specifically evaluating quasi-linear system models with bounded parameters as well as for the union and intersection of thick ellipsoids. These techniques are combined in such a way that a discrete-time state observer can be designed in a predictor-corrector framework. Estimation results are presented for a combined observer-based estimation of state variables as well as disturbance forces and torques in the sense of an unknown input estimator for a hovercraft.

Output Adaptive Observers Design for Linear Non-Stationary Systems with Polynomial Parameters

2021 ◽  
Vol 22 (8) ◽  
pp. 404-410
Author(s):  
K. B. Dang ◽  
A. A. Pyrkin ◽  
A. A. Bobtsov ◽  
A. A. Vedyakov ◽  
S. I. Nizovtsev
Keyword(s):  
Linear Time ◽  
State Observer ◽  
Observer Design ◽  
Model Parameters ◽  
Time Varying ◽  
State Variables ◽  
Unknown Constant ◽  
Established Method ◽  
Time Varying Parameters ◽  
True Values

The article deals with the problem of state observer design for a linear time-varying plant. To solve this problem, a number of realistic assumptions are considered, assuming that the model parameters are polynomial functions of time with unknown coefficients. The problem of observer design is solved in the class of identification approaches, which provide transformation of the original mathematical model of the plant to a static linear regression equation, in which, instead of unknown constant parameters, there are state variables of generators that model non-stationary parameters. To recover the unknown functions of the regression model, we use the recently well-established method of dynamic regressor extension and mixing (DREM), which allows to obtain monotone estimates, as well as to accelerate the convergence of estimates to the true values. Despite the fact that the article deals with the problem of state observer design, it is worth noting the possibility of using the proposed approach to solve an independent and actual estimation problem of unknown time-varying parameters.

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