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 State Observer Design for Delayed Genetic Regulatory Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li-Ping Tian ◽  
Zhi-Jun Wang ◽  
Amin Mohammadbagheri ◽  
Fang-Xiang Wu
Keyword(s):  
Regulatory Network ◽  
Regulatory Networks ◽  
Estimation Error ◽  
State Observer ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Observer Design ◽  
Linear Matrix ◽  
Globally Asymptotically Stable ◽  
Internal States

Genetic regulatory networks are dynamic systems which describe the interactions among gene products (mRNAs and proteins). The internal states of a genetic regulatory network consist of the concentrations of mRNA and proteins involved in it, which are very helpful in understanding its dynamic behaviors. However, because of some limitations such as experiment techniques, not all internal states of genetic regulatory network can be effectively measured. Therefore it becomes an important issue to estimate the unmeasured states via the available measurements. In this study, we design a state observer to estimate the states of genetic regulatory networks with time delays from available measurements. Furthermore, based on linear matrix inequality (LMI) approach, a criterion is established to guarantee that the dynamic of estimation error is globally asymptotically stable. A gene repressillatory network is employed to illustrate the effectiveness of our design approach.

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.

Robust Observer Design for Systems With Deterministic and Stochastic Uncertainties

2004 ◽  
Author(s):  
Jongchul Jung ◽  
Tae Hee Lee ◽  
Jeffrey L. Stein ◽  
Kunsoo Huh
Keyword(s):  
Optimization Problem ◽  
Design Method ◽  
Estimation Error ◽  
Error Variance ◽  
Error Modeling ◽  
Observer Design ◽  
Linear Matrix ◽  
Estimation Performance ◽  
L2 Norm ◽  
Stochastic Uncertainties

An observer design method for stochastic and deterministic robustness is developed so that the observer is less sensitive to uncertainties in transient and in steady-state observer performance. The uncertainties include not only deterministic factors such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic factors such as disturbance and sensor noise. From a stochastic perspective, a small value in estimation error variance represents robustness to the stochastic uncertainties. It is shown that the upper bound of the error variance can be minimized by reducing the observer gain and by increasing the decay rate of the observer. From a deterministic perspective, a small value in the L2 norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic uncertainties. An optimization problem constrained by a linear matrix inequality condition is formulated for both the deterministic and the stochastic robustness. The observer gain can be selected as a trade-off solution and the estimation performance to stochastic and deterministic uncertainties is demonstrated on simulation examples.

Sampled-data extended state observer-based backstepping control of two-link flexible manipulator

2019 ◽  
Vol 41 (13) ◽  
pp. 3581-3599 ◽  
Author(s):  
Umesh Kumar Sahu ◽  
Bidyadhar Subudhi ◽  
Dipti Patra
Keyword(s):  
Control Strategies ◽  
Estimation Error ◽  
Experimental Studies ◽  
State Observer ◽  
Lyapunov Theory ◽  
Extended State Observer ◽  
Flexible Manipulator ◽  
Sampled Data ◽  
Extended State ◽  
Model Uncertainties

Currently, space robots such as planetary robots and flexible-link manipulators (FLMs) are finding specific applications to reduce the cost of launching. However, the structural flexible nature of their arms and joints leads to errors in tip positioning owing to tip deflection. The internal model uncertainties and disturbance are the key challenges in the development of control strategies for tip-tracking of FLMs. To deal with these challenges, we design a tip-tracking controller for a two-link flexible manipulator (TLFM) by developing a sampled-data extended state observer (SD-ESO). It is designed to reconstruct uncertain parameters for accurate tip-tracking control of a TLFM. Finally, a backstepping (BS) controller is designed to attenuate the estimation error and other bounded disturbances. Convergence and stability of the proposed control system are investigated by using Lyapunov theory. The benefits (control performance and robustness) of the proposed SD-ESO-based BS controller are compared with other similar approaches by pursuing both simulation and experimental studies. It is observed from the results obtained that SD-ESO-based BS Controller effectively compensates the deviation in tip-tracking performance of TLFM due to non-minimum phase behavior and model uncertainties with an improved transient response.

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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