Observer-Based Control for Uncertain Nonlinear Systems Applied to Continuous Biochemical Reactors

The purpose of this paper is to present an observer-based control design with application to continuous bioreactors. For this purpose, phenomenological bioreactor models were represented by identified linear models plus unknown modelling error terms. Therefore, an uncertainty-based observer with a polynomial structure capable of estimating the unknown modelling error of the reactor representation is coupled to a linear input-output controller. The proposed methodology was evaluated in a sulphate reduction bioprocess and an acetone-butanol-ethanol (ABE) fermentation process for butanol (biofuel) production, under continuous regimes. Experimentally validated mathematical models were considered for this purpose. A theoretical framework is presented to demonstrate the corresponding closed-loop stability of the systems, and numerical simulations were carried out to corroborate the satisfactory performance of the proposed methodology.

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On the variance parameter estimator in general linear models

Metrika ◽

10.1007/s00184-019-00751-4 ◽

2019 ◽

Vol 83 (2) ◽

pp. 243-254

Author(s):

Mathias Lindholm ◽

Felix Wahl

Keyword(s):

Sample Size ◽

Linear Models ◽

General Linear ◽

Finite Sample ◽

Parameter Estimator ◽

General Linear Models ◽

Vector Autoregressive ◽

Finite Sample Size ◽

Error Terms ◽

Variance Parameter

Abstract In the present note we consider general linear models where the covariates may be both random and non-random, and where the only restrictions on the error terms are that they are independent and have finite fourth moments. For this class of models we analyse the variance parameter estimator. In particular we obtain finite sample size bounds for the variance of the variance parameter estimator which are independent of covariate information regardless of whether the covariates are random or not. For the case with random covariates this immediately yields bounds on the unconditional variance of the variance estimator—a situation which in general is analytically intractable. The situation with random covariates is illustrated in an example where a certain vector autoregressive model which appears naturally within the area of insurance mathematics is analysed. Further, the obtained bounds are sharp in the sense that both the lower and upper bound will converge to the same asymptotic limit when scaled with the sample size. By using the derived bounds it is simple to show convergence in mean square of the variance parameter estimator for both random and non-random covariates. Moreover, the derivation of the bounds for the above general linear model is based on a lemma which applies in greater generality. This is illustrated by applying the used techniques to a class of mixed effects models.

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Modeling Approaches to Predicting Persistent Hotspots in SCORE Studies for Gaining Control of Schistosomiasis Mansoni in Kenya and Tanzania

The Journal of Infectious Diseases ◽

10.1093/infdis/jiz529 ◽

2019 ◽

Vol 221 (5) ◽

pp. 796-803 ◽

Cited By ~ 2

Author(s):

Ye Shen ◽

Meng-Hsuan Sung ◽

Charles H King ◽

Sue Binder ◽

Nupur Kittur ◽

...

Keyword(s):

Linear Models ◽

Predictive Accuracy ◽

Infection Intensity ◽

Intensity Of Infection ◽

Satisfactory Performance ◽

Total Prevalence ◽

Stable Performance ◽

Using Data ◽

Predictive Approaches ◽

Combined Data

Abstract Background Some villages, labeled “persistent hotspots (PHS),” fail to respond adequately in regard to prevalence and intensity of infection to mass drug administration (MDA) for schistosomiasis. Early identification of PHS, for example, before initiating or after 1 or 2 years of MDA could help guide programmatic decision making. Methods In a study with multiple rounds of MDA, data collected before the third MDA were used to predict PHS. We assessed 6 predictive approaches using data from before MDA and after 2 rounds of annual MDA from Kenya and Tanzania. Results Generalized linear models with variable selection possessed relatively stable performance compared with tree-based methods. Models applied to Kenya data alone or combined data from Kenya and Tanzania could reach over 80% predictive accuracy, whereas predicting PHS for Tanzania was challenging. Models developed from one country and validated in another failed to achieve satisfactory performance. Several Year-3 variables were identified as key predictors. Conclusions Statistical models applied to Year-3 data could help predict PHS and guide program decisions, with infection intensity, prevalence of heavy infections (≥400 eggs/gram of feces), and total prevalence being particularly important factors. Additional studies including more variables and locations could help in developing generalizable models.

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Robust Piecewise-Linear State Observers for Flexible Link Mechanisms

Volume 3: Dynamic Systems and Controls, Symposium on Design and Analysis of Advanced Structures, and Tribology ◽

10.1115/esda2006-95445 ◽

2006 ◽

Author(s):

Roberto Caracciolo ◽

Dario Richiedei ◽

Alberto Trevisani

Keyword(s):

Nonlinear Model ◽

Closed Loop ◽

Linear Models ◽

Piecewise Linear ◽

Equilibrium Points ◽

Loop System ◽

State Variables ◽

Flexible Link ◽

Closed Loop System ◽

State Observers

This paper tackles the problem of designing state observers for flexible link mechanisms: an investigation is made on the possibility of employing observers making use of suitable piecewise-linear truncated dynamics models. A general approach is proposed, which provides an objective way of synthesizing observers preventing the instability that may arise from using reduced-order linearized models. The approach leads to the identification of the regions of the domain of the state variables where the linear approximations of the nonlinear model can be considered acceptable. To this purpose, first of all, the stability of the equilibrium points of the closed-loop system is assessed by applying the eigenvalue analysis to appropriate piecewise-linear models. Admittedly, the dynamics of such a closed-loop system is affected by the pole perturbation caused by spillover, and by the discrepancies between the linearized models of the plant and the one of the observer. Additionally, when nodal elastic displacements and velocities are not bounded in the infinitesimal neighborhoods of the equilibrium points, the difference between the nonlinear model and the locally-linearized one is expressed in terms of unstructured uncertainty and stability is assessed by H∞ robust analysis. The method is demonstrated by applying it to a closed-chain flexible link mechanism.

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Aligned Rank Tests for Linear Models with Autocorrelated Error Terms

Journal of Multivariate Analysis ◽

10.1006/jmva.1994.1040 ◽

1994 ◽

Vol 50 (2) ◽

pp. 175-237 ◽

Cited By ~ 51

Author(s):

M. Hallin ◽

M.L. Puri

Keyword(s):

Linear Models ◽

Rank Tests ◽

Autocorrelated Error ◽

Error Terms ◽

Aligned Rank

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ALIGNED RANK TESTS FOR LINEAR MODELS WITH AUTOCORRELATED ERROR TERMS

Time Series, Fuzzy Analysis and Miscellaneous Topics ◽

10.1515/9783110917833.288 ◽

2012 ◽

Author(s):

MARC HALLIN ◽

MADAN L. PURI

Keyword(s):

Linear Models ◽

Rank Tests ◽

Autocorrelated Error ◽

Error Terms ◽

Aligned Rank

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Chilled Water Temperature Control of HVAC System Using GPC Based Controller

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.151.626 ◽

2012 ◽

Vol 151 ◽

pp. 626-631

Author(s):

Qiang Ma ◽

Jian Gang Lu ◽

Qin Min Yang ◽

Jin Shui Chen ◽

You Xian Sun

Keyword(s):

Predictive Control ◽

Pid Controller ◽

Closed Loop ◽

Controller Design ◽

Simulation Environment ◽

Closed Loop System ◽

Satisfactory Performance ◽

Chilled Water ◽

The Stability ◽

Theoretical Results

This work proposes a generalized predictive control (GPC) based controller for the temperature of HVAC chilled water supply. In this paper, several models of evaporator are firstly introduced, wherein an identified black-box model is selected for the purpose of controller design. Based on this model, a GPC based controller is employed to obtain a satisfactory performance even with the presence of disturbance. The theoretical results show the stability of the closed-loop system and the performance of this scheme is compared with that of traditional PID controller under simulation environment.

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Robust Piecewise-Linear State Observers for Flexible Link Mechanisms

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2909600 ◽

2008 ◽

Vol 130 (3) ◽

Cited By ~ 12

Author(s):

Roberto Caracciolo ◽

Dario Richiedei ◽

Alberto Trevisani

Keyword(s):

Nonlinear Model ◽

Closed Loop ◽

Linear Models ◽

Piecewise Linear ◽

Equilibrium Points ◽

Loop System ◽

State Variables ◽

Flexible Link ◽

Closed Loop System ◽

State Observers

This paper tackles the problem of designing state observers for flexible link mechanisms: An investigation is made on the possibility of employing observers making use of suitable piecewise-linear truncated dynamics models. A general and novel approach is proposed, which provides an objective way of synthesizing observers preventing the instability that may arise from using reduced-order linearized models. The approach leads to the identification of the regions of the domain of the state variables where the linear approximations of the nonlinear model can be considered acceptable. To this purpose, first of all, the stability of the equilibrium points of the closed-loop system is assessed by applying the eigenvalue analysis to appropriate piecewise-linear models. Admittedly, the dynamics of such a closed-loop system is affected by the perturbation of the poles caused by spillover and by the discrepancies between the linearized models of the plant and the one of the observer. Additionally, when nodal elastic displacements and velocities are not bounded in the infinitesimal neighborhoods of the equilibrium points, the difference between the nonlinear model and the locally linearized one is expressed in terms of unstructured uncertainty and stability is assessed through H∞ robust analysis. The method is demonstrated by applying it to a closed-chain flexible link mechanism.

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Block external bootstrap in partially linear models with nonstationary strong mixing error terms

Canadian Journal of Statistics ◽

10.2307/3316019 ◽

2004 ◽

Vol 32 (4) ◽

pp. 335-346 ◽

Cited By ~ 1

Author(s):

Jinhong You ◽

Gemai Chen

Keyword(s):

Linear Models ◽

Strong Mixing ◽

Partially Linear Models ◽

Partially Linear ◽

Error Terms

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Comparison of acetone–butanol–ethanol fermentation and ethanol catalytic upgrading as pathways for butanol production: A techno-economic and environmental assessment

Biofuel Research Journal ◽

10.18331/brj2021.8.2.4 ◽

2021 ◽

Vol 8 (2) ◽

pp. 1384-1399

Author(s):

Estefanny Carmona-Garcia ◽

Paula Andrea Marín-Valencia ◽

Juan Camilo Solarte-Toro ◽

Konstantinos Moustakas ◽

Carlos Ariel Cardona-Alzate

Keyword(s):

Environmental Impact ◽

Fermentation Process ◽

Value Added ◽

Abe Fermentation ◽

Economic Feasibility ◽

Biofuel Production ◽

Selling Price ◽

Butanol Production ◽

Catalytic Upgrading ◽

Acetone Butanol Ethanol

Butanol is an important compound used as a building block for producing value-added products and an energy carrier. The main butanol production pathways are conventional acetone–butanol–ethanol (ABE) fermentation and catalytic upgrading of ethanol. On the other hand, the application of biomass as a promising substrate for biofuel production has been widely considered recently. However, few studies have compared different butanol production pathways using biomass as raw material. In light of that, the present work aims (i) to provide a short review of the catalytic ethanol upgrading and (ii) to compare conventional ABE fermentation and catalytic ethanol upgrading processes from the economic and environmental perspectives. Aspen Plus v9.0 was used to simulate both processes. The economic and environmental assessments were carried out considering the Colombian economic context, a gate-to-gate approach, and single impact categories. Considering a processing scale of 1000 ton/d, the conventional ABE fermentation process presented a more favorable technical, economic, and environmental performance for butanol production from biomass. It also offered lower net energy consumption (i.e., 57.9 GJ/ton of butanol) and higher butanol production (i.e., 2.59 ton/h). Nevertheless, the proposed processing scale was insufficient to reach economic feasibility for both processes. To overcome this challenge, the minimum processing scale had to be higher than 1584 ton/d and 1920 ton/d for conventional ABE fermentation and catalytic ethanol upgrading, respectively. Another critical factor in enhancing the economic feasibility of both butanol production pathways was the minimum selling price of butanol. More specifically, prices higher than 1.56 USD/kg and 1.80 USD/kg would be required for conventional ABE fermentation and catalytic ethanol upgrading, respectively. From the environmental impact point of view, the conventional ABE fermentation process led to a lower potential environmental impact than catalytic ethanol upgrading (0.12 PEI/kg vs. 0.18 PEI/kg, respectively).

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