Robust sensor fault detection and isolation of an anerarobic bioreactor modeled as a descriptor-LPV...
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Transcript of Robust sensor fault detection and isolation of an anerarobic bioreactor modeled as a descriptor-LPV...
ROBUST SENSOR FAULT DETECTION AND ISOLATION OF AN ANERAROBIC BIOREACTOR
MODELED AS A DESCRIPTOR-LPV SYSTEM
F.R. LÓPEZ ESTRADA, J.H. CASTAÑON-GONZALES (TecNM - Instituto Tecnológico de Tuxla Gutiérrez, México)
J.C. PONSART, D. THEILLIOL (CRAN – University of Lorraine, Nancy, France)
C. M. ASTORGA-Z (CENIDET, Cuernavaca, México)
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21st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
Introduction
Process description and modeling
FDI Observer design
Simulation results
Conclusions
31st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
Introduction
Process description and modeling
FDI Observer design
Simulation results
Conclusions
41st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
INTRODUCTION
Variety ofapplications
A bioreactor is a vessel in which a bioprocess is carried out which involves microorganism or biochemical active substances derived from such organism.
The bioreactors are usually used for microorganism reproduction or to obtain a final product from the cultivated medium
51st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
INTRODUCTION
• Bioreactors are heavy, complex, and in some cases remotely installed• They can be instrumented with pH, temperature, biomass, pressure,
among others• Also they have different type of actuators as valves, motors, pumps,
among others• The bio-reaction can take months, therefore the safety of the process and
the product is essential.• Monitoring can be guaranteed with fault detection algorithms.
61st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
INTRODUCTION
• A mathematical model of a bioreactor describes how the bio-reaction between the bacterias and the subtract is produced
• The model is composed by nonlinear differential equations that describe the slow dynamic of the system, and algebraic equations describe the fast dynamic
• By integrating these both dynamics, it is possible to model a bioreactor as a descriptor nonlinear system
Nonlinear systems are complex, and the equations are difficult to handle
How to reduce the complexity of these equations without loss compromise between representation and controllability ?
71st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
Introduction
Process description and modeling
FDI Observer design
Simulation results
Conclusions
81st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
PROCESS DESCRIPTION
• The modeled process in an up-flow anaerobic sludge blanket bioreactor (UASB)
• The objective of the process is to produce biogas by means of the consumption of the organic matter with anaerobic bacterias
• Security is essential: if a sensor fails without any detection, all the process and the equipment can be lost
91st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
PROCESS MODEL
Variable Description
concentration of the anaerobic biomass
concentration of organic matter
outlet flow of methane bio-gas
specific growth rate
Dilution rate & concentration of COD
More details in the paper
The process is represented by the following set of differential and algebraic equations
(1)
101st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
LPV MODEL
The descriptor nonlinear model can be written as
The non-constant elements are considered as scheduling variables bounded in the following segments
(2)
111st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
LPV MODEL
For each variable, two gain scheduling functions are obtained as
24=16 scheduling functions are computed as the product of the weighting functions that correspond to each local model
with
The scheduling functions are in function of the states that can be unmeasurable, and need to be estimated
(4)
(3)
(5)
121st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
D-qLPV MODEL
Then, a Descriptor quasi-LPV model is obtained as
where
(6)
131st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
Introduction
Process description and modeling
FDI Observer design
Simulation results
Conclusions
141st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
FAULT DETECTION AND ESTIMATION PROBLEM
The system can be affected by sensor faults
The challenge is to detect and estimate these faults, despite the problem of unknown gain scheduling functions
depending on the system's states
Then, a suitable design needs the estimation of the scheduling functions and the states
(7)
151st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
OBSERVER DESIGN
In order to estimate the unmeasurable Gain scheduling function the first challenge is to design an observer state by considering the system without faults.
Then, for the D-qLPV system
The following LPV observer is proposed
Note that the observer and thesystems scheduling functions
are different
are unknown gain matrices to be synthesized
(8)
(9)
161st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
OBSERVER DESIGN
To deal with Unmeasurable Gain scheduling Functions, the D-qLPV system is transformed into an uncertain system with estimated scheduling function as follows:
where
(10)
171st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
ESTIMATION ERROR
The residual estimation error dynamic is obtained as follows (see paper for details)
Finally by considering H_infinity approach in order to be robust to disturbance, noise and to guarantee asymptotic stability,
the following Theorem is obtained
(11)
181st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
Theorem 1: Robust state observer
OBSERVER SOLUTION
Given system (8), observer (9) and let the attenuation level > 0, the residual state-space
error system (11) is asymptotically stable with performance if it satisfies
and if there exist matrices
such that:
Then, the gain matrices of observer (9) are given by
(12)
H
191st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
SENSOR FAULT ESTIMATION
The same observer design can be considering to estimate sensor faults by considering the Generalized Observer Scheme
Then for p faults, a bank of p observers are designed as
Fault isolation is done by comparing the residuals with the Diagnosis Matrix
(13)
201st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
Introduction
Process description and modeling
FDI Observer design
Simulation results
Conclusions
211st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
SIMULATION RESULTS: MODEL VALIDATION
Initial conditions
X(1) = 0.23
X(2) = 0.6450
X(3) = 0.00001
X(4) = 0.001
221st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
SIMULATION RESULTS: STATE ESTIMATION
Computed attenuation level
= 0.0527
231st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
SIMULATION RESULTS: SCHEDULING FUNCTIONS
241st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
SIMULATION RESULTS: FAULT DETECTION
251st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
Introduction
Process description and modeling
FDI Observer design
Simulation results
Conclusions
261st IFAC Workshop LPVS 2015 – Grenoble - October, 7-9 2015
CONCLUSIONS
A D-LPV modeling and a fault detection system for an anaerobic bioreactor was proposed
An exact representation of the nonlinear-descriptor system was obtained by considering the sector nonlinearity approach
Unmeasurable gain scheduling functions (UGF) are considers. This consideration increases the level of abstraction, but also the applicability
An observer was designed with H_infinity performance
The H_infinity guarantee robustness and asymptotic stability
The proposed method was successfully applied to detect and to isolate sensor faults
Future work will be addressed to detect actuator faults and fault tolerant control
ROBUST SENSOR FAULT DETECTION AND ISOLATION OF AN ANERAROBIC BIOREACTOR
MODELED AS A DESCRIPTOR-LPV SYSTEM
F.R. LÓPEZ ESTRADA, J.H. Castañón-Gonzales (TecNM - Instituto Tecnológico de Tuxla Gutiérrez, México)
J.C. PONSART, D. THEILLIOL (CRAN – University of Lorraine, Nancy, France)
C. M. ASTORGA-ZARAGOZA, M. FLORES-MONTIEL (CENIDET, Cuernavaca, México)