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)

frlopez@ittg.edu.mx

Request for the paper

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)

Didier.Theilliol@univ-lorraine.fr