TY - JOUR
T1 - Uniform step-by-step observer for aerobic bioreactor based on super-twisting algorithm
AU - Martínez-Fonseca, N.
AU - Chairez, I.
AU - Poznyak, A.
N1 - Publisher Copyright:
© 2014 Springer-Verlag Berlin Heidelberg.
PY - 2014/11/5
Y1 - 2014/11/5
N2 - This paper describes a fixed-time convergent step-by-step high order sliding mode observer for a certain type of aerobic bioreactor system. The observer was developed using a hierarchical structure based on a modified super-twisting algorithm. The modification included nonlinear gains of the output error that were used to prove uniform convergence of the estimation error. An energetic function similar to a Lyapunov one was used for proving the convergence between the observer and the bioreactor variables. A nonsmooth analysis was proposed to prove the fixed-time convergence of the observer states to the bioreactor variables. The observer was tested to solve the state estimation problem of an aerobic bioreactor described by the time evolution of biomass, substrate and dissolved oxygen. This last variable was used as the output information because it is feasible to measure it online by regular sensors. Numerical simulations showed the superior behavior of this observer compared to the one having linear output error injection terms (high-gain type) and one having an output injection obtaining first-order sliding mode structure. A set of numerical simulations was developed to demonstrate how the proposed observer served to estimate real information obtained from a real aerobic process with substrate inhibition.
AB - This paper describes a fixed-time convergent step-by-step high order sliding mode observer for a certain type of aerobic bioreactor system. The observer was developed using a hierarchical structure based on a modified super-twisting algorithm. The modification included nonlinear gains of the output error that were used to prove uniform convergence of the estimation error. An energetic function similar to a Lyapunov one was used for proving the convergence between the observer and the bioreactor variables. A nonsmooth analysis was proposed to prove the fixed-time convergence of the observer states to the bioreactor variables. The observer was tested to solve the state estimation problem of an aerobic bioreactor described by the time evolution of biomass, substrate and dissolved oxygen. This last variable was used as the output information because it is feasible to measure it online by regular sensors. Numerical simulations showed the superior behavior of this observer compared to the one having linear output error injection terms (high-gain type) and one having an output injection obtaining first-order sliding mode structure. A set of numerical simulations was developed to demonstrate how the proposed observer served to estimate real information obtained from a real aerobic process with substrate inhibition.
KW - Continuous stirred tanks reactor
KW - Fixed-time convergence
KW - State observer
KW - Step-by-step observation
KW - Super-twisting observer
UR - http://www.scopus.com/inward/record.url?scp=84937965805&partnerID=8YFLogxK
U2 - 10.1007/s00449-014-1227-0
DO - 10.1007/s00449-014-1227-0
M3 - Artículo
C2 - 24906429
SN - 1615-7591
VL - 37
SP - 2493
EP - 2503
JO - Bioprocess and Biosystems Engineering
JF - Bioprocess and Biosystems Engineering
IS - 12
M1 - 1227
ER -