Kalman Filter based Newton Extremum Seeking Control for Maximum Gases Production Rates of Anaerobic Digestion Process (original) (raw)
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Mathematics
In this paper, a new Newton-based extremum-seeking control for dynamic systems is proposed using Kalman filter for gradient and Hessian estimation as well as a stochastic perturbation signal with time-varying amplitude. The obtained Kalman filter based Newton extremum-seeking control (KFNESC) makes it possible to accelerate the convergence to the extremum and attenuate the steady-state oscillations. The convergence and oscillation attenuation properties of the closed-loop system with KFNESC are considered, and the proposed control is applied to a two-stages anaerobic digestion process in order to maximize the hydrogen production rate, which has better robustness and a slower steady-state oscillation with the comparison of Newton-based ESC and sliding mode ESC.
On the Extremum-Seeking Control Design and Application for Anaerobic Digestion Processes
Ecological Engineering and Environment Protection
The paper deals with the optimization of nonlinear systems by using Extremum Seeking Control (ESC) without any prior knowledge of the system model. An Extend Kalman Filter based Extremum Seeking Control (EKF based ESC) is proposed, which can make the amplitude of perturbation signal variable and ensure convergence to zero, i.e. without steady-state oscillation. The proposed ESC algorithm makes also possible to obtain more accurate gradient estimate and more rapid ESC convergence. The proposed EKF based ESC algorithm is applied to a fifth-order model of anaerobic digestion process and its performances are compared with the performances of the classical ESC algorithm. Key Words: ESC, EKF, steady state oscillation, anaerobic digestion processes
Ecological Engineering and Environment Protection
In this paper, a new structure of extremum seeking algorithm is applied to the two-stage anaerobic digestion process to maximize the outflow rate of both hydrogen and methane. The model of the two-stage AD process is presented, which provides the characteristics of the total gas production rate. Based on the original Extremum Seeking Control (ESC), a novel Composed Recursive Model Free Controller (CRMFC) is added for maximum tracking for the gas production in the bioreactors. The proposed controller comprises a recursive model free stabilization term and a recursive time delay compensation term. Standard ESC, Newton-based ESC and Kalman filter (KF) based ESC are respectively combined with the new model-free controller to verify the proposed structure. Numerical simulations illustrate the performance of the proposed controller.
Extremum Seeking Control of a Three-Stage Anaerobic Digestion Model
IFAC-PapersOnLine, 2020
Anaerobic digestion systems are of increasing interest as they are able to produce biogas while treating waste/wastewater. However, their dynamics is complex and not fully understood, which makes their operation and optimization difficult. In this paper, an extremum seeking control algorithm is applied to a three-stage anaerobic digestion system to maximize the outflow rate of methane. In a first stage, the stability analysis of the three-stage model is performed, which provides valuable information on the type of steady states the system possesses, the occurrence of the optimal steady state and good practices to successfully operate the system. In a second stage, an extremum seeking controller, which employs a recursive least-squares algorithm for block-oriented models, is implemented and tested on the anaerobic digestion model. Simulation results show that the proposed controller globally stabilizes the process dynamics at the optimal operating point. Compared to the classical extremum seeking algorithms, the proposed technique allows for a faster convergence, in an imposed time period assigned by the designer.
Identification and extremum seeking control of the anaerobic digestion of organic wastes
The principle of extremum seeking control has been applied to 2 nd and 4 th order models of anaerobic digestion. In the case of variations of the inlet organics the maximum biogas flow rate was obtained. Laboratory experiments have been provided with step and impuls changes of acetate addition (new control input). Based on the dynamical responses of the biogas flow rate, non-linear optimization and simulations some of the model coefficients have been estimated more precisely. Inputoutput static characteristics, optimal steady-state and some constraints have been derived analytically.
Kalman Filter Design for a Second-order Model of Anaerobic Digestion
International Journal Bioautomotion
The paper deals with the state estimation of a second-order model of anaerobic digestion. This estimation is necessary to implement the sophisticated control algorithms that have already been developed for this process. Hereby design and performance of a classical Kalman filter (compared with other two deterministic estimation approaches) for the main variables of this model have been discussed and analysed by simulations. The performance analysis has been conducted at realistic random perturbations, comparable with experimental data, on the one hand, and on the other -with and without parameter perturbations. Although at random perturbations alone the Kalman filter has a clear advantage over the two equipollent deterministic estimators, at the presence also of parameter perturbations, to which the Kalman filter is more sensitive, no such advantage is guaranteed.
Water Science and Technology, 2006
A state-dependent variable-gain control system is implemented to follow the characteristics of a laboratory-scale up-flow anaerobic fixed-bed reactor dynamically. The transition from one state to another is determined on an hourly basis, depending on difference between the setpoint of the reactor pH and its true value. Considerable improvement of the process stability-reduction of oscillation in both the reactor pH and biogas production rate during high-rate operation, has been achieved, although the control structure is simple and intuitive.
Nonlinear adaptive stabilizing control of an anaerobic digestion model with unknown kinetics
2012
In this paper, we consider a nonlinear model of a biological wastewater treatment process, on the basis of two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically validated and reliable. We propose a feedback control law for asymptotic stabilization of the closed-loop system towards a previously chosen operating point. A numerical extremum seeking algorithm is applied to stabilize the dynamics towards an equilibrium point with maximal methane flow rate. Computer simulations are reported to illustrate the theoretical results.
Modelling and dynamic compensator control of the anaerobic digestion of organic wastes
The paper deals with the modelling and control of anaerobic fermentation processes (anaerobic digestion). Laboratory experiments have been carried out on an automated laboratory-scale biogas unit. For this process 2nd and 5th order non-linear models have been considered. A simple methodology for parameters estimation, based on non-linear optimisation method, has been developed. The control is reduced to the regulation of biogas production rate or the concentration of the outlet polluted organic matter. For design purposes the non-linear model has been transformed into a linear one with interval parameters. In both cases (the regulation of biogas production rate or the concentration of the polluting organics) compensators have been designed according to the internal model principle. The effectiveness of the algorithms designed has been illustrated by simulation experiments. An important feature of the proposed algorithms is their robustness over the parameter uncertainties in the process models.
Water Science and Technology, 2005
In this work, an optimization method is implemented in an anaerobic digestion model to estimate its kinetic parameters and yield coefficients. This method combines the use of advanced state estimation schemes and powerful nonlinear programming techniques to yield fast and accurate estimates of the aforementioned parameters. In this method, we first implement an asymptotic observer to provide estimates of the non-measured variables (such as biomass concentration) and good guesses for the initial conditions of the parameter estimation algorithm. These results are then used by the successive quadratic programming (SQP) technique to calculate the kinetic parameters and yield coefficients of the anaerobic digestion process. The model, provided with the estimated parameters, is tested with experimental data from a pilot-scale fixed bed reactor treating raw industrial wine distillery wastewater. It is shown that SQP reaches a fast and accurate estimation of the kinetic parameters despite highly noise corrupted experimental data and time varying inputs variables. A statistical analysis is also performed to validate the combined estimation method. Finally, a comparison between the proposed method and the traditional Marquardt technique shows that both yield similar results; however, the calculation time of the traditional technique is considerable higher than that of the proposed method.