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.

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.

This paper deals with the theoretical comparison of biogas and energy yields of one-stage anaerobic digestion processes (OSAD) with biomethane production and two-stage anaerobic digestion processes (TSAD) producing biohydrogen and biomethane. The comparative study of the biogas yield from OSAD and TSAD systems is performed on the base on mathematical models obtained in our previous papers. The possible maximal yields of biohydrogen and biomethane are calculated by the static characteristics and extremum points of both systems. Simulation results suggest that in comparison to OSAD, the increase in biogas (biohydrogen and biomethgane) production of TSAD can reach to 75.18%. The energy produced from two-stage anaerobic digestion processes is 1.32 to 1.486 times greater than those from one-stage anaerobic digestion processes (depending of the inlet organics concentrations), which means TSAD is a better choice considering biogas and energy production.

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