Victor Alcaraz-Gonzalez

Background: The anaerobic digestion (AD) of the organic fraction of municipal solid waste (OFMSW) is a widely used waste-to-energy technology. However, inhibition effects can drive the process toward acidification or washout, with a consequent loss of treatment efficiency. Feedback control can prevent these undesirable conditions, but the biomass concentration is not measurable online. Methods: This work proposes an observer-based control scheme for the AD of the soluble fraction of OFMSW near an inhibited nominal operating condition. An extended Kalman filter (EKF) estimates the acidogenic biomass from the online measurement of the soluble organic substrate. A proportional–integral (PI) controller regulates the estimated biomass by manipulating the dilution rate. Three tuning methods are compared: approximate M-constrained integral gain optimization (AMIGO), Skogestad internal model control (SIMC), and frequency-domain auto-tuning. The convergence of the scheme is analyzed through Lyapunov and input-to-state stability arguments. The evaluation is simulation-based. Results: In an open loop, the observer converged under initial offsets of up to 35%, with steady-state error norms below 0.31 mg/L. The convergence time ranged from 45.3 to 81.3 d, depending on the initial estimation error. In a closed loop, nine controller designs tracked the reference and rejected feed perturbations over a 1000 d horizon. Under a stoichiometric mismatch of $\pm 5\%$, the true-state tracking error of design S2 increased from 459.5 to 1783.5 mg d/L. The estimated-state error remained at 558.4 mg d/L. Estimated-state tracking can therefore conceal substantial true-state errors. The fastest design achieved the lowest estimated-state IAE, 501.1 mg d/L, but exhibited the lowest gain margin, 5.8 dB. The lowest true-state IAE, 450.2 mg d/L, corresponded to a design with a phase margin of ${60}^{\circ }$. Conversely, the most conservative designs paired the largest IAE values with the largest gain margins, up to 15.2 dB. Conclusions: The proposed scheme maintains the anaerobic process around its inhibited nominal operating condition under the tested feed disturbances. The scheme uses a standard analytical measurement. The results support its feasibility as a soft sensor-based control strategy for anaerobic reactors near this operating condition. The prevention of acidification or washout under increased inhibition disturbances is beyond the tested scope.

This paper presents a control design framework that systematically translates nonlinear equilibrium operability analysis into frequency-domain robust synthesis for continuous microbial electrolysis cells (MEC). Since MEC operation is threatened by washout and highly variable influent conditions, analytical local conditions for the existence and local stability of normal operating conditions (NOC) and washout equilibria are first established. Departing from these nonlinear properties, the model is linearized within the locally validated NOC region, and a parametric sensitivity screening is used to identify dominant uncertainty sources ($\alpha$, ${\mu }_{max}$, $K_d$). These are embedded into an unstructured multiplicative uncertainty weight, enabling the synthesis of nominal and robust $H_{\infty }$ controllers that explicitly account for actuator effort, disturbance rejection, and measurement noise. Controller order reduction via balanced truncation is performed while preserving closed-loop local robustness properties. As a benchmark, an internal model control proportional–integral (IMC-PI) controller is derived, and its single tuning parameter is selected by solving a univariate multi-objective optimization that balances integral absolute error and maximum control effort, yielding a Pareto-optimal compromise. Numerical simulations under simultaneous inlet disturbances, parametric variations, measurement noise, and actuator saturation show that the reduced-order robust $H_{\infty }$ controller outperforms the optimized IMC-PI in the tracking–effort trade-off, while the nominal $H_{\infty }$ controller satisfies an a posteriori robust stability test for the linearized dynamics. The proposed framework provides a systematic path from nonlinear operability analysis to implementable robust control, demonstrating that high-order $H_{\infty }$ designs can be reduced to low-order transfer functions suitable for standard industrial control hardware while preserving local stability properties against realistic process perturbations.