Ixbalank Torres-Zúñiga

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.