The saturated OF control problem for a class of four-state anaerobic digesters with volatile fatty acids (VFAs) measurement is addressed. The reactor must operate about an optimal steady-state, with maximum VFA consumption that is locally open-loop stable but not necessarily structurally stable. The problem is addressed as an interlaced control-observer design in the light of passivity, observability, and bifurcation properties. The result is a saturated linear PI controller with: (i) systematic construction and tuning and (ii) nonlocal robust stability conditions in terms of control gains and limits. The proposed approach is illustrated with a representative case example through numerical simulations, including a comparison with the switching control approach. (C) 2015 Elsevier Ltd. All rights reserved.