On the estimation problem of a class of continuous bioreactors with unknown input

• The global estimation problem for nonlinear continuous bioreactors is addressed.
• Feed and reactor substrate concentrations are estimated from a biomass measurement.
• The observability or detectability depends on the kind of motion and growth kinetics.
• With iso/nonisotonic kinetics the state motions are single/bivalued observable.
• A single/bivalued observer robustly estimates the only/two possible motion/motions.

The estimation problem of substrate–biomass reactors with isotonic or nonisotonic growth is addressed. The unmeasured reactor and time-varying feed substrate concentrations must be estimated from the dilution rate input and biomass measurements. First, the solvability conditions (nonlinear-global observability or detectability) are characterized, finding that: (i) the conditions depend on particular motions and growth mechanisms, and (ii) with isotonic (or nonisotonic) growth, the unknown input–state pair is observable in the classical (or nonstandard) single-valued (S) [or bivalued (B)] sense. Then, a robustly convergent S (or B)-observer is designed accordingly. The S-observer yields the estimate of the only unmeasured input–state trajectory pair associated with the measured input–output signal. The B-observer yields the estimates of the two possible unmeasured input–state trajectory pairs associated with the measured input–output signal, each one satisfying the reactor mass balances. The developments and findings are illustrated with representative (Monod and Haldane) examples through analytic assessment and numerical simulation.