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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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M7.2. Steady-State and Dynamic Behavior

We use the following parameters for a substrate inhibition model for this control study:

The steady-state dilution rate is Ds = 0.3 hr-1 (and the residence time is 3.33 hours) and the feed substrate concentration is x2fs = 4.0 g/liter.

Steady-State Conditions

The nonlinear process has the following three steady-state solutions (operating points) to Equation M7.1 for a dilution rate of 0.3 hr-1:

Steady stateBiomass concentrationSubstrate concentration stability
Equilibrium 1—wash outx1s = 0x2s = 4.0stable
Equilibrium 2—nontrivialx1s = 0.995103x2s = 1.512243unstable
Equilibrium 3—nontrivialx1s = 1.530163x2s

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