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

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M7.4. Unstable Steady-State Operating Point

Design an IMC-based PID controller to control the bioreactor at equilibrium point 2—the unstable nontrivial point. The steady state (also use this as the initial condition for your simulations) is

At this point, the state space model is

Use MATLAB to find that the eigenvalues are –0.3 and 0.169836 hr-1, so the system is unstable and the IMC-based PID method for unstable systems must be used (Table 9-3). Find the transfer function relating the dilution rate to the biomass concentration and use this for ...

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