11_Bio_calibrationW12

11_Bio_calibrationW12 - Page 1 of 2 CHE 361:...

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Unformatted text preview: Page 1 of 2 CHE 361: “BioCalibration” = Transfer Function Gains for Bioreactor Model The four steady-state relationships shown can be calculated using Equations (6a,6b) on pg. 5 of the handout for the range of a single input changed while the other input is held constant. ⎛ ⎞ ⎛ ⎞ F /V F /V N = KS ⎜ and B = Y ( Ni − N ) ⎜ ⎟ ⎟ ⎜ μ − F /V ⎟ ⎝ F /V + M Y ⎠ ⎝ max ⎠ The "local" slopes of these curves are the gains of the "local" transfer functions at any feasible nominal steady-state value of one of the inputs. For the BASE CASE parameters to characterize the reactor, the "Bugs" and the nominal steady state: For the reactor : V = 1 , For the "Bugs": M = 0.1, μ max = 2, Y = 0.5, K S = 1 with inputs: F = 1 and N i = 5.2, which yield outputs: B = 2 and N = 1 Feasible Steady-state Flow Rates Feasible Steady-state Ni Concentrations 2.5 4.5 4 2 3.5 Bugs (g/liter) Bugs (g/liter) 3 1.5 1 2.5 2 1.5 B G11 ( s ) = F 0.5 0 0 0.2 0.4 0.6 0.8 1 1.2 Flow (liter/h) G12 ( s ) = 1 B Ni 0.5 1.4 1.6 0 1.8 0 2 4 6 Ni (g/liter) 8 10 12 Feasible Steady-state Ni Concentrations Feasible Steady-state Flow Rates 6 2 1.8 1.6 Nutrient Out (g/liter) Nutrient (g/liter) 5 4 3 G21 ( s ) = 2 N F 1.4 1.2 1 0.8 0.6 G22 ( s ) = 0.4 1 N Ni 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 Flow (liter/h) 1.4 1.6 1.8 0 0 2 4 6 Ni (g/liter) 8 10 12 Page 2 of 2 The BASE CASE transfer function was for B (g/liter) as the output with F (liter/h) as the input. An alternative evaluation of the process is to consider the production rate of bugs BxF (g/h) instead of the concentration as the output. Both the concentration B (solid curve) and the production BxF (dashed curve) are shown in the plot below, where the maximum steady-state production rate as well as maximum concentration of bugs can be seen and are shown to occur at different steady-state flow rates. Because the gain of the transfer function (slope of steady-state curve) changes sign at these maximum values of an "output", linear controllers are not appropriate for trying to maintain the output at its maximum value. For such operations at maximum output values, an advanced, nonlinear optimizing controller is required. Bug Concentration and Production for Feasible SS Flows Conc. = solid (g/liter), Production = dashed, (g/h) 2.5 2 1.5 1 0.5 0 0 0.2 0.4 0.6 0.8 1 Flow (liter/h) 1.2 1.4 1.6 1.8 ...
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This note was uploaded on 03/01/2012 for the course CHE 361 taught by Professor Staff during the Winter '08 term at Oregon State.

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