Methodology Proposed

The methodology proposed for on-line operation is composed of three steps as shown in Figure 3.1: Step 1: On-line identification of system parameters; Step 2: Optimization of feed rate control profiles; Step 3: Application of the optimal feed rate control profiles.

Step 1 On-line identification of system parameters

A deliberate inlet single feed stream that is fed to the hybridoma cells culture is used to identify the kinetic model. The actual values of the state variables are measured at every sampling time, and the estimated values of state variables are calculated from the model based on the candidate solutions (parameters) of a real-valued GA at the same time. Both measured values and estimated values of state variables are used to evaluate the fitness of individuals using the objective function defined in Equation 3.3. At the termination of the GA for each sampling data, the best population is stored. All the best populations obtained are added together as an initial population which carry the information of the parameters for the whole sampling period instead of one particular sampling point. The GA is run again using the initial population and the objective function, which is described in Equation 3.2. The aim is to minimize the error between actual values and estimated values for the whole samples instead of one sample. This chosen initial population and variation in objective function may prevent the GA from premature convergence which will lead the GA stuck in a local minimum.

Step 2 Optimization of feed rate control profiles

In this step, the optimal multi-feeding control profiles are worked out based on the estimated model obtained from the previous step. The time axis of the control trajectories (from the end of identification to the end of fermentation) is discretized into a number of steps. The control values at each step are the variables to be optimized by the GA and become the elements of the chromosomes. The GA creates candidate solutions in the form of floatingpoint representation of variables: chromosomes. These candidate solutions are real values with random numbers within the search domain; ie. constraints on the feed flow (e.g. 0 < F < 0.5L/d). A numerical integration method is used to simulate the system for each chromosome in the population. Subsequently the resulting objective values for the different chromosomes are evaluated and used for the selection. The program is stopped when a predefined maximum number of iteration is reached. Constraints on state variables (e.g. maximum volume) are implemented by penalties in the objective function.

Step 3 Application of the optimal control profiles

In this step, the fed-batch culture of hybridoma cells is run automatically under the control of optimal feed rate control profiles obtained from Step 2.

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