**8. Conclusion**

The paper proposed a new neural identification and control methodology for distributed parameter bioprocess plant. The simplification of the DPS given by PDEs is realized using the orthogonal collocation method in four collocation points, converting the PDE plant description in ODE one. The system is identified using RTNN model and BP and L-M learning, where a high precision of convergence is achieved (the final MSE% for both BP and L-M learning algorithms is of order of E-4 in the worse case). The comparative results showed a slight priority in precision and convergence of the L-M over the BP which could be seen in Figures 8, 11, and Tables 2, 3 (the worse case MSE for the L-M RTNN learning is 2.5476E-4 vs. BP RTNN learning which is 2.8282E-4). The obtained comparative simulation results of centralized adaptive direct, indirect SM and optimal control with I-term exhibited a good RTNN convergence and precise reference tracking. The MSE% of plant outputs tracking for the three considered methods of control is of order of E-5 in the worse case. The graphical simulation results showed that all control methods with I-term could compensate constant plant input noises and the I-term removal caused a system outputs deviation from the reference signals (see Fig. 21). The MSE study ordered the control methods used as: optimal, direct, and indirect, but the difference between them is little (see Tables 4.5.6 where worse case final MSE for DANC is 1.7568E-5; for SMC is 2.1347E-5; for the optimal control it is 1.4949E-5).
