**7.2 Simulation results of the centralized direct adaptive neural control with I-term using L-M learning**

The real-time DANC (see Fig. 4) contained a neural identifier RTNN-1 and a neural controller RTNN-2 with topology (40, 10, 2). Both RTNNs-1, 2 are learnt by the L-M algorithm with parameters: RTNN-1 (=1, ρ*=*0.0001, Po=10 I with dimension 420x420); RTNN-2 (=1, ρ*=*0.01, Po=0.8 I with dimension 430x430). The simulation results of DANC are obtained on-line during 1000 days with a step of 0.1 day. The control signals are shown on Fig. 13. The Fig. 14-16 compared the plant output X1 with the reference signal in different measurement points. The form of the set points (train of pulses with random amplitude) of the variable X1 in the different measurement points is equal but the amplitude is different depending on the point position. This means that the plant has different signal amplification in each measurement point which needs to be taken in consideration.

Fig. 13. Plant input control signals generated by I-term DANC: a) Sin1, and b) Sin2


Table 4. MSE of the centralized I-term DANC of the bioprocess output variables in the collocation points, using the L-M RTNN learning

The given on Fig. 14-16 graphical results of I-term DANC showed smooth exponential behavior. It could be seen also that the L-M learning converge fast and the I-term remove the constant noise Of, and the plant uncertainties. The obtained numerical results (see Table 4) of final MSE of L-M learning possessed small values (1.7568E-5 in the worse case).

Centralized Distributed Parameter Bioprocess

**term using L-M learning** 

and b) Sin2

Identification and I-Term Control Using Recurrent Neural Network Model 195

Fig. 16. Three dimensional plot of the I-term DANC of the plant output X1 in four

**7.3 Simulation results of the centralized indirect (SM) adaptive neural control with I-**

In this case the indirect adaptive I-term control is a sum of the I-term control signal and the SM control, computed using the state and parameter information issued from the RTNN-1 neural identifier. The control signals are shown on Fig. 17. The X1 control simulation results are given on Fig. 18-20. The simulation results of SMC are obtained on-line during 1000 days with a step of 0.1 day. The given on Fig. 18-20 graphical results of I-term SMC demonstrated smooth behavior. It could be seen also that the L-M learning converge fast and the I-term

Fig. 17. Plant input control signals generated by the I-term centralized indirect SMC: a) Sin1,

measurement points of L-M learning : z=0.2H, z=0.4H, z=0.6H, z=0.8H

remove the constant noise Of, and the plant uncertainties.

Fig. 14. Graphical simulation results of the I-term DANC of the plant output X1 vs. system reference in 4 measurement points for the total time of L-M learning: a)z=0.2H, b) z=0.4H, c) z=0.6H, d)z=0.8H

Fig. 15. Graphical simulation results of the I-term DANC of the output X1 vs. system reference in four measurement points for the beginning of L-M learning: a) z=0.2H, b) z=0.4H, c) z=0.6H,d) z=0.8H

Fig. 14. Graphical simulation results of the I-term DANC of the plant output X1 vs. system reference in 4 measurement points for the total time of L-M learning: a)z=0.2H, b) z=0.4H, c)

Fig. 15. Graphical simulation results of the I-term DANC of the output X1 vs. system reference in four measurement points for the beginning of L-M learning: a) z=0.2H, b)

z=0.6H, d)z=0.8H

z=0.4H, c) z=0.6H,d) z=0.8H

Fig. 16. Three dimensional plot of the I-term DANC of the plant output X1 in four measurement points of L-M learning : z=0.2H, z=0.4H, z=0.6H, z=0.8H
