## 3 Results
Training reference amplitude = 100.0 Training reference frequency = 0.0 Training reference acceleration = 0.0 Training reference deceleration = 0.0 Training disturbance type = sine Training disturbance amplitude = 3.0 Training disturbance frequency = 20.0 Training disturbance acceleration = 0.0 Training disturbance deceleration = 0.0 In this example configuration, the neural network-based controller has a clearly higher performance than the optimal PI controller with the following costs:  
Cost PI = 11.036012620309064  
Cost ANN = 4.474398851829462  
In another scenario with the following reference-disturbance pairs, the neural network-based controller has a higher performance than the optimal PI controller. The result is shown in Figure 9 below. Training reference type = sine  
Training reference amplitude = 100.0 Training reference frequency = 3.0 Training reference acceleration = 0.0 Training reference deceleration = 0.0 Training disturbance type = step Training disturbance amplitude = 3.0 Training disturbance frequency = 0.0 Training disturbance acceleration = 0.0 Cost PI = 4.365012134434239  
Cost ANN = 3.639447860741749  
These results show that, for the expected reference-disturbance pairs, the neural network-based controller has a clearly higher performance than the optimal PI controller. An important concept in artificial intelligence is generalization performance, which means the performance of the system for examples unseen during training. So, in order to test the generalization performance, new examples different from the training set must be shown to the system. This new set is called test-set and has samples different from that of the training set. Below is shown in Tables 3 and 4 the reference-disturbance signal values for the test set used in this study. Figure 9: Another illustrative example of neural controller’s high performance. Note that some reference signals used for the test set are the same as those of the training set, but this does not violate the dissimilarity of reference-disturbance pairs. It is important that the reference-disturbance pair must be different in the training set and test set. All the reference-disturbance pairs in the training set are different from every reference-disturbance pair used in the test set. The average error for the optimal PI controller on the test set is obtained to be 53.30442198786117 rad/s. The average error for the optimal neural network-based controller on the test set is reduced to 52.893195124124276 rad/s. A slight reduction in error is observed for unexpected reference-disturbance pairs. Note that this small improvement in error for unexpected reference-disturbance pairs is not that crucial but gives an extra advantage compared to the proposed system since the main objective is to design an automatic controller automatically for the expected reference-disturbance pairs. But this also shows that the proposed system has better generalization performance than the optimal PI controller. Note that the performance of the proposed controller is very high on low-disturbance experiments, as shown in Figures 10 and 11 below. Training reference type = step  
Training reference amplitude = 50.0  
Training reference frequency = 0.0  
Training reference acceleration = 0.0  
Training difference deceleration = 0.0  
Training disturbance type = step  
Training disturbance amplitude = 1.0  
Training disturbance frequency = 0.0  
Training disturbance acceleration = 0.0 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Signal** & **Type** & **Amplitude** & **Frequency** & **Acc. Time** & **Dec. Time** \\
**Number** & **Type** & **(Volts)** & **(Hz)** & **(ms)** & **(ms)** \\ \hline
1 & square & 1 & 5 & NA & NA \\
2 & square & 1 & 10 & NA & NA \\
3 & square & 1 & 20 & NA & NA \\
4 & square & 2 & 5 & NA & NA \\
5 & square & 2 & 10 & NA & NA \\
6 & square & 2 & 20 & NA & NA \\
7 & sawtooth & 1 & 5 & NA & NA \\
8 & sawtooth & 1 & 20 & NA & NA \\
9 & sawtooth & 2 & 5 & NA & NA \\
10 & sawtooth & 2 & 20 & NA & NA \\ \hline \hline \end{tabular}
\end{table}