## 4 Experiments and Results  
The purpose of our experimental work was to show that the results of the proposed OAC-DES are comparable with (if not better than) the results of the linear PI-controller on the non-linear control plant. In line with this, several experiments were performed:  
* proof of concept,
* real-time test,
* step response tests,
* influence of the spring constant. In the first test, the OAC-DES and the linear PI-controller were compared according to the error between the desired and actual values of the rotational velocity in order to show that the former is capable of adapting, in contrast to the latter. The purpose of the real-time test was to show that the time complexities of the OAC-DES components allow for its online response (i.e., reacting in less than 5 ms). In the next experiment, step responses of the OAC-DES, obtained in different tests, were compared to the responses of the linear PI-controller on the same step function. The last experiment highlights the influence of the spring constant \(k\). Indeed, the step response tests were measured at two reference velocities: \(\omega_{r}=10\) rad/s and \(\omega_{r}=30\) rad/s. For all tests, initialization of the OAC-DES was performed using weights as found after the introductory ANN-learning phase. However, these alone do not guarantee controller stability, and therefore, a reduced introductory ANN-learning was conducted on input/output pairs obtained by the linear PI-controller with a duration of \(T=0.5\) s before each OAC-DES startup. The purpose of this procedure was twofold: (1) to avoid the need for ANN-learning from scratch, which lasts about 12-15 min, and (2) to ensure that ANN-learning is adapted to current control loop demands prior OAC-DES operation. During the experiments, the same velocity and current feedback loops were used in order to compare both observed velocity controllers as fairly as possible. The linear current PI- and velocity PI-controllers were tuned manually using the Ziegler-Nichols method [39], which is a popular method of tuning the parameters of linear PI-controllers with a linear control plant. The PI-controller parameters thus obtained were then changed slightly to adapt them to the non-linear plant. On the other hand, the proposed OAC-DES controls the velocity controller automatically [23]. The current controller constants as presented in Table 2 were set equally for both of the velocity controllers in the tests. Table 3 specifies the topology of the ANN used by the OAC-DES. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Controller Constant Meaning** & **Constant** & **Value** \\ \hline Current proportional gain & \(K_{p-current}\) & 0.6 \\ Current integral gain & \(K_{i-current}\) & 0.8 \\ Velocity proportional gain & \(K_{p-velocity}\) & 1 \\ Velocity integral gain & \(K_{i-velocity}\) & 0.1 \\ Velocity sampling time & \(T_{sv}\) & 3 ms \\ Current sampling time & \(T_{sc}\) & 25 μs \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Linear current PI- and linear velocity PI-controllers constants. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Inputs and Layers** & **Variable** & **Value** \\ \hline Inputs & \(i_{r}\), \(\omega_{a}\) & 2 \\ Hidden layer & n/a & 10 \\ Output layer & \(\hat{\omega}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Topology of the ANN. We should mention that the proper topology was obtained after extensive testing. Moreover, the BPG algorithm was run at exactly \(n_{BPG}=20\) epochs, while both the learning rates were set as \(\epsilon_{I}=\epsilon_{L}=0.06\) during the control process. The parameter setup of the (1+1)-DES used during the experiments is presented in Table 4, from which it can be seen that the initial reference current value was set to \(x_{0}=0\) A and the maximum reference current to \(i_{r}=\pm 1\) A. For a short time, actual current may exceed maximum reference current. The (1+1)-DES terminates, when the maximum number of generations \(MAX\_GEN=10\) is reached. In the remainder of the paper, the experiments are described in detail.