## 2 Laboratory Setup
### Controller  
The controller, illustrated in Figure 3, consists of a non-linear mechanism that is controlled by the inner current (faster) and outer velocity (slower) feedback controllers. Current control is designed using the linear PI-antiwindup controller with sampling time \(T_{\mathrm{sc}}\). The velocity controller runs at sampling time \(T_{\mathrm{sc}}\) and can be implemented either as a classical PI-antiwindup or as the proposed OAC-DES controller, using a simple switch to select the desired mode. To guarantee equal conditions for both velocity controllers, the same sampling times are taken. Antiwindup controllers are used to prevent the integral (I element in PI-controller) windup that can cause sudden increases of a control variable and cause saturations of the non-linear robotic mechanism.  
As can be seen from Figure 3, design of the OAC-DES (presented in the upper rectangle) is more complex than the linear PI-controller, because of the coexistence of the (1+1)-DES and ANN. Although two ANNs are denoted in the OAC-DES box, i.e., ANN-learning and ANN-simulation, only a single ANN is used, although it plays two different roles. At first, ANN-learning is used to model the behavior of the estimated velocity \(\hat{\omega}\) according to the actual rotational velocity \(\omega_{a}\) in real time. Next, the learned ANN is used to predict the velocity \(\hat{\omega}\) in the ANN-simulation needed for the calculation of the fitness function in (1+1)-DES. It is noteworthy that both phases, i.e., ANN-learning and (1+1)-DES are run sequentially one after another within one velocity sampling time \(T_{\mathrm{sc}}\). In each velocity sampling time \(T_{\mathrm{sc}}\), weights are updated according to the behavior of the control plant.  
To prove that the control plant is really non-linear, a simple test was performed. Using the actual rotational velocity \(\omega_{a}\) and reference current of a DC-motor \(i_{r}\), a non-linear characteristic was simultaneously recorded. The latter was varied within the interval \([-1,+1]\) A, and the actual rotational  
Figure 3: Block scheme of controller with design of the OAC-DES.  
Figure 2: A non-linear robotic mechanism: overview of singular position.  
velocity \(\omega_{a}\) was recorded. As a result, the double hysteresis-like curve of the non-linear characteristics \(\omega_{a}=f(i_{r})\) was obtained, as shown in Figure 4.  
Figure 4 shows the measured non-linear characteristic. First, when the reference current was increased, the DC-motor did not move due to the load of the spring. Next, when the reference current was increased still further, the DC-motor started to move, but did not rotate. By even further increasing the current, the DC-motor overcame the load at some point. As a consequence, the non-linear robotic mechanism started rotating at maximum velocity (the sudden jump of the blue line). Finally, additional increases in the reference current \(i_{r}\) did not results in any further acceleration of the DC-motor.  
Once rotating, the DC-motor did not react to slight decreases in the reference current. A significant decrease in \(i_{r}\) was needed to reduce velocity, and two additional reference decreases were necessary to fully stop the DC-motor. Stopping the DC-motor was somewhat more gradual than starting it had been. The difference can be explained by static friction in the DC-motor and load, which is present only when starting the DC-motor.