# Automation of a Hybrid Control for Electrohydraulic Servo-Actuators with Residual Dynamics
## 7 Discussion  
We began the simulation tests by activating the subsystem (\(S_{1}\)). When the position reached the static phase imposed by its desired trajectory, the subsystem (\(S_{2}\)) was activated to control an applied force on the load. We observe from Figures 7 and 8 that, when the proposed method was applied, there were no adverse effects on the system status. Further, the simulation test was performed even with a variable frequency of the desired effort trajectory to solicit different dynamics applied to the load.  
Figure 6: Evolution of the desired position.  
Figure 7: Evolution of the effort (**upper**) and the position (**below**) with their desired trajectories.  
As shown in Figure 7, there are more than two switches for the position controller, so it is necessary in this case to impose two dead zones (\(T_{ZM(1)}\) and \(T_{ZM(2)}\)) in the desired trajectory of the effort. Therefore, a desired generator trajectory of the effort was updated. Then, the computation of the width of the dead zones was carried out using Equation (47).  
When the subsystem (\(S_{2}\)) was activated, the effort was under control but not the displacement. At this stage, we noticed that the effort was very close to the desired pre-calculated trajectory of the effort (see Figure 7 upper). On the other hand, the displacement did not follow its desired trajectory, but, under the effect of a causal relationship between these two physical variables, the displacement will be of the same form as the effort trajectory.  
Figure 8 shows some modifications to the trajectories of the velocity and the acceleration, as well as their desired trajectories. From this figure, good trajectory tracking is shown for the synthesized hybrid position/effort controller. We can conclude that the simulation test allowed direct validation of the hybrid position/force controller and the proposed solution in order to impose switching times that ensured no adverse effects in terms of tracking the trajectories.  
The results obtained show the efficiency of automation of time-dependent switching signals. This is generated via the definition of a force trajectory generator that is updated instantaneously according to system conditions. This update prevents harmful problems that may be caused by the residual dynamics. Indeed, any undesirable effect on speed and acceleration is avoided. In addition, it should be noted that the controller has a good follow-up of the desired trajectories, whether for the position or the effort.  
By referring to the work carried out in Ref. [32], we have proposed another hybrid position/force control approach. This approach in Ref. [32] was based on a linearized control model in which the structure of the control law remained the same and only the parameterization changed. The switching signal used was based on a hysteresis function. Admittedly, the tracking quality was good, but the peaks of the effort during transitions were recorded. On the other hand, our current approach consists in automatically generating the force trajectory in order to avoid these peaks and, thus, all damage to the system.  
Figure 8: Evolution of the velocity (**upper**) and the acceleration (**below**) with their desired trajectories.  
The trajectory generator is defined by a mathematical calculation taking into account the residual dynamics.