## 3 Results
### Stage 3
#### 3.3.3 Graph Transfer Matrix vs. Optimum Control
These changes can have subtle effects on the frequency response and the form of the system response. The type of behavior without oscillations did not vary. This indicates that the Ackerman control maintained the stability of the system and prevented unwanted oscillations. The system exhibited an overdamped response, which means that it converged rapidly towards its stable state without excessive oscillations. This feature is desirable in many applications where a fast and stable system response is required. In summary, selecting a damping value greater than 1 ensures an over-damped behavior in the system, where the poles remain real and there is no presence of oscillations in the transient response. This provides stability and rapid system response. Figure 7: Diagram of poles and zeros after optimal control. Sensitivity Analysis of Simulation Models  
Figure 8 shows a sensitivity analysis for different scenarios of variable c. The value of k3 varies from 0.019 to 0.035, and in intervals of 0.004, where it provides us with important information when seeing different scenarios that change the values of k3, but none identifies the set time of 125 min which seeks 63.2% of the final value and a settlement time of approximately 180 min of (95-98%) of the final value. Figure 9 shows a sensitivity analysis for different scenarios of variable c. The value of k1 varies from 0.029 to 0.045, and in intervals of 0.004. It is useful to have different results in the simulation model, which provides multiple results, but none identifies the set time above 125 min looking for 63.2% of the final value and a settlement time of approximately 180 min of (95-98) % of the final value, which is the maximum achieved. \[\text{Poles}:\,-0.0371,\,-0.0279\text{ and }-0.0085 \tag{45}\]0 Variable c, varying with a sensitivity analysis the variable k3. \[\text{Poles}:\,-0.0371,\,-0.0279\text{ and }-0.0085 \tag{45}\]1 Variable c, varying with a sensitivity analysis the variable k2. Figure 10 shows a sensitivity analysis for different scenarios of variable c. The value of k1 varies from 0.004 to 0.0012, and in intervals of 0.002. It is useful to have different results in the simulation model, which provides multiple results, but none identifies the set time above 125 min looking for 63.2% of the final value and a settlement time of approximately 180 min of 98% of the final value, which is the maximum achieved. In conclusion, sensitivity analysis is a valuable tool for evaluating the impact of variables on model results and exploring different scenarios in the context of the present research. However, it is essential to take into account the limitations inherent in this technique and consider other relevant factors to make informed decisions. In this study, a methodology based on the state space and control approach has been implemented using the Ackermann technique. This methodology allows the obtaining of the optimal values required when considering the internal and external dynamics of the system, and when relating the output equation with the input using the transfer function. It is important to note that the sensitivity analysis, although valuable, should be complemented by other techniques and approaches to obtain a more complete and accurate understanding of the system under study.