## 3 Results and Analysis
### Steady-State Results  
Here, this manuscript presents the results for the steady-state operation of the buck converter with a DC motor that is controlled by the ZAD-FPIC technique are presented. The goal of this analysis is to present the dynamic behavior of the closed loop system when the control parameter \(K_{S3}\) changes. An additional purpose is to define a tuning criteria for control parameters, while evaluating the dynamic characteristics of the system stability via bifurcations diagrams. The control parameter \(K_{S3}\) defined in Equation (10) was selected as the bifurcation parameter because this parameter is more sensible than the two others control parameters (\(K_{S1}\) and \(K_{S2}\)). Figures 4 and 5 show numerical and experimental results of the duty cycle and the motor speed with respect to the control parameter \(K_{S3}\), respectively. Three different quantization levels were considered for the variables as follows. Firstly, \(W_{m}\) with 28 bits; \(i_{a}\), \(v_{c}\), and \(i_{L}\), each with 12 bits; and a  
Figure 3: Numerical and experimental behavior when there is a change in the speed reference signal (\(W_{mre}\)): (**a**) motor speed signals (\(W_{m}\)); (**b**) motor supply voltage \((V_{a}=v_{c})\); (**c**) speed error; and (**d**) duty cycle. duty cycle of 10 bits. Secondly, \(W_{m}\) with 26 bits; \(i_{a}\), \(v_{c}\), and \(i_{L}\), each with 10 bits; and a duty cycle of 8 bits. Thirdly, \(W_{m}\) with 24 bits; \(i_{a}\), \(v_{c}\), and \(i_{L}\), each with 8 bits; and a duty cycle of 6 bits. In the experimental test, the steady-state error is higher when the resistance \(r_{Med}\) increases, for which the bifurcation diagrams presented in Figure 4 show a slight difference between the simulation and experimental results. To improve this difference, it is recommended to perform a better calibration of the parasitic resistance, along with real-time sensing of the resistances \(r_{Med}\), \(r_{L}\), and \(r_{s}\). Thus, a greater correlation between the simulation and experimental results can be found. In general, Figures 4 and 5 show a good correlation between numerical and experimental results. Figure 4a shows that for the highest quantization levels, the stability limit at the numerical test has a value close to \(K_{S3}=22\) a, while for the experimental test (Figure 4b) this value is \(K_{S3}=12\). For the lowest quantization level, the numerical test (Figure 4e) shows that the stability limit is close to \(K_{S3}=270\), while for the experimental test (Figure 4f) it is \(K_{S3}=170\). Therefore, from these results we can conclude that the experimental test presents a more stable behavior for lower values of \(K_{S3}\), and that as the quantization levels are reduced for both the simulation and experimental tests, the stability is lost and it is necessary to increase the value of \(K_{S3}\) to obtain stability in the controlled signal \(W_{m}\). Figure 4: Numerical and experimental bifurcation diagrams for the duty cycle \(d\) with respect to the control parameter \(K_{S3}\). These diagrams are plotted considering the following quantization levels: (**a**) \(W_{m}\) with 28 bits, analog-digital (ADC) inputs with 12 bits, \(d\) with 10 bits; (**b**) \(W_{m}\) with 28 bits, ADC with 12 bits, and \(d\) with 10 bits; (**c**) \(W_{m}\) with 26 bits, ADC with 10 bits, and \(d\) with 8 bits; (**d**) \(W_{m}\) with 26 bits, ADC with 10 bits, and \(d\) with 8 bits; (**e**) \(W_{m}\) with 24 bits, ADC with 8 bits, and \(d\) with 6 bits; and (**f**) \(W_{m}\) with 24 bits, ADC with 8 bits, and \(d\) with 6 bits. Figure 5 shows that there is no clear stability limit, however by means of the duty cycle \(d\) it can be measured when the stability is lost. Both numerical and experimental tests showed that the system begins to be more unstable and that the bifurcation point moves to the right because of resolution lost in the measured variables. For all quantization levels, the responses of the controller were good and the regulation was performed to the desired reference point.