## 4 Sensitivity Analysis
### Simplified Models  
From the analysis carried out, it is easy to deduce the models that are sufficiently accurate and simpler than the full state-space model developed in [17] (referred to as the reference model). Thus, for the push-pull buck topology, the following non-idealities must be taken into account: switching devices (\(R_{DS}\)), HF transformer (\(L_{P_{x}}\) and \(L_{S_{x}}\)), rectifier diodes (\(R_{D}\) and \(V_{\gamma}\)) and output \(LC\) filter (\(R_{LF}\) and \(R_{CF}\)). On the other hand, for the push-pull boost topology, switching devices (\(R_{DS}\)), HF transformer (\(L_{P_{x}}\) and \(L_{S_{x}}\)), rectifier diodes(\(R_{D}\)) and output \(LC\) filter (\(R_{LF}\)) must be taken into account. Based on the above, the simplified non-ideal equivalent circuits for the push-pull buck and boost topologies are shown in Figure 6a,b, respectively. This allows to simplify the state-space model (1) so that now the state vector will be \(x_{s}=\left[i_{L_{B_{1}}},i_{L_{B_{2}}},i_{L_{S_{1}}},i_{L_{F}},v_{C_{F}}\right]^ {T},\) remaining unchanged with respect to \(u(k)\) and \(y(k)\). This makes it possible to reduce the model order from thirteen to six. To do this, simply cancel the terms of matrices \(A\), \(B\), \(C\), \(D\) and \(E\) of the reference (full) model (1) associated with those state variables that are not present in the simplified state vector \(x_{s}\).  
Finally, to demonstrate the practical application of the results obtained from the sensitivity analysis, the dynamic and steady-state response of the simplified models was compared with that obtained from the reference model for a step-type input signal.  
Figures 7 and 8 show the percentage errors of the dynamic and steady-state response of the simplified models for each case of the buck and boost topologies, respectively. Figure 9 shows the time response and the corresponding validation of the simplified model (Simp) for cases 1 (a) and 4 (b) with respect to the reference model (Ref) and the ideal model (Ideal) for the central values of the switching frequency range for each case and both topologies.  
Note that the absolute error percentages shown in Figures 7 and 8 are in all cases lower than five. Likewise, Figure 9 verifies that the dynamic and steady-state behaviour of the simplified models show a similar profile to the reference model and in turn show much higher performances than the ideal model of Figure 1 (the most widespread in the scientific literature).  
Based on the results, it is shown that the sensitivity analysis developed for the push-pull converter topology is a very powerful tool for the definition of reduced-order control-oriented models for applications where simplicity and accuracy are fundamental requirements.  
Figure 6: Simplified non-ideal equivalent circuits for (a) buck and (b) boost topologies, respectively.  
Figure 8: Overshoot error, rise time error, settling time error, steady-state error and peak time error of the simplified models for the boost topology in each case.  
Figure 7: Overshoot error, rise time error, settling time error, steady-state error and peak time error of the simplified models for the buck topology in each case.