# Variable Guide Vane Scheduling Method Based on the Kinematic Model and Dual Schedule Curves
## 5 Engine Application Test  
The proposed VGV scheduling method was applied to a real engine system. The initial link geometry is presented in Table 4, and the relation between the VGV angle and actuator stroke, which is derived from the analytical model in Section 3, is shown in Figure 10. Three-stage VGVs have different ranges of angles within the actuator stroke limit, and the VIGV has a wider range of angles.  
Figure 8: VGV scheduling methodology flow chart.  
Figure 9: In-House software for scheduling VGVs.  
The stroke command used to manipulate the target VGV angle can be obtained from the relations between the VGV angle and actuator stroke. The graph shown in Figure 11 is the target angle with respect to engine RPM that VGV vanes should fit. First, the stroke commands are obtained with respect to engine RPM to satisfy the target VIGV angles from the analytical mechanism model without considering RPM increasing or decreasing. However, the stroke commands make a discrepancy from the target value near 100% RPM in the cases of VGV1 and VGV2, as shown in Figure 12a (Error: 1.03 degree (VGV1), 2.16 degree (VGV2)). The bell crank length, one of the link adjusting parameters, can be adjusted to change the slope in Figure 12a. Changing the bell crank lengths from 48 to 49 mm for VGV1 and from 35 to 38 mm for VGV2 provides more accurate vane angles when the engine RPM is around 100%, as depicted in Figure 12b (Error: 0.39 degree (VGV1), 0.08 degree (VGV2)).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **VIGV** & **VGV1** & **VGV2** \\ \hline \(L_{e}\) & 112.3 & 112.3 & 112.3 \\ \(L_{b}\) & 74.0 & 48.0 & 35.0 \\ \(L_{c}\) & 497.1 & 493.7 & 498.8 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Geometry parameters of the initial link mechanism (unit: mm).  
Figure 11: VGV scheduling target.  
Figure 10: Link mechanism results based on the initial geometry.  
Through the real engine application test, we verified the effectiveness of the control method using dual schedule curves on the VIGV stage. The vane angles were measured using the potentiometers on the stem of the vanes, and VIGV angles with respect to the actuator stroke were obtained, as shown in Figure 13. This hysteresis data was divided into two stroke-angle relations to represent the extension and compression cases of the actuator stroke. Inherent mechanical hysteresis is about 1.6 degrees, as shown in Figure 13. These two stroke-angle curves were applied to the engine controller for the RPM up (increasing) and RPM down (decreasing) case, respectively.  
The engine test results are presented in Figure 14. The data in Figure 14 includes all transient data during the entire engine run (over 30,000 samples) and includes multiple engine RPM rises and falls with 10 Hz sampling rate. The angular errors in the VIGV are summarized in Table 5. The mean error was 0.55 degree while inherent mechanical hysteresis was 1.6 degree, as describe in Figure 13. This represents overall hysteresis was reduced about 1.1 degree, in the VIGV stage. The resultant VIGV angles also trace the target angles well, and 0.47 mean angle error was measured especially in the range from 99% RPM to 100% RPM that is the engine design operating point. Considering that compressor instability during increase of the engine RPM, this tracking performance does not limit operation of the compressor.  
Figure 12: Scheduling results. (**a**) before link adjustment, (**b**) after link adjustment.