# Variable Guide Vane Scheduling Method Based on the Kinematic Model and Dual Schedule Curves
## 4 VGV Scheduling Method  
Control commands from the engine controller are actuator stroke commands for scheduling the vane angle. The actuator controller accepts these control commands and calculates the error by sensing the actuator stroke from the LVDT (linear variable displacement transducer) module. Afterwards, it generates control signals to servo-valves of the hydraulic actuator to control the position of the actuator rod end, as shown in the lower part of Figure 7.  
In this research, the stroke command of the controller was first established to satisfy the VIGV schedule, because the inlet mass flow rate of the compressor depends greatly on the VIGV angle. However, because all three VGV stages are mechanically coupled to the one actuation system, the angular difference of the vanes between schedules in VGV1 and VGV2 is inevitable, due to the stroke command only for the VIGV. The link adjusting parameters described in the previous section can be used to satisfy the schedules of all the VGV stages.  
A real VGV mechanism has angle hysteresis according to the actuator stroke, due to DOF redundancy and eccentricity of the unison ring, thus, an ideal tabulated stroke command is not enough to realize the VGV schedule. In this research, the VIGV hysteresis was eliminated by applying two distinct schedule curves, the use of which depends on the moving direction of the actuator stroke. Compression or extension of the actuator stroke is equivalent to decrease or increase of the vane angle  
Figure 6: Effect of link lengths on relations between vane angle and actuator stroke. (**a**) Effect of bell crank length (\(L_{b}\)); (**b**) Effect of vertical link length (\(L_{c}\)).  
when the engine RPM is changing. Thus, the engine controller decides which look-up table is correct for the current state by figuring out the RPM trends.  
If the measured engine RPM is used as the look-up table switching criterion, unnecessary frequent switching of the look-up table occurs due to noise signals in the engine RPM, and this also causes instability of the actuator system. For this reason, the look-up table is switched based on engine RPM demand under the assumption that the engine RPM tracking error is maintained within a stable range.  
Although this hysteresis elimination method only applies to the VIGV stage, if each VGV stage constitutes an independent link mechanism, then all the hysteresis can be eliminated with a software application. Moreover, it can flexibly cope with the unexpected mechanical hysteresis such as the thermal growth of the parts, small deflection of the links, and wearing of the structures because the modification in each case can be done by adjustment of stroke commands in the control software without change of the mechanical parts. Figures 7 and 8 summarize the control scheme and scheduling methodology developed in this research.  
The stepwise method shown in Figure 8 was implemented using in-house software with a MATLAB GUI (graphical user interface), as shown in Figure 9. The derived mechanism model is calculated under the MATLAB environment, thus MATLAB GUI is the best platform to integrate the stepwise VGV scheduling method and to utilize efficient user interface. The user can obtain the solutions by entering few design parameters and only pressing push buttons. In this way, analysis of the link adjusting parameter and calculation of the stroke command to obtain the VIGV angle schedule can be performed sim  
Figure 7: VGV link mechanism control diagram.