# MFC/IMC Control Algorithm for Reduction of Load Torque Disturbance in PMSM Servo Drive Systems
## 4 Theoretical Analysis
### Reduction of Load Torque Disturbance Influence  
The experiment was conducted with two PMSM drives whose shafts were coupled (Figure 6). The main PMSM (1) is the one on which both control schemes were tested: the classical cascade and the proposed MFC/IMC method. The auxiliary PMSM (2), controlled in the current loop, generated various load torques--it was the disturbance source.  
Figure 5: The test stand developed for experiments. The highlighted components are: main PMSM (**1**), auxiliary PMSM (**2**), PLC controller (**3**), PC work station (**4**) and industrial servo drive (**5**).  
Figure 6: The test stand utilized in experiments.  
The goal of the experiment was to compare the performance of the proposed method and the classical approach while maintaining a fixed velocity. As that reference velocity (\(\omega_{ref}\)) was chosen to be zero, the main PMSM (1) should remain at a standstill for the entirety of the experiment while being affected by the auxiliary PMSM (2) which exerted external torque disturbance.  
The developed control-measurement system compared the deviation from the reference velocity value of the classical cascade and MFC/IMC cascade control algorithms in terms of IAE, ISE and ITAE performance indices. Motor's motionless state was desired, as such, any non-zero velocity attributed to the error signal. Moreover, in the case of the MFC/IMC control scheme, an additional control signal was measured in order to prove that values of the generated auxiliary current signal (\(i_{q\_add}\)) are within the PMSM operating range. Load torques generated by the auxiliary PMSM in the conducted experiments are presented in Figure 7:  
Figures 8-11 represent the results of the undertaken experiments for the classical cascade and the proposed MFC/IMC solution. Each subfigure contains measured reference velocity (\(\omega_{ref}\)) and actual velocity (\(\omega_{act}\)) of the main PMSM, the latter being a response to a specific set of external load disturbances depicted in the matching subsection of Figure 7. In each case, the proposed algorithm exhibits higher insensitivity to the load torque disturbance than the classical cascade control structure.  
Figure 7: Load torques generated by the auxiliary PMSM. The signals used are: (**a**) positive ramp; (**b**) negative ramp; (**c**) sine wave; (**d**) triangle wave.  
Figure 8: Systems’ responses to the disturbance presented in Figure 7a. Measured reference and actual velocity of PMSM for: (**a**) cascade (**b**) MFC /IMC cascade structure.  
Figure 10: Systems’ responses to the disturbance presented in Figure 7c. Measured reference and actual velocity of PMSM for: (**a**) cascade (**b**) MFC /IMC cascade structure.  
Figure 9: Systems’ responses to the disturbance presented in Figure 7b. Measured reference and actual velocity of PMSM for: (**a**) cascade (**b**) MFC /IMC cascade structure.  
The additive control signal (\(i_{q\_add}\)) generated by the MFC/IMC algorithm is presented in Figure 12:  
Figure 11: Systems’ responses to the disturbance presented in Figure 7d. Measured reference and actual velocity of PMSM for: (**a**) cascade (**b**) MFC/IMC cascade structure.  
Figure 12: Additional control signal (\(i_{q\_add}\)) of the MFC/IMC control algorithm measured in each of the experiments. The subfigure order matches the one used in Figure 7 where generated disturbances were shown: (**a**) positive ramp; (**b**) negative ramp; (**c**) sine wave; (**d**) triangle wave.  
For each of the experiments the performance indices are calculated as a difference between the reference velocity and actual velocity. Table 2 presents the obtained results: