# Predictive Speed-Control Algorithm Based on a Novel Extended-State Observer for PMSM Drives
## 5 Simulation and Experimental Results
### Experimental Results
The recovering time against disturbance is about \(0.5\) s, \(0.6\) s and \(0.45\) s, respectively at \(200\) r/min, \(600\) r/min and \(800\) r/min, faster than PI control. After a period of time, the abrupt load is removed. To further illustrate the strengths of the proposed method, this paper introduces the comparison of disturbance rejection performance from the two controllers under different reference speeds. The complete results are shown in Table 2.  
Figures 10 and 11 show the response curves of the current with load disturbance under \(n=200\) r/min. The three-phase current response curves of GPC+ESO and PI method are shown in Figures 10a and 11a, respectively. The \(d\)-\(q\) axis current curves of GPC+ESO and PI method are shown in Figures 10b and 11b, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Control Methods**} & **PI** & **GPC+ESO** & **PI** & **GPC+ESO** & **PI** & **GPC+ESO** \\ \cline{2-6}  & \(n=200\) \(\mu\)min & \(n=600\) \(\mu\)min & \(n=800\) \(\mu\)min & \(n=800\) \(\mu\)min \\ \hline Speed fluctuation when a sudden load is added (r-min) & \(-43\) & \(-24\) & \(-39\) & \(-20\) & \(-39\) & \(-29\) \\ Speed fluctuation when a sudden load is removed (r-min) & \(+40\) & \(+20\) & \(+34\) & \(+18\) & \(+38\) & \(+26\) \\ speed adjustment time when a sudden load is added (s) & \(1\) & \(0.3\) & \(1.5\) & \(0.4\) & \(1.7\) & \(0.4\) \\ speed adjustment time when a sudden load is removed (s) & \(1.3\) & \(0.5\) & \(1.8\) & \(0.6\) & \(1.8\) & \(0.45\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of disturbance rejection performance. Figure 9: Experimental speed curves when a sudden load is added or removed. (**a**) \(n=200\) r/min; (**b**) \(n=600\) r/min and (**c**) \(n=800\) r/min. The estimated load disturbance of the ESO is shown in Figure 12, and the observed load torque value was used for the GPC controller which can improve the robustness of the system. The Figure 12 shows that the proposed ESO can estimate the external load disturbance accurately and has small fluctuation. Figure 11: Experimental current curves based on PI method under load disturbance. (**a**) three-phase current response curves; (**b**) \(d\)-\(q\) axis current response curves. Figure 10: Experimental current curves based on GPC+ESO method under load disturbance. (**a**) three-phase current response curves; (**b**) \(d\)-\(q\) axis current response curves. From these experimental curves, it is evident that the predictive speed-control algorithm based on a novel extended-state observer for PMSM drives is practicable. It can also ensure and improve the ability to reject load disturbance while possessing a good dynamic performance of the control system. In the long-term operation of the motor, the motor parameters will change with the increase of the temperature. It is necessary to verify the ability of the proposed controller under parameter disturbance. Suppose \(x=x_{o}\left(1+\Delta x\right)\), \(x=\left(R_{s},J,L,\Phi\right)\), where \(x_{o}\) represents the rated parameter values of PMSM, \(\Delta x\) represents the parameter disturbance. All the parameter disturbances are applied at 10s. Under the parameter disturbance, the experimental results are shown in Figures 13-16. Figures 13 and 14 show the motor speed curves under the GPC+ESO controller with a sudden change of rotor flux value and inductance value, respectively. Figure 13 shows that the fluctuation of the motor under the GPC+ESO method is 74\(r\) and 26\(r\), respectively in case of rotor flux value increases 50% and decreases 50%. The recovering time to the reference speed is about 1 s and 3.8 s, respectively in case of rotor flux value increases 50% and decreases 50%. The specific experimental results are presented in Table 3.  
the speed ripple of the motor under the GPC+ESO method is reduce when the stator resistance value increases 100%. Figure 15b shows that the speed ripple of the motor under the GPC+ESO method is increase when the stator resistance value decreases 50%.