# Precision Analysis and Design of Rotating Coil Magnetic Measurements System
## 4 Results and Discussion
### Test Results of the Speed Control System with a PI Controller  
In this experiment, the scope of the control variables was defined for designing to achieve the desired response. The specifications of a speed control system with a PI controller are percent overshoot (not more than 5%), rise time (less than 2 s), settling time (less than 5 s), and steady-state error (less than 2%). The results from optimization with MATLAB-Simulink in relation to signal constrain function used to find the optimization PI controller are shown as Table 2.  
From Table 2, take the value of the P and the I controller to test the speed control system of a DC motor if they are as designed at 60, 90, and 120 rpm. The step response of closed-loop speed-control system with PI controller are shown in Figure 12.  
Figure 12 illustrates that the speed control system can work under the conditions specified for each speed. It was found that the highest whirling speed was 5.527 percent at a speed of 60 rpm and the lowest whirling speed was 2.79 percent at a speed of 120 rpm as shown in Table 3.  
\begin{table}
\begin{tabular}{c c c} \hline
**Controller** & **K\({}_{\mathbf{P}}\)** & **K\({}_{\mathbf{i}}\)** \\ \hline Gain & 0.00697 & 0.03100 \\ \hline \end{tabular}
\end{table}
Table 2: The value of the PI controller.  
Figure 11: The results of the comparison between the mathematical model and the experimental results of the DC motor.  
From the experimental results shown in Figures 13-15, it was found that when the rotational speed was higher, the electromotive force was higher as well and had the highest electromotive force at a rotational speed \(\omega\) of 120 rpm. In addition, increasing the electric current to the dipole magnet enhanced the electromotive force too, and the magnetic field value was the highest at 15 amp. The results from the experiment in Section 4.2. reveal that the controller design had a higher number of errors than that of the magnetic measurement system. It affected the magnitude of the electromotive force changes with the speed of rotation. This can be observed from the highest and lowest values as shown in Figure 14a, Figure 15a, and Figure 16a in each movement of the coil around the magnetic cavity. Then, the signal in the form of a spectrum was analyzed as shown in Figure 14b, Figure 15b, and Figure 16b with Equation (16).  
\[Order=\frac{CPM}{RPM}, \tag{16}\]  
From Equation (16), when comparing the induced electromotive force signal obtained from the measurement (\(CPM\), cycles per minute) with the speed of the rotating coil (\(RPM\), revolutions per minute), other harmonic signals are characterized. This research considers this in four orders. It was found that at every rotation speed, a third harmonic (Order 3) occurred. It may cause an error in controlling the speed of a rotating coil which is not within the specified limit or mechanical looseness according to ISO10816-1 in assembly of measuring instruments. This affects the electromagnetic field's measurement. The measured value is shown in Table 4.  
Figure 16: The comparison of the movement characters of the rotating coil at 60 RPM: (**a**) shaft orbit at DE side; (**b**) shaft orbit at center; (**c**) shaft orbit at NDE side.  
Figure 15: This figure shows the speed of the rotating coil 120 rpm (2 Hz): (**a**) the electromotive force of the magnetic field at 120 rpm; (**b**) the spectrum of the electromotive force of the magnetic field.