# Re-Optimized Design for the ADR-Based Dual-Loop Controller of 100 m Class Aperture Radio Telescope
## 4 Simulation Results and Analysis
### Position Switching Performance Analysis  
Astronomical observations require radio telescopes to be able to switch quickly between target sources and calibration sources to reduce their overhead time for gain/phase calibration. The fast switching performance corresponds to the step response in servo control. Typical switching angles for radio telescopes are related to their sensitivity, and the typical switching angles for 100 m class radio telescopes such as the GBT do not exceed 2 deg. The switching angle can be used to test the performance of the telescope servo system. Due to an actual telescope system's speed and acceleration saturation limitations, the step signal used for servo system performance testing is usually a small-angle signal; \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Mean** & **Max.** & **Median** & **RMS** \\ \hline PD-DLADRC & \(-0.0005\) & \(0.0161\) & \(0.0010\) & \(0.0086\) \\ P-DLADRC & \(-0.0005\) & \(0.0169\) & \(0.0010\) & \(0.0087\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Error statistics (in deg) of position responses under two position controllers in \(K_{\rm p}=16\) and \(K_{\rm d}=0.55\). Figure 6: Position response under DLADRC control: (**a**) \(K_{\rm d}=0.05\), (**b**) \(K_{\rm d}=0.55\), and (**c**) motor’s input voltages at \(K_{\rm d}=0.55\). a 0.05 deg test signal was used for the 100 m class antenna in this paper, after careful consideration. The feedback and feedforward controllers of the RPID-controlled system's position-loop are  
\[G_{\rm p1}(s)=\frac{800(s+0.6)}{s+25},G_{\rm F}(s)=0.485\frac{(s+0.3)}{(s+0.38)^{ 2}}, \tag{28}\]  
The position controller of the LADRC-controlled system is  
\[G_{\rm p2}(s)=16\frac{0.05s+1}{(1/10s+1)}, \tag{29}\]  
The position response curves of the motor, the base, and the dish of the system are shown in Figure 7a. Figure 7b,c shows the motor speed and input voltage response curves of the system, respectively. The response curves of the system using LADRC and DLADRC are smoother than those of RPID in the double-closed-loop case, which indicates that these two methods are less likely to excite the structural resonance of the system compared with the RPID. When encountering external disturbances, they not only can quickly suppress disturbance but also have a lower peak response magnitude, giving the advantages of high control precision and saving power. Table 3 gives the indicators measuring the system switching performance in terms of the overshoot (in %), settling time (in s), and the typical four kinds of wind-response errors under an average wind of V = 6 m/s and 3 m/s, respectively. The maximum disturbance response amplitudes of the base under the LADRC and DLADRC are reduced by 51.9% and 60.2% compaed to that of RPID, respectively, and the response times of the LADRC and DLADRC are reduced by about 50 s, indicating their better anti-disturbance performance. The maximum disturbance response amplitude of DLADRC is reduced by 17.3%, and the response time is slightly reduced compared to LADRC. The RMS pointing errors of the systems controlled by the RPID, LADRC, and DLADRC at the base are 0.0092 deg (33.12 arcsecs), 0.0032 deg (11.52 arcsecs), and 0.0025 deg (9 arcsecs) at a wind of 6 m/s, respectively, while they are 9 arcsecs, 2.88 arcsecs, and **2.1 arcsecs (0.0006 deg)** at a wind of 3 m/s, indicating the DLADRC meets the **design specification of 2.5 arcsec RMS**. So, Figure 7 and Table 3 illustrate the advantages of DLADRC over LADRC and RPID. The difference in response between the base and the dish in Figure 7a is due to the structure flexibility of the antenna. When the antenna system is in a steady state, there are stable response errors between the base and the dish, which are independent of the control method.