# Research on Fractional-Order Control of Anchor Drilling Machine Optimized by Intelligent Algorithms
## 5 Conclusions  
This study addresses the demand for unmanned operations in coal mine roadway support by developing a novel anchor drilling rig. The rig integrates a chain-type anchor bolt magazine with a robotic manipulator, enabling automated anchor rod grasping and loading. The adoption of modular hollow self-drilling anchors combined with grouting  
Figure 14: Robustness evaluation diagram of the closed-loop system with an \(\mathsf{Ho}\) controller and triple lag compensation; (**a**) Bode plot of the system with an \(\mathsf{Ho}\) controller; (**b**) step response of the system with an \(\mathsf{Ho}\) controller; (**c**) Nyquist plot of the system with an \(\mathsf{Ho}\) controller; (**d**) pole-zero plot of the system with an \(\mathsf{Ho}\) controller.  
significantly enhances the automation level of the drilling rig, improving operational efficiency and reliability.  
To achieve precise anchor rod loading under unmanned conditions, we introduced a composite control strategy based on an improved particle swarm optimization (ILPSO)-optimized fractional-order proportional-integral-derivative (FOPID) controller. A fractional-order simulation model of the valve-controlled hydraulic cylinder in the rig's robotic manipulator was established, and simulation experiments compared various algorithms and PID/FOPID controller combinations. Results demonstrated that the fractional-order FOPID controller achieves only 1-2% overshoot, significantly outperforming conventional PID controllers (over 22% overshoot), exhibiting enhanced disturbance rejection and faster response speeds (approximately 0.06 s reduction). Additionally, the ILPSO-FOPID combination exhibited superior dynamic performance compared to alternative algorithms.  
Further stability and robustness analyses were conducted for the above system. Considering the vibration disturbances and varying loads typically encountered by drilling rigs, rapid response speeds could result in overshoot and mechanical impacts. Therefore, we introduced an outer-loop robust controller based on H\(\infty\) control theory. By slightly compromising response speed (increasing settling time to 0.1 s and the H\(\infty\) norm to 1.3), the system's robustness and stability were significantly enhanced, rendering it more suitable for complex operating conditions.  
Conceptualization, [PERSON] ([PERSON]), [PERSON], [PERSON], [PERSON] and [PERSON]. ([PERSON]); methodology, [PERSON] ([PERSON]) and [PERSON]; validation, [PERSON] ([PERSON]), [PERSON], [PERSON], [PERSON] and [PERSON]. ([PERSON]); software, [PERSON]; formal analysis, [PERSON] ([PERSON]), [PERSON] and [PERSON]. ([PERSON]); investigation, [PERSON] ([PERSON]) and [PERSON]; writing--original draft preparation, [PERSON] ([PERSON]) and [PERSON]; writing--review and editing, [PERSON] ([PERSON]), [PERSON], [PERSON] and [PERSON]. ([PERSON]); supervision, [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
The authors gratefully acknowledge the financial support from the National Key R&D Program of China (Grant No. 2024 YFB471601), and the Shanxi Provincial Key Research and Development Program of China (Grant Nos. 202302100401009 and 202302100401010).