Active Disturbance Rejection Control for Speed Control of PMSM Based on Auxiliary Model and Supervisory RBF
Round 1
Reviewer 1 Report
The study was conducted at a high level. The only thing that would be worth considering in more detail is the world experience in controlling interference suppression for speed control.
Author Response
Response: Thank you very much for your comments. Based on your suggestion, I investigated the interference suppression methods for speed control. I screened several typical anti-interference algorithms and gave representative references in Introduction Section, including fuzzy control, neural networks control, robust control, sliding mode control (SMC) and etc. In addition, through the comparison of different algorithms, ADCR has the advantages of simple structure and convenient design. Especially ADRC has the ability to estimate and compensate for disturbances under the condition of model uncertainty. This is conducive to the practical engineering application, so more attention has been paid to the application of ADRC for speed control in recent years. More detailed descriptions have been added to the Introduction Section. Thank you again for your comments.
Reviewer 2 Report
Strengths
Authors showed, due to friction disturbance, the phenomena of low-speed crawling and vibration near zero may occur in the speed control of PMSM. To overcome these problems, SRBF-MADRC algorithm is proposed to improve the system's friction compensation accuracy and anti-interference performance in the work. By introducing auxiliary model and reduced-order processing method, MRESO achieves higher efficiency and stability of state estimation than single ESO. SRBF is designed to supplement the deficiency of NLSEF and promote the response speed to feedback error. The hybrid control algorithm reasonably distributes the friction compensation burden, and realizes the accurate compensation of the total disturbances. The control performance of the optimized algorithm is verified by simulation and experimental results.
Weakness
1. References to Figures 2, 3 after their appearance in the text.
2. NPD not PD (Line 286).
3. Where is the load in Figure 11?
4. Only two publication of the authors in the reference
Comments for author File: 
Comments.pdf
Author Response
Thank you very much for your detailed comments, and I apologize for the mistakes in the manuscript. According to your comments, I have made the following modifications.
- References to Figures 2, 3 after their appearance in the text.
Response: Due to careless typesetting, the location of Figure 2, 3 is not appropriate. Figures 2, 3 has been adjusted to the back of their appearance in the text. The locations of other pictures are also checked.
- NPD not PD (Line 286).
Response: Thank you for your careful review. PD has been changed to NPD at Line 286. PD stands for proportional differential. NPD stands for nonlinear proportional differential. To avoid confusion, the spelling of the full text has been checked.
- Where is the load in Figure 11?
Response: The Load is missing assembly in Figure 11. The load has been reassembled and marked. The picture has been replaced and modified.
- Only two publication of the authors in the reference.
Response: According to my understanding of your suggestion, the problem may arise in two aspects.
On the one hand, there are only two comparison algorithms in the experiment, namely NPD and typical ARDC. The main reason is that they are typical standard algorithms and serve as reference standards for SRBF-MADRC to ensure the comparison has a unified reference standard.
On the other hand, there are too few references to the publication of the authors of this manuscript. The reason is that our team's research on speed control has just started. We will try to do more in-depth research and give more publications. We hope you can understand our problem. Thank you again for your comments.
Reviewer 3 Report
1. The authors have to explain how the parameters kp and Kd are taken. The authors used two PI controllers and have to give the gains for the PI controllers.
2. How the convergence is guaranteed in tuning the RBF network and the authors have to show the convergence graph.
3. The authors can compare their methodology with some latest evolutionary technique and can show the convergence details.
Author Response
Thank you very much for your detailed comments, and I apologize for my inadequate consideration in the manuscript. According to your comments, I have made the following modifications.
- The authors have to explain how the parameters kp and Kd are taken. The authors used two PI controllers and have to give the gains for the PI controllers.
Response: I'm sorry that the parameter selection method was not introduced before the parameters were taken. The parameters kp, ki and kd of PID controller are taken according to the bandwidth based parametric tuning method. The PID parameters can be adjusted according to the closed-loop bandwidth. The approximate relationship between PID parameters and control bandwidth is given in Simulation Section. In addition, according to the specific requirements of control bandwidth of current control loop and speed control loop, their controller parameters are calculated respectively. According to the approximate formula, the parameters of PD controller in speed control loop are set as kp=20 and kd=5. In order to reduce the influence of current response delay on speed control, the bandwidth of current control loop should be much larger than that of speed control loop. The parameters of two PI controllers in current control loop are set as kp=400 and kI=40000. For more detailed description, please see the Simulation Section.
- How the convergence is guaranteed in tuning the RBF network and the authors have to show the convergence graph.
Response: In the RBF based supervisory control system, the NPD control plays a leading role and the SRBF plays a regulating role when control errors occur. In the study, the SRBF employs the gradient descent method to realize the learning of neural network weights, and finally makes the output errors converge to the threshold. So the learning rate factor is adjusted to coordinate the learning speed and stability of SRBF. According to the adjustment method proposed in Reference “Liu, J.K. RBF neural network control for mechanical systems: Design, Analysis and Matlab Simulation. Tsinghua university press. Beijing, China, 2014.”, when the learning rate factor is 0.3, SRBF obtains a fine learning speed and stability. The convergence graph of network approximation error is added in the manuscript. For more detailed description, please see the Simulation Section.
- The authors can compare their methodology with some latest evolutionary technique and can show the convergence details.
Response: Thank you very much for your further research suggestions. In the work, the reason why RBF is chosen as the supervised neural network is that RBF is a real-time neural network and has a very fast convergence speed. The advantages of RBF over other networks have been verified by the listed references, so more evolutionary technique comparisons have not been implemented. Some latest learning algorithms that can be studied include: genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm, adaptive fuzzy inference, etc. Due to the limited modification time allowed by the editor, we hope that the comparative work can be allowed to be put into our further research. Thank you again for your comments.
Reviewer 4 Report
It is a good work, and supported by simulation and experimental results. However, I did not find the plots of control efforts, so that to see it in view of control gains, which importance have been stressed (in the abstract, introduction too) and of course detrimental on occasions for contributing to vibrations.
Control gains may also be considered for comparing to the other techniques in the literature.
Author Response
Response: Thank you very much for your comments. The focus of this work is to compare the performance of the control algorithms with different structures under the condition of the same control gain. By comparing the control effects of NPD, ADRC and SRBF-MADRC, the effectiveness of the proposed improved algorithm in the work is verified. So that there is little consideration and research work on control gain. In order to remedy this problem, the introduction to the setting method of control parameters is added into Simulation Section. The parameters kp, ki and kd of PID controller are taken according to the bandwidth based parametric tuning method. The PID parameters can be adjusted according to the closed-loop bandwidth. The approximate relationship between PID control gains and control bandwidth is given in Simulation Section. In addition, according to the specific requirements of control bandwidth of current control loop and speed control loop, their control gains are calculated respectively. According to the approximate formula, the parameters of PD controller in speed control loop are set as kp=20 and kd=5. In order to reduce the influence of current response delay on speed control, the bandwidth of current control loop should be much larger than that of speed control loop. The parameters of two PI controllers in current control loop are set as kp=400 and kI=40000. For more detailed description, please see the Simulation Section. Due to the limited modification time allowed by the editor, we hope that the comparative work on control gains can be allowed to be put into our further research. Thank you again for your comments.
