Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

TITLE:

Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

MANUSCRIPT ID:

mathematics-1157713

Comment 1:

Interesting research in a very, very high-quality manuscript. The authors should be proud. Verbiage is very well stated with classical, pithy referencing of the corresponding equations and figures. Very good graphics. Very legible.  Transmit considerable information.

Response  1:

The authors would like to thank the referee for her/his excellent review work. What’s more, the authors thank you for your high evaluation of the article.

Comment 2:

Please consider enlarging the bounding limits in figure 5, since they are marginally legible.

Response  2:

Thanks very much for this comment. The authors re-drew Fig. 5 and enlarged the symbols in Fig. 5. The boundaries of Fig. 5 have been expanded.

Comment 3:

Major weakness: complete lack of tables of quantitative data validating claims of performance. The reviewer offers to the authors one single example: figure 16b is an excellent qualitative validation, but where is a quantitative companion? Those two signals are very easily converted to means and standard deviations of errors which make wonderful quantitative comparisons. Using such figures of merit, it is very easy to amplify the abstract and Conclusions to include percentage improved performance, validating claims in broadest terminology. It would also help to highlight the major elimination of overshoot and oscillation that is ubiquitously experienced with feedback pole-placement designs.

Response  3:

Thanks very much for these comments. The author agrees with your suggestion very much. The author marked the mean and standard deviations of errors in Fig. 16(b). And the errors of all six kinds of experimental data are analyzed, and the error analysis results are put into Tab.2. In addition, the author added the analysis result of the error in the conclusion. As follows:

Table 2. Error indicators of six groups of experimental data

3)The simulation and experimental results show that the control method combined with the RBF neural network and the pole placement strategy can effectively reduce the error of the flexible manipulator's rotation angle. According to the Tab. 2, compared with pole placement strategy alone, the mean error is reduced by nearly 60%. Therefore, the combined control method can effectively reduce the angle error. Therefore, the control method proposed in this paper can effectively improve the control accuracy of the flexible manipulator.

Comment 4:

Very strong Conclusion specified in listed developments. Please add a (very) few sentences expressing the recommendations for future research. The seemingly validated claims of this reference include elimination of overshoot and settling, just like the authors’ work, so this would make a wonderful comparison for future researchers. 

Response  4:

Thanks very much for these comments. At the end of the conclusion, the author added the future thinking about improving the motion accuracy of the flexible manipulator, as shown below.

This paper uses the control method to improve the motion accuracy of flexible manipulators. It is hoped that the vibration isolation device can be added between flexible manipulators and end-effectors in the future. In this way, the motion accuracy of flexible manipulators can be improved.

TITLE:

Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

MANUSCRIPT ID:

mathematics-1157713

Comment 1:

Introduction can be improved with recent researches concerning control methods for flexible manipulators, to show in brief other approaches, that are using today.

Response  1:

The authors would like to thank the referee for her/his excellent review work. The author adds references to the control of flexible manipulators in recent years in the introduction part according to experts’ suggestions, as shown below.

In Literature [13], the nonlinear self-tuning PID controller is used to control the flexible manipulators. In Literature [15], the sliding mode controller with observer is used to control the angle of manipulators. In Literature [16], the linear quadratic Gaussian and the weighted H infinity controller are adopted to control flexible manipulators.

Comment 2:

Conclusion section should also summaries novelty of presented control method.

Response  2:

Thanks very much for this comment. The author summarized the innovations of the paper in the conclusion part, and added the statistical result explanation for the experimental error.

6. Conclusion

In this paper, a dynamic model of flexible manipulators with gravity is established. The innovation of this paper is to consider the factor of gravity and the combined control strategy is used to improve the motion accuracy. The control method combining the pole placement strategy and the RBF neural network is applied to reduce the fluctuation of the rotation angle of flexible manipulators. Then the motion precision of flexible manipulators is improved. Among them, the RBF neural network is used to distinguish the uncertain items of the system. The uncertain items include both the flexible factors and the time-varying characteristics of the dynamic parameters. Simulation analysis and experiments show that the proposed control method can effectively suppress the rotation angle's vibration and improve the motion accuracy of the end-effector. The specific conclusions are as follows:

3）The simulation and experimental results show that the control method combined with the RBF neural network and the pole placement strategy can effectively reduce the error of the flexible manipulator's rotation angle. According to the Tab. 2, compared with pole placement strategy alone, the mean error is reduced by nearly 60%. Therefore, the combined control method can effectively reduce the angle error. Therefore, the control method proposed in this paper can effectively improve the control accuracy of the flexible manipulator.

Comment 3:

Abstract should include some results of provided research not only its overview.

Response  3:

Thanks very much for this comment. The author added the experimental results at the end of the abstract. Add content as shown below.

Finally, numerical analysis and control experiments prove the effectiveness of the control method proposed in this paper. The means and standard deviations of rotation angle error are reduced by the control method. The results show that the control method can effectively reduce the rotation angle error and improve motion accuracy.

Comment 4:

Please check English spelling in sections 1 and 4 especially.

Response  4:

Thanks very much for this comment. The author corrected the English errors in the paper and marked them in red.