Observer Design for Nonlinear Invertible System from the View of Both Local and Global Levels
Round 1
Reviewer 1 Report
The paper describes a state observer approach that were developed with the aim to monitor the parameters/states of interconnected subsystems; thereby providing useful information set for advanced predictive maintenance techniques. The motivation of the work is well claimed, the text of the paper is technically sound, logically structured, and easy to follow. I think that the topic is relevant to the scope of the journal, however there are critical issues to be fixed in the revised version.
I recommend that the paper should be major revised. I hope that the authors find the following comments constructive for the extension of their work:
- Language/text: I recommend that the text should be proofread.
The English is more or less OK, there are many minor issues, but the text is clear and easy to follow. Some typos (there are more…!!):
Line 46: “for modern control system For”
Line 95: “Finally, conclusion is made in section.”
Line 118: “purpose is to monitoring”
Line 186 “The new process subsystem (12)” isn’t it (8)?
Line 289 “unmeasured according to realistic.”
Line 303 “where Aa is the diaphragm”
Line 355: “In addition to noise, No error was”
Line 390: “Compare to curve”
Line 438: “on the global output.directly. In order”
The abbreviations are not introduced before their usage in the text, such as: ISS/ISDS. Similarly, NIO has been used multiple times in the text but was never introduced.
I think that from line 190, Assumption 1, Assumption 2, and Assumption 3 should be used instead of A(1), A(2) and A(3). Apply some formatting, since this is a list, use enumeration.
The equations are not correctly addressed in the text, such as:
”process subsystem described in (1):” -> “process subsystem described in Equation (1):”
Do not use the pronouns "we" and "our" in the text, use passive instead.
Many equations are not labelled, such as the third equation at line 165, or the equations at line numbers 296, 301. This should be fixed.
The units of physical quantities should be fixed.
- The abstract well captures the presented work, however I think one sentence should be added, which highlight the significance of the work compared to the state of art methods.
- The introduction is well written, the field of study is presented in detail. However, paragraph where the contribution is discussed should be extended (before line 90). It is not obvious for the reader that what are the contributions and differences of the proposed technique compared to the already existing observer methods, such as refs [29],[31]? It should be emphasized that compared to the standard observer algorithm what significance and advantages the proposed one provides. This is important for the readers and should be added with clear explanation.
- Figures should be regenerated.
Fix Figure 2, since the text is shifted behind the shapes.
The simulation results (Figs. 3, 4, 5, 6, 7, 8, 9, 10) are very low resolution images, these should be regenerated. Use vector format for these graphs, since the details should be visible for the reader.
Moreover, these figures are not in harmony. For example Figs. 3 and 4 highlight a 200 sec long simulation, however the information (where the dynamics happens) is in the first 40 seconds. Moreover, the y axis of Figs. 4a and 4b are not the same. These issues are also true for the rest of the simulation results. These issues should be fixed. Use high quality graphs that are in harmony and capture the information.
- In line 307, how did the authors constuct state vector xa? pc1 and pc2 were not introduced earlier, only pc as the pneumatic pressure. Similarly, X1 and X2 were not introduced earlier.
- How did the authors choose the tuning parameters? Since this influences the dynamics, therefore its crucial to be described in detail.
- During the discussion of the results the authors sometimes use UIO sometimes NIO, its very confusing for the reader. For example: “Fig. 5 shows the computation and estimation of process fluid flow rate Fp using UIO and Observer 2.” However, the legend on the Figure shows NIO.
- It is important to extend the analysis to an independent system (i.e., as an additional case study), such as the inverted pendulum on cart. The inverted pendulum on cart has its well known mathematical model, where the actuator subsystem can be characterized both as first or second order system. This analysis can be easily carried out and increase the significance of the work.
- In the conclusion, the significance and advantages of the works should be emphasized moreover future work/developments should be described.
Author Response
Dear Prof,
We feel great thanks for your professional review work on our paper. We acknowledge your comments and suggestions very much, which are valuable in improving the quality of our manuscript. As you are concerned, there are problems that need to be addressed. According to your nice suggestion, we have made extensive corrections to our previous manuscript. We have added data to supplement our results and edited our paper extensively. We would like to know if there are still somewhere need to be amended.
Please see the attachment for the response of your questions one by one.
Yours sincerely,
Mei ZHANG
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The following comments are provided.
1) Instead of focusing only at attractiveness ("converging observer"), asymptotic stability of the estimation error (which is stronger than attractiveness) should be stated since this stems from the disclosed theoretical results.
2) Generally speaking, the presentation is quite confused, especially the statement of Theorem 1.
3) Concerning, the cascaded dynamics , the authors may refer also to A. Alessandri, P. Bagnerini, R. Cianci, State observation for Lipschitz nonlinear dynamical systems based on Lyapunov functions and functionals," Mathematics, vol. 8, no. 9, 2020, where a stability analysis involving cascading is shown.
On the overall, the paper can be accepted after a careful revision.
Author Response
Dear Prof,
We feel great thanks for your professional review work on our paper. We acknowledge your comments and suggestions very much, which are valuable in improving the quality of our manuscript. As you are concerned, there are problems that need to be addressed. According to your nice suggestion, we have made extensive corrections to our previous manuscript. We have added data to supplement our results and edited our paper extensively. We would like to know if there are still somewhere need to be amended.
Please see the attachment for the response of your questions one by one.
Yours sincerely,
Mei ZHANG
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors took into account the reviewer's comments, incorporated the recommendations into the text and improved the overall quality of the manuscript. Moreover, the figures have been updated based on the comments. The answers of the authors are clear and the presented explanations are accepted. However, i still think that another case study under the simulations section (e.g., the case study of inverted pendulum on a cart which is well known by the whole control community) would increase both the significance and presentation of the techniques.
Author Response
Dear Prof, We feel great thanks for your professional review work on our paper. We acknowledge your comments and suggestions very much, which are valuable in improving the quality of our manuscript. According to your nice suggestion, we are suggested to add another case study (the case study of inverted pendulum on a cart) to enhance significance and presentation of the proposed method. However, unfortunately, after carefully referring to inverted pendulum modeling papers（see following references like in [1-5] ), we found that the proposed method is not suitable for the inverted pendulum case. Please see the attachment to find the explanations. However, due to our limited knowledge, the analysis for inverted pendulum may not be correct. if there is anything improper, please kindly help us to point out and mentor us how to deal with it. We thank you in advance. If you have any other questions about this paper, I would quite appreciate it if you could let me know at your earliest convenience. Yours sincerely, Mei ZHANG
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
The authors gave clear explanations to my suggestion. I accept the work in the current form since it has theoretical significance. However, it should be realized that in real world of engineering the introduced constrains make the usage of proposed method highly limited.
