Adaptive Sliding Mode Control Method for Z-Axis Vibrating Gyroscope Using Prescribed Performance Approach

Round 1

Reviewer 1 Report

Dear Authors,

paper is well organized and high quality. However,

1. Line 188 should start from Fig not fig.
2. Fig.2 - you use black solid line for all plots. It is difficult (almost impossible) to find the correct one.
3. Line 196 comma and dot at the end of line.
4. Line 197 similar remark to 1.
5. You have to read text carefully, because there are many editorial issues.

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Reviewer 2 Report

Comments to the authors

Manuscript number: applsci-826175

Title: Adaptive sliding mode control method for Z-axis vibrating gyroscope using prescribed performance approach

 

1) English issues:

a) As is shown in fig.1, the

 

2) The error bound function (6) needs to be justified.

 

3) According to (7), the error bound rho should be non-zero. This issue should be mentioned clearly in the manuscript.

 

4) In Theorem 1 and 2, quadratic Lyapunov functions are used to prove the convergence. As discussed in [R1] and [R2], a non-quadratic Lyapunov function can significantly improve convergence properties. The authors are recommended to discuss this issue as a remark.

[R1]. “Performance enhanced model reference adaptive control through switching non-quadratic Lyapunov functions,” Systems & Control Letters, 2015.

[R2]. “Model reference adaptive control with L^(1+alpha) tracking,” International Journal of Control, 1996.

 

5) Provide a list of used abbreviations in the manuscript. The simulation results are comprehensive, however due to the high number of acronyms it is not easy to follow the discussions.

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Reviewer 3 Report

The paper deals with a sliding mode controller designed to improve control of vibrating mass MEMS gyroscope. Overall, the analysis of the system represented by the state space model in Equation 5 is sound.

 

1. The authors need to explain adequately the basic principles of operation of the gyroscope and the need for a control loop. It is unclear what exactly is the purpose of the control system and what is being controlled.
2. What constitutes the actuators? What variables are measured? Positions only or also velocities? Using what sensors?
3. It is unclear what constitutes the desired trajectory q_d, and how it is defined and generated.
4. L154-156: the paragraph does not state control objectives, only maybe specific objectives of this work.
5. The simulations and the results are limited to trajectory tracking performance for the moving mass. It remains unclear how this results in improved measurement of rotational speed. I would expect graphical results showing analysis such as speed measurement error, rate of convergence, response when measuring variable speed.

 

The paper also contains various typographical and stylistic errors that need to be corrected. Some are listed below, but please proof read the whole paper.

• Spelling of Coriolis
• Define q_0 (L128)
• APPSMC is defined only in the Abstract, not in the main body text.
• Redundant “in the” in L137
• Avoid using “… and so on” (L14, 33, 35, 53, 88, 137 …)
• L19: change to: quantitative analysis
• L182: “can that”
• L191: “converges 0”
• L263: the meaning of “AC can be used in the paper” is unclear

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Round 2

Reviewer 2 Report

The authors have addressed the concerns. However, I have two more comments:

1) The justification of Eq. (6) should be mentioned in the manuscript. 

2) The reviewer fails to locate the implementation of Comment#4 regarding non-quadratic Lyapunov functions. 

Author Response

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Reviewer 3 Report

The authors have answered my previous questions and I am satisfied with the amendments made in the paper.

I am happy for the paper to be published in its present form.

Author Response

Thank the reviewer for your time and effort. Our response letter has been uploaded in the attachment. Please see the attachment for our response letter.

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