Review Reports

Round 1

Reviewer 1 Report

1) The description,

‘’In this paper a problem of influence of an input gain uncertainty on the tracking performance of a control system designed for a second-order plant in accordance with the Active Disturbance Rejection Control (ARDC) paradigm is considered.’’ (Page. 1. Abstract)

, is too complicated, and some short sentences are necessary.

 

2) This description,

‘the necessary and sufficient condition for the uncertain input gain’ (Page.2. Introduction)

, is very strange.

 

3) The description,

‘’the ordinary state domain ADRC approach by the presence of \ddot{r} in the total disturbance only’’ (Page.3. Introduction)

, may cause ambiguity.

 

4) There may be some errors in equation (6).

 

‘’$\dot{\tilde{z}}_{3}=(b-\hat{b}) \hat{b}^{-1} \dot{v}+\frac{d}{d t}(\delta-\ddot{r})-b \hat{b}^{-1} k_{3} \tilde{z}_{1}$’’

to be modified to

‘’$\dot{\tilde{z}}_{3}=(b-\hat{b}) \hat{b}^{-1} \dot{v}+\frac{d}{d t}(\delta-\ddot{r})-(b-\hat{b}) \hat{b}^{-1} k_{3} \tilde{z}_{1}$’’

may be correct.

 

5) Under the condition of uncertain input gain $b$, use the bandwidth parameterization method of literature [22] to determine the observer and controller parameters. Is this reasonable?

 

6) Shouldn't the stable regions in Figure 1 be a solid area? And the one in this article seems to be a curved surface.

 

7) Punctuation is wrong, in Theorem 1. Such as  ‘such, that’ (Page.5. Theorem 1).

 

8) How is the matrix A of Theorem 1 obtained? Is it correct?

 

 

9) The simulation is only done with a set of selected observer and controller parameters $\omega_{\mathrm{o}}=100, \omega_{\mathrm{c}}=1$, the proposed method has a certain effect. But is there the same result in all stable regions?

In addition, how to determine the parameters of the controller and observer?

According to the author's knowledge, when the eigenvalue of the matrix H is large enough, the influence of disturbance can be well suppressed, but this article only gives the stable region, which is one step away from sufficiently good control performance.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This paper studies that in the Active Disturbance Rejection Controller, if the controller is designed in the error domain, consciously selecting input gain parameters that are different from the actual model may lead to a significant improvement in control accuracy. The structure of the paper is rigorous, the expression is concise, and the semantics are precise. The goal and innovation expressed in the article are more prominent. This paper has certain practical application value, and the simulation results can better reflect the function of strengthening the EADRC.Recommend to accept the paper.

There are some shortcomings in this paper, as follows:

1. The Active Disturbance Rejection Controller was first proposed by Jingqing Han in 1998, and the earliest document given in this paper was Zhiqiang Gao in 2001.
2. The literature review contains less content and lacks literature comparison.
3. The block diagram of the designed control system should be added to the paper to facilitate understanding.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

This manuscript proposes an methodology for online parameter estimation of the input term,
which is  necessary for implementing the active disturbance rejection control strategy (ADRC).
Here are my concerns about this manuscript :

* Notation of the vector r(t) = [r , \dot{r}] might be slightly confusing, please change the notation.
* It would be more clear if e_1(t) and e_2(t) are defined.
* There is a typo in assumption 1, and it would be better if it explicitly says that
 the n-time derivative of a C^n class function is continuous and bounded by a positive constant.
* The subcaptions of Figure 1 should be improved.
* There are mistakes when defining the extended state vector, after equation (3),
because of the previous notation of the vectors x(t) and e(t),
 please verify each term and correct wherever it is necessary. 
* Verify that definition of equation 7 is not in conflict with the previous definitions of e_1 and e_2, 
if this is the case, then, change the notation.
* In  equation (7), \hat{b}*\hat{b}^{-1}=1 ?
* I think there is a mistake in equation 6, in the last term,
since it does not correspond with \tilde{z}=z-\hat{z}, please verify it carefully. 
The last term in equation 6 should be ((b+\tilde{b})b^{-1}-k_3)\tilde{z}_1 or something similar,
 but not the expression that you wrote.
* The position of Figure 1 is not so good, since it is in the middle of Theorem 1, 
please find a better location for it.

*Subcaptions of figures 2-4 should be improved as well.

Given this context, I will suggest to accept this paper for a publication after a minor revision.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

1. Why not prove the stability of the entire closed-loop system (observation error, feedback control error system) in Theorem 1? It is hard to know exactly what you are proving. The description of Theorem 1 does not match the foregoing content very well. This may confuse the readers. (Page. 6-7.)

 

2. Can the author explain why ‘’From Theorem 1 it can be shown that for beta in (0, 9) it is possible to find $w_{o}$ high enough, to stabilize the closed-loop system’’. Why beta in (0, 9)? (Page. 7. Line 199-200)

 

3. Based on the reviewer’s experience, increasing beta may lead a non-trivial equilibrium point more close to zeros according to (16)-(18) ($beta * k_{3}$), eso's observation accuracy will be improved, and this will lead a increase of the tracking quality. Can we imagine that the same goal can be achieved by increasing k_{3}? These can be tested and verified by the author. These are the improvement of control accuracy by setting high gain. But in practical applications, we have to consider the sensor noise problem, can these gains (beta, k_{3}) be increased all the time? The answer is negative. The author should dig deep into what is the essence of the improvement of control accuracy, rather than express the phenomenon.

 

4. Some expressions in this article need to be improved.

Author Response

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Author Response File: Author Response.pdf