FPI-Based Adaptive Control with Simultaneous Noise Filtering and Low Frequency Delay

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper develops a large-signal model containing the comprehensive dynamical behavior of the DC MGs based on the theory of high-order fully actuated systems, and proposes distributed optimal control based on this. The proposed secondary control method can achieve the two goals of voltage recovery and current sharing for multi-bus DC MGs.

This paper contains some interesting results. Please find the following comments that may help improve the paper.

1) It is suggested to highlight the challenges of the investigated problem in the very first section.

2) Adaptive sliding mode control design has been presented in [25,26], where finite-time convergence is achieved. A more interesting future topic is the fixed-time control. Please see my following comments.

3) Are there any assumptions being made in the problem formulation? If yes, please clearly list them.

4) Please confirm the expression of (8).

5) In experiment, the results seems good. But please discuss if the experimental results 100% match that of simulation results. If not, what are the causes.

6) The language of this paper can be further improved. For example, page 5, exponentially decaying error  ---> exponentially decaying errors

7) The conclusion section can be enhanced by discussing some future directions such as extending the asymptotic adaptive control to the fixed-time counterpart. The authors may refer to Collective behaviors of mobile robots beyond the nearest neighbor rules with switching topology (TCYB 2018, doi: 10.1109/TCYB.2017.2708321). At least some comparison against TCYB 2018 should be discussed in this manuscript. The author may also refer to this literature: A. Polyakov, IEEE Trans. Autom. Control, vol. 57, no. 8, pp. 2106-2110, 2012. (DOI: 10.1109/TAC.2011.2179869)

8) Overall, this paper is organized well, and a revision is suggested in this round.

Author Response

See attached pdf.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The problem under study  is related to an adaptive control synthesis under noise filtering and lower frequency delays. It is of interest, especially in some applications. The performed works is exhaustive  and the paper organization is fine although details are not sufficiently justified in some developments, in our opinion. However, in our opinion, there are several different approximations used in different parts of the technical study which are mixed with mathematical developments without giving the necessary explanations and also, some of the steps used for that have a lack of rigor. Therefore, the steps of the implemetation have to be described more clearly, especially related to the various performed approximations, and the mathematical rigor should be improved.

Eqns. 3: How is the approximate deformation function designed?. Eqns. 2b and 3b are not mutually coherent as now written.  Note that the two first terms in both of them are identical while the respective last terms mutually contradict each other. q/dot/Def (3a) has to be used to achieve the approximation of (3b) but it does not appear  as argument in the left-hand-side of (3b).

Eqn. 6 is not very clear unless some explanation about the integral error (left-hand-side of the equation be added). Is the left-hand-side first equalized to (4b) and is it then approximated by the right-hand-side by selecting appropriate coefficients in the expansion?.

The group of equations (4b), (5) and (6) have to be explained together in a clear way. If (5) is got from (4b) as indicated then it is virtually impossible to fulfill (5) via the selection of a parameter Lamda. If  (5) is integrated to lead to (6) then (6) would not be identical, in genera, to (4b). It is not clear  also that this could be achieved with time-parameter functions C(.) in (6) and, if so, how is it guarantetd the boundedness of those functions?.

The convergence of the solution of (12) if the derivative absolute value is less than unity is clear, but  the convergence  problem is local so that, in our opinion, the initial conditions should be sifficiently close to the convergence limit point. Please, explain this concern more in detail.

The Laplace transforms (16) of Eqns. 15 are for null initial conditions  which allows to involve transfer functions. This is not mentioned explicitly. However, what happens for nonzero initial conditions and how is the complete problem ( nonzero initial conditions + forcing term)  addressed in that case?.

The introduction of a delay in the noise signal  (cf. (20)-(21)  seems to be artificial , at a first glance, since it is not based in some given previous potential hypothesis  (to be reflected in the describing time equations) of having a noise delay.

Why is the terminology "adaptive control "used  for this  synthesis control  problem?. Apparently, there is no parameter estimation via  either a numerical algorithm or through some instrumental implementation as it is typical in the adaptive control context.

Eqn. 22 and the closely allocated wording  text have to be explained more clearly since a delayed function is comnpared to a non-delayed one. Do yo mean some replacement of terms in some previous equation to perform a subsequent parallel analysis to the given one?.

Author Response

See attached pdf.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

No further comments. This paper can be accepted now.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper has been improved according to the given suggestions.