Model-Free Sliding Mode Enhanced Proportional, Integral, and Derivative (SMPID) Control

Round 1

Reviewer 1 Report

Dear Author,

Thank you for the presentation on the new kind of PID and SMC-related controller. It decreases significantly the weaknesses of the SMC control systems (chattering) and includes its quick action in the PID controllers.

The paper is very well structured and written. It clearly explains the background, Author's attitude and achieved results, and finally, the conclusions strictly related to those results. 

I found only two syntaxes: on page 15 in line 16 from the top except "plan" should be "plant" and in References on page 25 the first Fliess work coauthor's name should be corrected.

Reading the paper was a pleasure for me and I hope the same will be for the other readers after its publishing.

Author Response

Thanks for the encouragement. These typos have been corrected.

Reviewer 2 Report

The article is devoted to the development of the sliding mode method.

The sliding mode is hopelessly outdated, like flintlock guns, stone axes and paddle steamers.

The reason that sliding mode is hopelessly obsolete is that this mode causes the control signal to jump between two extremes on the assumption that the average value of the control signals will be exactly what is needed. This mode is vicious in that if all the time constants or the signal delay time in a closed loop are not accurately taken into account, the actual amplitude of these oscillations in practice will be many times greater, the frequency of these oscillations will be much lower, and if there are restrictions in any of the elements of the system the result of applying such a controller will be completely different, fundamentally not coinciding with the result of calculation or simulation. In addition, systems using the sliding mode fundamentally cannot be robust, since a small unaccounted for delay in the path will radically change the transient process, and this property is the opposite of the robustness property.

However, the reviewer acknowledges that not all theorists agree with this, so various scientific schools continue to write articles about the application of the sliding mode, so most likely the journal should not reject the article just because the reviewer considers this method outdated and inefficient.

 The author claims that Figure 1-C illustrates an idea that could not be found anywhere else. If this idea is only that the object is covered by one feedback in the PID controller, and then the resulting system as an object is covered by another external loop with another PID controller, then this idea is far from original. If the idea consists in something else, then the above illustration does not reveal it.

In lines from 10 from the end to 5 from the end on the first page it is not clear what is being discussed, the author claims some difficulty without revealing it, and claims some merit without explaining it.

The author states that PID controllers are common for low order linear slow processes. The author incorrectly refers to the low order and the slow development of the process. High object order or high speed or both do not complicate the use of the PID controller in any way, so this limitation of their scope is used unreasonably.

  Referring to the Ziegler–Nichols method is also no longer desirable, since this method is outdated long ago, it is not efficient enough, it makes sense to use it only if the object model is completely unknown, the developer does not have elementary knowledge of regulator design methods and there is no good computer with adequate software for modeling and numerical optimization. If at least one of these restrictions is not met, then it is unreasonable to apply the Ziegler–Nichols method.

The third paragraph on page 4 begins with the words "From the above analysis." But no analysis is given above, there is only a listing of publications known to the author with very superficial comments, often erroneous or immature. This is not an analysis.

 There are a number of questions about the structure of the article. It would be necessary to set the task. The author is invited to start by acquainting readers with what problem this article solves. For example, to give a mathematical model of an object for which traditional methods do not allow obtaining a solution of the desired quality. After that, it would suffice to briefly list the known methods and explain why they are unsuitable. Then it would be desirable to inform the readers of the main ideas of the proposed solution method, and then to reveal them as clearly as possible through schemes or systems of equations. After that, it would be necessary to solve one or more representative examples with the proposed method and compare the results of the solution with the results of using the best known methods. If the solution obtained with the new method has an advantage, then this proves the value of the proposed method.

This, unfortunately, was not found in the article.

 Usually the "Introduction" section is not numbered. And this section, as a rule, simply briefly describes the goals, objectives, methods and results. The next section is "Problem Statement". The author preferred to number the "Introduction" section and expand it up to the fifth page inclusive, only the last two lines and the heading before them refer to the next section number 2.

Since section 2 is called "Preliminary", it should be interpreted as a part that replaces the introduction or statement of the problem, that is, not the original part of the article. But in this case, only section 3 begins the original part of the article, that is, from the second half of page 8. Should the introduction be stretched so much? An introductory and non-original part of 8 pages is an overkill.

The structure with the so-called U-regulator is not something fundamentally new. In fact, part of the controller is covered by feedback. It is known that if an object is covered, for example, with an integral feedback, then it acquires the properties of a differentiating device, and vice versa, the differentiating feedback imparts integral properties to the element. Therefore, a closed-loop controller is just another controller that can be calculated in other ways. Such feedback can actually increase the order of the controller. These are well-known things, the complication of the structure only obscures the essence.

The ideas presented in Section 3 are essentially based on the introduction of nonlinear elements into the control system. It is known that linear objects are preferred for control, and it is also known that ideal linear objects never occur in practice. Therefore, the most effective method of using non-linearities in the controller is to use such non-linearities that compensate for the plant non-linearities. For example, if the object model has a quadratic dependence, then it is useful to set the dependence as a square root at its input, if the dependence is exponential, then it is useful to use a logarithmic dependence for compensation, and so on. In any case, the element shown in Fig. 3-a is clearly a bad solution in any case as it is a dead zone. The introduction of such an element always worsens the ability to manage the object, there are no exceptions to this rule. If such a nonlinearity is a property of the object, this should have been discussed at the beginning of the article in the “problem statement” section, and the use of such an element as a solution to the problem is futile.

An example of an object given by relation (4.6) is rather unrepresentative, there are too many zero elements in the matrices of the mathematical model, which greatly simplifies control. With the exception of the arc tangent function, this equation can be considered linear, and the arc tangent function near the equilibrium state is also close to linear. Therefore, even if the author managed to provide management of such an object, this does not prove anything, since the object model is very simple, there is no comparison of using traditional management methods for this object. It is not possible to evaluate the usefulness of the proposed solution, since the author did not bother to use other methods. In particular, since the author has a Simulink package, it would make sense to simply calculate the PID controller for this model and compare the results by comparing transient curves in the same axes.

At the end of the article, the author cites figures from number 5 to number 29, but there are no comments on these figures in the text of the article. It turns out that readers are invited to independently understand what kind of drawings they are, what follows from them, how they should be treated. You can't write articles like that. There are generally accepted rules for writing articles. If there is a figure in the article, then it should be referred to in the text, indicate that it shows what it demonstrates, and so on. This is not. Consequently, the article is written sloppily and in this form it cannot be published.

Author Response

please find the response file enclosed

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

It would be highly desirable to comment on what exactly readers should see from the figures from figure 24 to figure 29. From the fact that the authors added group references to figures 17-19, figures 20-22, figures 24-29 with the mention that these figures clearly illustrate the comparison, clarity has not been added.

Obviously, the authors do not understand their negligence in the design of articles.

The article can be published in the presented form, then the article would greatly benefit if a comment of at least one phrase was added to each figure separately.

Author Response

Thank you for the advice. All have been supplanted/highlighted in the revised draft.