Dynamic High-Type Interval Type-2 Fuzzy Logic Control for Photoelectric Tracking System

Round 1

Reviewer 1 Report

In my opinion this paper should be accepted with minor revision.

The authors should consider the following comments:

The main contribution should be extended and explained with more detail in the introduction section.

The future works and conclusions should be extended

More references should be include in the state of the art. I suggest at least 40 references.

Author Response

Dear reviewer,

Thank you for taking time out of your busy schedule to review my paper and provide comments and suggestions. In response to your question, I have made the following changes to the paper:

Point 1: The main contribution should be extended and explained with more detail in the introduction section.

Response 1：The following changes have been made in the conclusion section:

Fuzzy logic control (FLC) can dynamically change the output value according to the input change, and has the advantages of fast response speed and strong ability to handle uncertainties.Therefore, in this paper, the FLC is introduced into the high-type control system, and the output of the FLC is used as the gain of the integrator to control the on-off to achieve the goal of dynamic switching type, which is successfully verified in the experiment. .IT2FLC introduces a three-dimensional membership function, which further improves the FLC's ability to handle uncertainties. From the experimental results, compared with T1FLC, IT2FLC's ability to handle uncertainties is signifi-cantly improved. In addition, in order to speed up the calculation speed of IT2FLC, this paper proposes an improved type reduction algorithm, which is called weighted-trapezoidal Nie-Tan(WTNT). Compared with the traditional type reduction algorithm, WTNT has faster cal-culation speed and better steady-state accuracy, and has been successfully applied to real-time control systems, which has good engineering application value.Finally, in order to reduce the in-terference of human factors and improve the automation level of the system, multi-population genetic algorithm(MPGA) is used to iteratively optimize the parameters of the FLC, which im-proves the output accuracy.

 

Point 2: The future works and conclusions should be extended.

Response 2：The following changes have been made in the conclusion section:

Adding an integrator to a traditional closed-loop control system can effectively improve the steady-state accuracy of the system. However, the increase of integrators will aggravate the oscillation of the system. In order to avoid system divergence, a dynamic adjustment mechanism is introduced to change the number of integrators with the state of the system, that is, the type of the system. From the experimental re-sults, the dynamic high-type controller can effectively improve the steady-state accu-racy of the system while avoiding the system oscillation.

Compared with traditional position controllers, fuzzy logic controller shows great advantages in handling uncertainties, which benefits from the inherent characteristics of FLC. In this paper, a FLC is introduced as the on-off switch of the integrator, and also control the gain of the integrator. By reasonably designing the fuzzy rule base and membership function, the FLC can adjust the on-off and gain of the integrator in real time according to the system state, which effectively improves the system's response speed, steady-state accuracy and ability to handle uncertainties.

IT2FLC introduces a three-dimensional membership function, which further im-proves the fuzzy controller's ability to handle uncertainties. From the experimental results, compared with T1FLC, IT2FLC's ability to handle uncertainties is significantly improved. In addition, in order to speed up the calculation speed of IT2FLC, the WTNT type reduction algorithm constructed in this paper has faster calculation speed and better steady-state accuracy than the traditional TR algorithm, and has been success-fully applied to real-time control systems, with good engineering application value.

Future work will continue on the combination of FLC and DHTC. DHTC is a rel-atively new field. The current mainstream control structure type does not exceed type-3, and the combination of FLC and DHTC does not exceed type-2. If the type can be broken to a higher level, the steady-state accuracy of the system can undoubtedly be further improved, which has important research significance in the engineering field that requires high precision. In addition, the research of the type-2 FLC is also in the preliminary stage, the application field is almost blank, and there are many worthy research areas waiting for us to explore. I believe that in the near future, fuzzy control and high-type control can shine in the field of control, let us wait and see.

 

Point 3: More references should be include in the state of the art. I suggest at least 40 references.

Response 3：Already revised. Expand the number of references to 40.

 

 

Reviewer 2 Report

The article under review is devoted to the study of the dynamic high-type control method proposed by the author for tracking systems.

The article describes the structure diagram and algorithm of the dynamic high-type control, its design. Experimental verification of the proposed system was carried out on a specially created experimental platform.

In general, this is an interesting work that deals with the actual problem of creating tracking systems that implement an interval type-2 fuzzy logic controller. The results of the presented studies may be useful to specialists in the field of automated control systems.

As a whole, the paper can be accepted as it is. However, I would like to ask the authors for a few clarifications:

1. Why are disturbances not indicated in Figure 1 and Figure 2?
2. Why in the proposed dynamic high-type control system, exactly 2 integrators are connected in parallel in the forward path not their other number?
3. What software was used for the research?
4. How were the characteristics in Figure 11 obtained?
5. Why didn't the authors research their ideas using mathematical modeling methods?

Author Response

Dear reviewer,

Thank you for taking time out of your busy schedule to review my paper and provide comments and suggestions. In response to your question, I have made the following changes to the paper:

 

Point 1:Why are disturbances not indicated in Figure 1 and Figure 2?

Response 1:There are high-type disturbance variables in the actual system, which are incorporated into Gv in the analysis process; because the disturbance quantity coefficient is very small, it is omitted from the figure to facilitate subsequent mathematical analysis. It can be seen in the experiment that the interference mostly exists in the form of white noise, which has no significant effect on the experimental results.

 

Point 2: Why in the proposed dynamic high-type control system, exactly 2 integrators are connected in parallel in the forward path not their other number?

Response 2: In [11], the author proposes a PID-III type controller with three integrators in an open loop, similar to the model constructed in this paper. The greater the number of integrators, the exponential increase in control difficulty, which is described in the literature [11], and the same is true from the point of view of simulation and experimental results. Two integrators are used in this paper, and it can be concluded from the experimental verification results that the steady-state accuracy of the system is better than that of one integrator and more stable than three integrators. In fact, the focus of my future work is to increase the integrator to achieve higher-type control. But at the present stage, only two integrators can be connected in parallel for stable control.

 

Point 3: What software was used for the research?

Response 3：The softwares used in this experiment are as follows:

Use Matlab for simulation verification in the early design stage;

The code implementation phase is written in C language;

The embedded operating system is Vxworks of Wind River System (WRS);

The interface operation software is self-developed by the experimental team;

In addition, it is also applied to ANSYS Workbench software for debugging.

 

Point 4: How were the characteristics in Figure 11 obtained?

Response 4：On the experimental platform in Figure 10, the frequency sweep experiment is performed from 0 to 100 Hz to obtain the amplitude of the corresponding frequency, and data integration is performed with matlab to obtain the original object curve of the blue line in Figure 11; the identification method in the automatic control principle is applied. By analyzing the curve shape of the original object, we know that the object contains two second order oscillation elements (SOOE), a second order differentiation element (SODE), and a large pole inertial element (first order inertial element, FOIE) and a delay element (DE); the coefficients of each link are obtained through empirical analysis and experiments, so that the error between the identified object and the original object is kept within 2%, which meets the experimental requirements.

 

Point 5: Why didn't the authors research their ideas using mathematical modeling methods?

Response 5：According to the opinion of the instructor Tao Zhao (E-mail:zhaotaozhaogang@126.com), the type of fuzzy controller used in this paper has no mathematical modeling in the academic world, so mathematical analysis cannot be carried out.

 

 

 

Reviewer 3 Report

This paper proposes a dynamic high-type control (DHTC) method based on an interval 10 type-2 fuzzy logic controller (IT2-FLC), which is used in the photoelectric tracking system. 

The general idea of the paper seems to be good. However, the paper organization is not acceptable and there are several major technical challenges that should be effectively addressed.

Comments:

• There are some grammatical errors and typos that should be corrected before publication.
• It is recommended to provide a nomenclature at the beginning of the paper to define all variables clearly.

• The general idea of the paper seems to be good. However, the paper organization is not acceptable and there are several major technical challenges that should be effectively addressed.

• In paragraf 2.1. DHTC is mentioned on Fig, 1 Gv and Cv in accordance to expression (1). But in (1) there is no clear place for Cv.
• According to Figure 5 there are both T1FLC and IT2FLC involved in Cp. Why are T1FLC and IT2FLC involved in Cp as controllers? Shouldn't there be much less computational burden if there is only IT2FLC or T1 FLC and new jitter will be avoided. 
•   There is no explanation what UMF, LMF, SGA  etc. are abbreviations of.
• How is number N of MPGA defined?
• Is it related to any outside factor as number of iterations of closed loop or scale of input in IT2FLC MF?
• According to Figure 9 only Population 1 and Population N are judging Elite Population. why is Population 1 involved in Elite population? Shouldn't there be only the last population selected as Elite?
•   Please explain how are MFs of IT2FLC chosen?
• Please explain better in Conclusion why Type-2 Fuzzy Logic Controler is better then others.

Author Response

Dear reviewer,

Thank you for taking time out of your busy schedule to review my paper and provide comments and suggestions. In response to your question, I have made the following changes to the paper:

Point 1: In paragraf 2.1. DHTC is mentioned on Fig, 1 Gv and Cv in accordance to expression (1). But in (1) there is no clear place for Cv.

Response 1:

Cv has been incorporated into G(s). In order to simplify the expression, the calculation process of the closed-loop function is omitted, and the final expression of G(s) is directly obtained.

 

Point 2: According to Figure 5 there are both T1FLC and IT2FLC involved in Cp. Why are T1FLC and IT2FLC involved in Cp as controllers? Shouldn't there be much less computational burden if there is only IT2FLC or T1 FLC and new jitter will be avoided. 

Response 2: The control of the Cp position in Fig. 5 is divided into two types, T1-FLC "OR" IT2-FLC, also to simplify the space, the two cases are combined into one diagram. In the experiment, T1-FLC and IT2-FLC were used for comparison. It can be clearly seen from chapters 4.2 and 4.3 that IT2-FLC is better than T1-FLC in terms of accuracy, response speed and ability to handle uncertainties.

 

Point 3: There is no explanation what UMF, LMF, SGA  etc. are abbreviations of.

Response 3：

UMF:Uper membership function

LMF:Lower membership function

SGA:Standard Genetic Algorithm

The above abbreviations have been marked in the corresponding parts of the paper.

 

Point 4: How is number N of MPGA defined?

Response 4:

The number N represents the population number of MPGA.MPGA breaks through the framework of SGA that only relies on a single population for genetic evolution, introducing multiple populations for simultaneous optimization searches.

The calculation speed and accuracy of MPGA are related to N. Based on experience and experimental comparison, in this paper, N=10.

 

Point 5: Is it related to any outside factor as number of iterations of closed loop or scale of input in IT2FLC MF?

Response 5:

Yes, from the experimental comparison, under different number of iterations of closed loop or scale of input in IT2FLC MF, to achieve the best control effect, the value of N is not the same. However, the purpose of this experiment is to explore the possibility of combining DHTC and FLC. The introduction of MPGA is to further improve the accuracy of the controller. Therefore, the structures of DHTC and FLC are first designed, and then the value of N is determined.

 

Point 6: According to Figure 9 only Population 1 and Population N are judging Elite Population. why is Population 1 involved in Elite population? Shouldn't there be only the last population selected as Elite?

Response 6：

Thanks for the reminder, it was my oversight! My drawing was wrong. The correct drawing method is as follows, and has been corrected in the paper.

The elite population is generated as follows:

Each population is connected through the immigration operator, whose function is to replace the optimal value of the former group with the worst quality one of the latter group, so as to realize the co-evolution of multiple populations. The acquisition of the optimal solution is the comprehensive result of the co-evolution of multiple populations.

The optimal individuals in each evolutionary generation of various groups are saved by artificial selection operators, and they form the elite population. The elite population is very different from other populations. It does not carry out genetic operations such as selection, crossover, and mutation, so as to ensure that the optimal individuals produced by various groups in the evolutionary process will not be destroyed and lost. At the same time, the elite population is also the basis for judging the termination of the algorithm. Here, the optimal individual minimum retention algebra is used as the termination criterion. This criterion makes full use of the knowledge accumulation of genetic algorithm in the evolution process, and is more reasonable than the maximum genetic algebra criterion.

Therefore, each population will produce an elite individual to form an elite population.

 

Point 7: Please explain how are MFs of IT2FLC chosen?

Response 7：

The more linguistic variables of MF, the higher the calculation accuracy, but the slower the calculation speed. In order to balance calculation speed and precision, the number of MF linguistic variables of IT2-FLC involved in this paper is 3.

The three variable ranges of the systematic error e are taken as (-25, 25). This range is based on the previous experimental results and the design rules in Figure 7. Experiments in the system with only the position controller Cp show that the maximum absolute value of the error during the step oscillation process does not exceed 25; according to the design rules in Figure 7, when the system is in states 1 and 3, the system is required to approach the equilibrium state as soon as possible , at this time, it is required that MF must have a large enough value to ensure the correction speed, so the absolute value with the largest error (-25, 25) is selected as the interval of MF. At the same time, this interval can ensure that the MF will not be too large to cause the system to diverge.

Similarly, the value of the systematic error Δe also follows this principle, and the value interval of MF is (-1.25, 1.25)

 

Point 8: Please explain better in Conclusion why Type-2 Fuzzy Logic Controler is better then others.

Response 8：

The following changes have been made in the conclusion section:

Adding an integrator to a traditional closed-loop control system can effectively improve the steady-state accuracy of the system. However, the increase of integrators will aggravate the oscillation of the system. In order to avoid system divergence, a dynamic adjustment mechanism is introduced to change the number of integrators with the state of the system, that is, the type of the system. From the experimental re-sults, the dynamic high-type controller can effectively improve the steady-state accu-racy of the system while avoiding the system oscillation.

Compared with traditional position controllers, fuzzy logic controller shows great advantages in handling uncertainties, which benefits from the inherent characteristics of FLC. In this paper, a FLC is introduced as the on-off switch of the integrator, and also control the gain of the integrator. By reasonably designing the fuzzy rule base and membership function, the FLC can adjust the on-off and gain of the integrator in real time according to the system state, which effectively improves the system's response speed, steady-state accuracy and ability to handle uncertainties.

IT2FLC introduces a three-dimensional membership function, which further im-proves the fuzzy controller's ability to handle uncertainties. From the experimental results, compared with T1FLC, IT2FLC's ability to handle uncertainties is significantly improved. In addition, in order to speed up the calculation speed of IT2FLC, the WTNT type reduction algorithm constructed in this paper has faster calculation speed and better steady-state accuracy than the traditional TR algorithm, and has been success-fully applied to real-time control systems, with good engineering application value.

Future work will continue on the combination of FLC and DHTC. DHTC is a rel-atively new field. The current mainstream control structure type does not exceed type-3, and the combination of FLC and DHTC does not exceed type-2. If the type can be broken to a higher level, the steady-state accuracy of the system can undoubtedly be further improved, which has important research significance in the engineering field that requires high precision. In addition, the research of the type-2 FLC is also in the preliminary stage, the application field is almost blank, and there are many worthy research areas waiting for us to explore. I believe that in the near future, fuzzy control and high-type control can shine in the field of control, let us wait and see.

 

Round 2

Reviewer 3 Report

Authors answer and include all my comments in the revised version of the paper. 

I recommend that authors add the list of abbreviations at the end of the paper not in the text.