Response Error Prediction and Feedback Control Method for Electro-Hydraulic Actuators Based on LSTM

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents an innovative approach to controlling electro-hydraulic actuators (EHAs) by integrating an error prediction algorithm based on a Long Short-Term Memory (LSTM) network with a traditional Proportional-Integral-Derivative (PID) controller. The core idea is to predict the future error of the system response using historical data, thereby enabling advanced correction in the PID control loop. The proposed framework involves preprocessing the error signal through frequency filtering using Discrete Fourier Transform (DFT) and Inverse Discrete Fourier Transform (IDFT), extracting key features using a Variational Autoencoder (VAE), and then utilizing an LSTM network to predict future error sequences. This predicted error is then used to modify the derivative term of the PID controller, aiming to improve response time and control smoothness while maintaining accuracy. The authors validate their method through simulations on an AGV steering hydraulic system, demonstrating improvements in overshoot, rise time, and steady-state error under various control instructions compared to traditional PID control.

Based on my review of the paper, I have the following suggestions for the authors to consider for future work or revisions:

• Expand the validation to more complex systems: The current study focuses on a specific AGV steering system with balanced valves. The authors themselves acknowledge the limitation of not exploring valve-controlled nonlinear hydraulic systems. It would significantly strengthen the paper to include validation of the proposed method on more complex and nonlinear hydraulic systems. This could involve simulations or even experimental studies on systems with different characteristics and challenges. Demonstrating the effectiveness of the approach in more diverse scenarios would increase its generalizability and impact.

• Provide a more detailed analysis of practical implementation aspects: While the simulation results are promising, the paper could benefit from a more thorough discussion of the practical challenges associated with implementing this method in real-world applications. Consider addressing aspects such as the computational cost of the LSTM and VAE, the real-time data processing requirements, the sensitivity of the model to noise and disturbances in a physical system, and the need for online adaptation or retraining of the neural network. Discussing these practical considerations would enhance the paper's relevance for researchers and engineers looking to apply this technique.

• Elaborate on the parameter tuning and optimization: The paper identifies the predicted starting parameter 'm' and the predicted step size 'D' as important parameters affecting the control performance. While an objective function for their selection is presented, further discussion on systematic methods for tuning these parameters would be valuable. Consider exploring different optimization algorithms or providing more specific guidelines on how to choose appropriate values for 'm' and 'D' based on the characteristics of the controlled system and the control objectives.

• Compare performance with other advanced control methods: The paper primarily compares the proposed method against traditional PID control. To better position the contribution, it would be beneficial to include a comparison with other advanced control techniques commonly used for EHAs, such as model predictive control (MPC), adaptive control, or sliding mode control. This would help to highlight the specific advantages and potential drawbacks of the proposed LSTM-based error prediction PID approach in relation to the state-of-the-art.

• Offer more insights into the contribution of the VAE and frequency filtering: The paper describes the use of the VAE for feature extraction and DFT/IDFT for frequency filtering. Providing a more in-depth analysis of how these specific components contribute to the improved error prediction accuracy and overall control performance would be valuable. For instance, ablation studies where these components are selectively removed or modified could illustrate their individual and combined impact.

• Clarify the data generation and training process: The simulation model in Simulink was used to generate the data for training the LSTM network. Providing more details about the specific input signals (e.g., amplitude, frequency range), the duration of the simulation runs, and the size and characteristics of the generated dataset would enhance the transparency and reproducibility of the research. Information about the training process of the LSTM and VAE (e.g., network architecture, training algorithm, hyperparameter settings) would also be beneficial.

By addressing these suggestions, the authors can further enhance the rigor, impact, and practical relevance of their research on error prediction and feedback control for electro-hydraulic actuators.

Author Response

Comments 1: Expand the validation to more complex systems: The current study focuses on a specific AGV steering system with balanced valves. The authors themselves acknowledge the limitation of not exploring valve-controlled nonlinear hydraulic systems. It would significantly strengthen the paper to include validation of the proposed method on more complex and nonlinear hydraulic systems. This could involve simulations or even experimental studies on systems with different characteristics and challenges. Demonstrating the effectiveness of the approach in more diverse scenarios would increase its generalizability and impact.

Response 1: Thanks for the suggestions provided by the reviewer. The previous manuscript had a verbal error. This article focuses on an EHA system with dual hydraulic cylinders, which is directly driven by a hydraulic pump. The movement of each hydraulic cylinder is directly determined by the flow rate of the pump. This dual hydraulic cylinder system is equivalent to a balance valve system (but without a real valve). The nonlinear characteristics of the valve control system are highly sensitive to operating conditions. Due to the high degree of coupling between leakage, pressure loss, and load in the valve control system, it is difficult to train a satisfactory neural network using simulation data and must rely on a large amount of real data. If the operating conditions of the test object and the experimental data collected differ too much, the effect cannot be satisfactory. Considering the validation of the proposed method on more complex and nonlinear hydraulic systems, which will greatly enhance the research in this paper, we have added a simulation system containing an overflow valve for comparative testing on the basis of the original experiment. This overflow valve is placed at the outlet of two quantitative pumps and provides the pressure required for hydraulic cylinder movement through the valve. The modified content is from line 495 to line 513.

Comments 2: Provide a more detailed analysis of practical implementation aspects: While the simulation results are promising, the paper could benefit from a more thorough discussion of the practical challenges associated with implementing this method in real-world applications. Consider addressing aspects such as the computational cost of the LSTM and VAE, the real-time data processing requirements, the sensitivity of the model to noise and disturbances in a physical system, and the need for online adaptation or retraining of the neural network. Discussing these practical considerations would enhance the paper's relevance for researchers and engineers looking to apply this technique.

Response 2: Thank you for the suggestion. The proposed method is developed for the port AGV steering system. Figure 1 shows the physical model of the established simulation model. This pump controlled bidirectional hydraulic cylinder controls the swing of the wheels by pushing the AGV steering frame through two piston rods. In order to enhance the relevance of this article to researchers and engineers who wish to apply this technology, we have made minor adjustments to the experimental section and added a section to introduce how to deploy this method on AGV steering systems, including how to address computational costs, real-time performance, noise sensitivity, and neural network retraining. Among them, we have highlighted that the challenges faced in deploying in hydraulic systems mainly come from outdoor computing resources. The modified content is from line 369 to line 392.

Comments 3:  Elaborate on the parameter tuning and optimization: The paper identifies the predicted starting parameter 'm' and the predicted step size 'D' as important parameters affecting the control performance. While an objective function for their selection is presented, further discussion on systematic methods for tuning these parameters would be valuable. Consider exploring different optimization algorithms or providing more specific guidelines on how to choose appropriate values for 'm' and 'D' based on the characteristics of the controlled system and the control objectives.

Response 3: Thank you for the suggestion. The previous manuscript briefly introduced the parameters that need to be optimized and their necessity. Further discussion on the systematic methods for adjusting these parameters would be valuable. As these parameters must run in a neural network model, it is not possible to obtain accurate solutions through dynamic programming and other means. We mainly use relaxation iteration strategy, algorithms, and real-time simulation to continuously try different combinations and finally determine a suitable parameter combination. In the new manuscript, we have improved this section and introduced how to choose the appropriate parameter combination. The modified content is from line 356 to line 367.

Comments 4: Compare performance with other advanced control methods: The paper primarily compares the proposed method against traditional PID control. To better position the contribution, it would be beneficial to include a comparison with other advanced control techniques commonly used for EHAs, such as model predictive control (MPC), adaptive control, or sliding mode control. This would help to highlight the specific advantages and potential drawbacks of the proposed LSTM-based error prediction PID approach in relation to the state-of-the-art.

Response 4: The reviewer's suggestion is constructive, and it is beneficial to compare the proposed method with other advanced control technologies commonly used in EHA. As mentioned earlier, EHA is a pump control system without hydraulic valves, and related methods focus on feedback control of the pump. Traditional methods such as state feedback control, sliding mode control, model predictive control, and adaptive control can directly regulate the motion characteristics of the hydraulic cylinder through the servo control of the pump. We have reproduced some classic methods and the latest developments in the hydraulic field literature and applied them to the designed simulation model for testing. The results show that the proposed method has advantages in improving response speed, but its tracking performance stability in dynamic input is not as good as other methods. In terms of control accuracy, the proposed method is close to the state-of-the-art method and there is no significant difference. The modified content is from line 527 to line 535.

Comments 5: Offer more insights into the contribution of the VAE and frequency filtering: The paper describes the use of the VAE for feature extraction and DFT/IDFT for frequency filtering. Providing a more in-depth analysis of how these specific components contribute to the improved error prediction accuracy and overall control performance would be valuable. For instance, ablation studies where these components are selectively removed or modified could illustrate their individual and combined impact.

Response 5: Thank you for the reviewer's suggestions. This article describes the use of VAE for feature extraction and DFT/IDFT for frequency filtering. A more in-depth analysis of how these specific components improve error prediction accuracy and overall control performance would be valuable. This article is based on LSTM for error prediction and improving the performance of the control loop. VAE is used as the feature extractor of LSTM, and a frequency filter is used to process the sampling noise in the signal. We supplemented a set of ablation experiments to control the effects of VAE module and filter module on prediction and control. We measured the performance of prediction using metrics such as root mean square, median, and variance of prediction error, and tested the time characteristics of the controller using adjustment times corresponding to different error limits. The modified content is from line 544 to line 549.

Comments 6: Clarify the data generation and training process: The simulation model in Simulink was used to generate the data for training the LSTM network. Providing more details about the specific input signals (e.g., amplitude, frequency range), the duration of the simulation runs, and the size and characteristics of the generated dataset would enhance the transparency and reproducibility of the research. Information about the training process of the LSTM and VAE (e.g., network architecture, training algorithm, hyperparameter settings) would also be beneficial.

Response 6: Thank you for the reviewer's suggestions. Clarifying the data generation and training process can help improve the structure and readability of the article. We have added a paragraph at the beginning of the experimental section, including the input signal characteristics used to collect simulation data, simulator parameters, and the dataset used to train the neural network. In addition, we have provided network parameters for testing, including the number of VAE layers, number of neurons, activation function, and LSTM network parameters. As LSTM is encapsulated as a callable standard component of PyTorch, we did not display some trivial parameter details in the manuscript. The modified content is from line 398 to line 416.

Reviewer 2 Report

Comments and Suggestions for Authors

The article titled "Response Error Prediction and Feedback Control Method for Electro-Hydraulic Actuators Based on LSTM" presents a novel approach to improving the control of electro-hydraulic actuators (EHA) using Long Short-Term Memory (LSTM) networks. The authors propose an advanced PID control strategy that incorporates error prediction to enhance the response time and control accuracy of EHA systems. The method involves using LSTM and variational autoencoders to predict error sequences, which are then used to adjust the PID controller's inputs. The study includes comprehensive simulations and experiments, demonstrating significant improvements in system performance, including faster response times and smoother control curves. The authors suggest that their approach could be beneficial for various applications, though they acknowledge the need for further validation in more complex hydraulic systems.

But unfortunately, the work contains a number of shortcomings, for example, in the introduction there was not a sufficiently broad review of the literature (the standard is 40-50 sources) and at the end of the first section there is a complete lack of article structure. Furthermore, in some places the article contains inappropriate formatting, which makes understanding difficult, when images and tables are not inserted under the first occurrence of their mention in the text. Also, mathematical equations lack sufficient description, when not all variables used are described in the text, which can further make understanding difficult. The punctuation used after the equations is also completely missing. Furthermore, some images contain a verbal description, which would be better to insert as normal text with a reference to the image. It is completely inappropriate to use screenshots from Simulink in the examples, it is always better to export data in the form of a vector image and insert it into the work. It would also be appropriate to supplement the table of parameter values ​​with abbreviations or designations of variables that were used in the scheme. Furthermore, the Future works chapter is completely missing and the list of abbreviations also does not contain all abbreviations used.

Overall, this is a scientifically interesting work, and therefore I rate it as Reconsider after major revisions. I recommend that the authors make the following changes:

1) Add keywords (the default is up to 10 keywords). And sort them alphabetically.

2) A space is usually placed before the quotation. So, not "...unfolding[1]." but write it as "...unfolding [1]." This applies everywhere in the text.

3) The article structure is completely missing at the end of Section 1. Please add it.

4) Conduct a broader literature review. The standard for a scientific journal is 40-50 sources.

5) There should always be at least a short introductory text between each chapter. For example, Sections 2 and 2.1 should be separated by text. This also applies to other sections of the article (2.2 and 2.2.1, 3 and 3.1.

6) Figures should not follow immediately after the chapter title (Figure 1).

7) Figure 1 is not described in the text and there is no reference to it in the text.

8) If I refer to figure 1 or equation 5 in the text, they should be written in capital letters. That is, write them as Figure 1, Equation 5, and so on.

9) A detailed description of all variables and parameters used in the equations should be described in detail in the text. This was missing in many places in the work, so I ask the authors to add it to make it clearer and more understandable.

10) Reformat the entire work so that tables and figures are displayed immediately after the reference in the text and not later in the text. This will contribute to better clarity.

11) All equations are missing punctuation. If they are preceded by a colon (:) and the sentence does not continue after the equation, they should be ended with a period (.). If the sentence continues after them, then with a comma (,). This applies to all equations.

12) Some images contain text that I would move as normal text with a link to the image and remove from the image (Figure 2, 3).

13) Figure 3 is missing a reference in the text.

14) On line 212 there is a space after z and then a period (" z ."). I would delete the space and the following Then: as well.

15) On line 221 there is a ,. after it, but I don't understand why? Also, the following word For doesn't have a space before it.

16) Equation (24) could be aligned according to =.

15) Points (a)Error signal generation, (b)Feedback mechanism and (c)Adaptive strategy could be in bold.

16) Sentences should not start with the mathematical expression "𝑚𝑚𝑖𝑛..." but rather "Variable 𝑚𝑚𝑖𝑛..." and the like. For example, line 300.

17) Add the table of parameters in Section 3 and the abbreviations to make it clear which blocks in Figure 6 they refer to.

18) Some blocks in Figure 6 are too small to display the variable name (K). I would like to ask the authors to enlarge them.

19) Figure 7 is completely inappropriate for a scientific text. I ask the authors to export the data and plot it in vector format in Matlab.

20) Figure 8 and 10 should also be in the vector format (for example, .eps).

21) It would be appropriate to supplement Table 2 with graphs to better support the results or at least describe it in more detail in the text.

22) Chapter headings should not be alone at the bottom of the page, for example, Subsection 3.5.

23) Add a Future works section where authors would outline further possible improvements to their work.

24) The table of abbreviations is not complete and could be sorted alphabetically.

Author Response

Thanks to the reviewer for carefully reviewing this work and pointing out many important issues. I have noticed that these issues mainly concern the formatting and content organization of the article. We are confident that handling these issues correctly can greatly improve the readability of the article. We have responded to each issue in the following reply, including modification measures and corresponding positions in the article. As most of the opinions involve issues scattered in different locations, we have marked them in red in the uploaded manuscript file. After reviewing, we are confident that we have rectified the issues you pointed out one by one. We hope that the new manuscript meets your requirements, and thank you again for your valuable time invested in this work. Due to the numerous revisions pointed out by the reviewer, the following response will be as concise as possible.

Comments 1: Add keywords (the default is up to 10 keywords). And sort them alphabetically.

Response 1: We have added more keywords in the new manuscript and arranged them in order. The revised content is on line 21.

Comments 2: A space is usually placed before the quotation. So, not "...unfolding[1]." but write it as "...unfolding [1]." This applies everywhere in the text.

Response 2: Thank you for pointing out this issue. The new manuscript includes a total of 43 references, and we have checked the spaces in each citation to ensure that the citation symbol no longer follows the character. The modified content is mainly distributed between lines 24 to 97.

Comments 3: The article structure is completely missing at the end of Section 1. Please add it.

Response 3: We added a section after the contribution, indicating the overall structure of the article, including the main content of each chapter, to ensure that readers can quickly locate the points of interest. The modified content is between lines 117 and 120.

Comments 4: Conduct a broader literature review. The standard for a scientific journal is 40-50 sources.

Response 4: Thank you for pointing out this issue. We have provided more detailed references to comprehensively display the sources of information corresponding to the early research conclusions in the introduction section. The modifications are mainly located from lines 24 to 97.

Comments 5: There should always be at least a short introductory text between each chapter. For example, Sections 2 and 2.1 should be separated by text. This also applies to other sections of the article (2.2 and 2.2.1, 3 and 3.1.

Response 5: This is a fundamental issue, and we have made revisions to the article by adding text before sections 2.1, 2.2.1, and 3.1 to introduce the content of this section and necessary experimental background. The revised content begins on lines 122, 221, and 370, respectively.

Comments 6: Figures should not follow immediately after the chapter title (Figure 1).

Response 6: We have adjusted the position of the images to ensure that they do not directly follow the chapter titles. The modified Figure 1 is on line 154.

Comments 7: Figure 1 is not described in the text and there is no reference to it in the text.

Response 8: Thank you very much for pointing out this major fundamental issue. The previous manuscript lacked the text content of Figure 1. We have added this paragraph before Figure 1, introducing the principle of AGV steering hydraulic system, the characteristics and advantages of EHA. The revised content is from line 144 to line 154.

Comments 8: If I refer to figure 1 or equation 5 in the text, they should be written in capital letters. That is, write them as Figure 1, Equation 5, and so on.

Response 8: According to your request, we have capitalized all references to figures, tables, and equations throughout the text. As the relevant content involves various parts of the entire text, including 31 equations, 13 figures, and 6 tables, the column and row positions will not be listed here. You can directly view them in the manuscript.

Comments 9: A detailed description of all variables and parameters used in the equations should be described in detail in the text. This was missing in many places in the work, so I ask the authors to add it to make it clearer and more understandable.

Response 9: We checked a total of 31 equations involved in the article and placed explanations for all variables and parameters at the end of each equation to make them clearer. The relevant modifications are located between lines 158 and 362.

Comments 10:  Reformat the entire work so that tables and figures are displayed immediately after the reference in the text and not later in the text. This will contribute to better clarity.

Response 10: We have reformatted the article structure, and all figures and tables will immediately appear after the cited paragraphs to ensure that readers can quickly see the objects referred to in the text. Due to the scattered position of the chart, the relevant line numbers are not specifically displayed here

Comments 11: All equations are missing punctuation. If they are preceded by a colon (:) and the sentence does not continue after the equation, they should be ended with a period (.). If the sentence continues after them, then with a comma (,). This applies to all equations.

Response 11: I understand what you mean. All equations have been revised according to this format and ended with a period (.) uniformly. The relevant content is located between lines 158 and 362.

Comments 12: Some images contain text that I would move as normal text with a link to the image and remove from the image (Figure 2, 3).

Response 12: Figures 2 and 3 have been modified according to your requirements. The descriptive text in the figures is mainly used to introduce the meanings of the relevant parameters. However, according to the modification suggestion (9), we have uniformly introduced all parameters after the equation, so these texts are not included in the new figures. The relevant content is located on lines 204 and 311.

Comments 13: Figure 3 is missing a reference in the text.

Response 13: We have added a paragraph at the beginning of this figure to introduce the control strategy of the electro-hydraulic actuator, including how to select state feedback variables and the collaborative working mode of error prediction model and PID. The relevant content is located on line 213.

Comments 14: On line 212 there is a space after z and then a period (" z ."). I would delete the space and the following Then: as well.

Response 14: We have checked the text and identified the issue you pointed out. The new manuscript has removed the extra 'then:', which is now at line 259.

Comments 15: On line 221 there is a ,. after it, but I don't understand why? Also, the following word For doesn't have a space before it.

Response 15: I have identified the issue you pointed out. Originally, it was'... ', but now I have deleted'... 'and added a space before' For '. The relevant content is now located on line 263.

Comments 16: Equation (24) could be aligned according to =.

Response 16: The new manuscript has adjusted equation (24) to align according to=, and the relevant content is on line 324.

Comments 17: Points (a)Error signal generation, (b)Feedback mechanism and (c)Adaptive strategy could be in bold.

Response 17: The three subheadings are now highlighted in bold, allowing readers to find the corresponding content more clearly. The relevant content is located on lines 321, 325, and 333.

Comments 18: Sentences should not start with the mathematical expression "????..." but rather "Variable ????..." and the like. For example, line 300.

Response 18: There are two types of variables in the text, one is physical variables used to describe the physical information of hydraulic systems, and the other is mathematical variables used to describe the input and output of mathematical operations in neural network design. We prefix all variables to ensure that they no longer appear separately. The relevant content is very scattered, and we cannot display all the line numbers here.

Comments 19: Add the table of parameters in Section 3 and the abbreviations to make it clear which blocks in Figure 6 they refer to.

Response 19: The previous Figure 6 is now Figure 8. We have expanded Table 1 by comparing the abbreviations and physical meanings in each block in Figure 8, ensuring that the information in Figure 8 is clear. The relevant content is located on line 429.

Comments 20: Some blocks in Figure 6 are too small to display the variable name (K). I would like to ask the authors to enlarge them.

Response 20: Figure 6 is now Figure 8. As it is a system diagram exported from MATLAB, the font inside cannot be enlarged. We can only enlarge the entire image and use software to further enhance its clarity. The relevant content is located on line 423.

Comments 21: Figure 7 is completely inappropriate for a scientific text. I ask the authors to export the data and plot it in vector format in Matlab.

Response 21: The previous Figure 7 is now Figure 9. We exported the data from Matlab and plotted it in vector format using SVG. After converting it to PDF, the clarity will not decrease. The relevant content is located on line 440.

Comments 22: Figure 8 and 10 should also be in the vector format (for example, .eps).

Response 22: The previous Figures 8 and 10 are now Figures 10 and 12, which have been re exported in SVG format and ensure high clarity in PDF. The relevant content is located on lines 474 and 491.

Comments 23: It would be appropriate to supplement Table 2 with graphs to better support the results or at least describe it in more detail in the text.

Response 23: The introduction to Table 2 in the previous manuscript was mainly placed in the annotations marked with an asterisk below Table 2. Now we have placed them in the main text and added more details to describe it. The relevant content is located from line 458 to line 465.

Comments 24: Chapter headings should not be alone at the bottom of the page, for example, Subsection 3.5.

Response 24: We conducted a comprehensive review of the new manuscript by adjusting the image size and paragraph order to avoid titles appearing separately at the bottom of the page.

Comments 25: Add a Future works section where authors would outline further possible improvements to their work.

Response 25: We have added a section titled 'Future Work' in the conclusion section specifically to introduce further possible improvements, which can be found on lines 588 to 591.

Comments 26: The table of abbreviations is not complete and could be sorted alphabetically.

Response 26: We have arranged all the abbreviations mentioned in the article in alphabetical order in the abbreviation table at the end of the article. Now readers can directly search for the meaning of each abbreviation based on this list, which is located on page 19.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors provided a revised version of the manuscript, incorporating and correcting most of my comments. I would like to thank the authors for their work. In some places, it would be appropriate to describe some mathematical equations and procedures in more detail, but otherwise I have no further comments.