Ship Steering Adaptive CGS Control Based on EKF Identification Method

Round 1

Reviewer 1 Report

Dear Authors

• In line 44, write closed-loop gain shaping (CGS),
• In line 51, write A proportional-integral-derivative controller (PID),
• In line 90, write The CGS,
• Check and rewrite the sentences in lines 90-92 ( incorrectly used 'and'),
• Check and revise Eq. 2 with line 118 (in Eq. 2 , b₁ and b₂ while in line 118 , b₁₁ and b_21,
• Explain why you estimated the values given in lines 122-123,
• Check the transfer function in Eq. 4 ( the correct is R(s) when you take Laplace transform of Eq. 3 ) 
•  In line 127, the correct is ' the transfer function 4' ,
• Check the symbols in Equations 4,6,7 depending on the symbols 'r' in Eq. 3 ,
• In line 143, the variable 'u' in not exist in Figure 3,
• Check Equation 8, why you write, y(s) ⁄r(s) ?,
• In line 213, what is the suitable selected for P(0)?,
• In line 243, check the sentence ' inequality (33)' ( Eq. 33 is not inequality),
• The EKF in general is not an optimal if the initial estimate is wrong. can you use another way of improving EKF ?. For example the iterated extended Kalman filter.
• The cited references must be mostly within the last 5 years.

Author Response

Response to Reviewer 1 Comments

 

Point 1:

In line 44, write closed-loop gain shaping (CGS),

Response 1:

In oder to improve the conherence of the paragraph, the original sentense “In this paper, a ship steering adaptive CGS controller is proposed to address the ship steering control problem based on the MASS planning and control concept.” had been deleted. The new sentense is “Especially, the MASS steering operation to maintain or change ship course is the key function of MC module. Hence ship steering controller design is one of the most important tasks of ship motion control.”(in line 43-45)

The first time of abbreviation “CGS” is appeared in the paper in line 99 and had been written “closed-loop gain shaping (CGS) controller”.

 

Point 2:

In line 51, write A proportional-integral-derivative controller (PID),

Response 2:

The abbreviation “PID” had given the full name “proportional-integral-derivative controller” as shown in line 49.

 

Point 3:

In line 90, write The CGS,

Response 3:

The same as the Response 1, the first time to use “CGS” (in line 99) had written “closed-loop gain shaping (CGS) controller”. Other terms of “closed-loop gain shaping” of the paper had been replaced with the abbreviation “CGS”.

 

Point 4:

Check and rewrite the sentences in lines 90-92 ( incorrectly used 'and'),

Response 4:

To indicate my contribution of the paper clearly, this sentences had been replaced with “Consequently, the proposed ship steering adaptive CGS controller would have a concise structure, the definite physical meaning of tuning parameters, and better dynamic response performance of the ship course-keeping and course-changing.” (in line 108-111)

 

Point 5:

Check and revise Eq. 2 with line 118 (in Eq. 2 , b1 and b2 while in line 118 , b11 and b21,

Response 3:

Thank you for the reviewer’s suggestion, the varibles b11 and b21 had beed replaced with the b₁ and b₂ (in line 126)

 

Point 6:

Explain why you estimated the values given in lines 122-123,

Response 6:

This part is typical estimation process to achieve the second-order linear Nomoto model. The details can be referred to the reference [22] (Perera, L. P.;  Oliveira, P.; Guedes Soares, C., System Identification of Nonlinear Vessel Steering. J. Offshore Mech. Arct. Eng., 2015, 137 (3)), the values of the equaiton T₁, T₂, T₃ and K_R could be estimated by the following equations. , ,, .

Hence to faciliate the reader to get the details from the reference [22], this sentense had been replaced with “According to the reference [22], their values could be estimated by , ,, .” (in line 129-131)

 

Point 7:

Check the transfer function in Eq. 4 ( the correct is R(s) when you take Laplace transform of Eq. 3 )

Response 7:

The equation (4) is the transfer function to describe the relationship between ship steering rudder to yaw motion, and is known as “control plant”. Hence the use of “G(s)” is more approriate. Such as the reference [14] (Zhang, X. K.; Yang, G. P.; Zhang, Q.; Zhang, G. Q.; Zhang, Y. Q., Improved Concise Backstepping Control of Course Keeping for Ships Using Nonlinear Feedback Technique. J. Navig., 2017, 70 (6), 1401-1414.) and [15]. (Zhang, X. K.; Han, X.; Guan, W.; Zhang, G. Q., Improvement of Integrator Backstepping Control for Ships with Concise Robust Control and Nonlinear Decoration. Ocean Eng., 2019, 189, 106349.1-106349.7.)

 

Point 8:

In line 127, the correct is ' the transfer function 4'

Response 8:

Thank you for the reviewer’s suggestion, the “the transfer function (3)'” had been replaced with “the transfer function (4)'” (in line 135)

 

Point 9:

Check the symbols in Equations 4,6,7 depending on the symbols 'r' in Eq. 3 ,

Response 9:

 is yaw angle (in line 121), and  is the yaw angular velocity (in line 124). Hence the relationship  is established. Hence the symbol  in euqation 3 and  in equation 4, 6, 7 have no problem.

 

 

 

Point 10:

In line 143, the variable 'u' in not exist in Figure 3,

Response 10:

Considering a typical structure of the ship steering control system as shown in figure 3, u could be defined as the ship steering rudder angle . Hence the figure 3 had been changed as . Also the meaning of the varible u had been described in line 149.

 

Point 11:

Check Equation 8, why you write, y(s) ⁄r(s) ?,

Response 11:

 

Thank you for the reviewer’s suggestion, the euqation (8) had been corrected as , since the purpose of the steering controller design is to make the output yaw angle  track the input demand course signal . Also the corrsponding change of figure 3 had been carried out. (described in line 151-152)

 

Point 12:

In line 213, what is the suitable selected for P(0)?

Response 12:

Since the initial value of estimated state  and error covariance matrix  have significant influence to the proposed adapitve CGS controler performance. Hence appropriate setting of the  and  values should be given enough attention.

In the paper, the remark 1 (in line 212-214) is used to rise the reader to pay more attention to this problem.

 

Point 13:

In line 243, check the sentence ' inequality (33)' ( Eq. 33 is not inequality),

Response 13:

 

Thank you for the reviewer’s suggestion, the sentence had been replaced with “Hence, while , we can achieve   (33)” (in line 253).

 

Point 14:

The EKF in general is not an optimal if the initial estimate is wrong. can you use another way of improving EKF ?. For example the iterated extended Kalman filter.

Response 14:

Thank you for the reviewer’s good question. A comprehensive researches on paramter identification technique had been carried by my team, and the EKF identification method is the finial selection for the adaptive CGS controller design. The reasons are as follows:

To enhance the adaptivity and improve the dynamic response performance of the CGS controller, the EKF, IEKF, UKF (Unscented Kalman Filter), PF (particle filter) and RLS (recursive least-squares method) were all optional solutions to solve this problem.

(1) RLS is the first selection as the identification method. Howerver, the peformance of RLS identification method is very sensitive to the prior data bank. Furthermore, the RLS identification method might be suitable for the time-invaried system, but be helpless for the time-varing system. Hence, the RLS is not suitable for the adaptive CGS controller design.

(2) In my oppion, the EKF method uses Jacobi matrices to carry out the linearization of the system by first-order Taylor series expansion and neglecting of the truncated high order terms to obtain a locally linearized Kalman filter. However, due to there exit the defects of hard to get the Jacobi matrices of the system (especially for the system has strong nonlinear and non-differential term), and the linearization error of the EKF method can not be ignored. The IEKF and UKF, which are both the improved EKF identification method, are proposed to solve these problems.

1. IEKF: To reduce the linearized error introduced by a inaccurate linearization reference point, the IEKF relinearizes the system equations around the one-step measurement state estimation, and iteratively utilizes the measurement state updates through more iterative steps. Hence the IEKF can effectively reduce the locally linearization error by linearizing the measurement states around one precise point. (In fact, the measurement update of the IEKF is a Gauss-Newton method for approximating a maximum a posteriori estimator.) However, to reduce the locally linearization error of the system, the IEKF is required to employ more times of iterative operation at only small size of states space points. Hence a augmented computation burden would be not avoided in these states space points. Otherwise, if the only one iterative step of the state points is set, the estimation results is similar with the EKF method.
2. UKF: In the EKF, the state distribution is approximated by a Gaussian random variable, which is propagated through the first-order linearization of the nonlinear system. This might introduce large errors in the true posterior mean and covariance of the transformed Gaussian random variables, which may lead to sub-optimal performance and sometimes divergence in paramters identification of the strong nonlinear system. The UKF addresses this problem by using a deterministic weighted sigma sampling point approach. These sigma sample points completely capture the true mean and covariance of the variables. Hence, when facing with the true strong nonlinear system, captures the posterior mean and covariance accurately to the 3rd order Taylor series expansion. In contrast, the EKF migh only achieve first-order Taylor expansion accuracy. However, the the computational burden of the UKF might be heavier due to the more iterative operations in each sigma point sampling point.
3. Similar with the IEKF and UKF, PF is also used to deal with the strong nonlinear system with on-differential terms. The PF addresses large lineariation errors problem by using sequential Monte Carlo sampling method in which the sample point is a set of weighted particles in the state space. That means, the PF identification method might lead to large computational burden and poor real-time parameter identification performance due to more and more iterative operations in each iterative esimation steps.

(3) The weak nonlinearity characteristics of the ship steering control system is one of the most important reason why we taken EKF as the on-line paramter identification technique in the proposed adaptive CGS controller design. The analytical soluton of Jacobi matrices could be obtained easily in the nonlinear ships steering controller design. Hence the use IEKF, UKF and PF in ship steering control is unnecessary. (IEKF, UKF and PF are all considered as the soluton of the strong nonlinear system with non-differential terms)

Furthermore, since the dynamic response performance of the adaptive CGS controller is the primary demand, the complexity and compution burden would have highest priority to be considered. Generally the high-accuracy means more iterative operations and heavier computation burden.

Finally, EKF estimation method is taken as on-line paramter primary demand identification technique of the proposed adaptive CGS controller.

 

Point 15:

The cited references must be mostly within the last 5 years.

Response 3:

Thank you for the reviewer’s suggestion, a more comprehensive and introduction had been rewritten, and the latest literatures had been enrished. The latest literatures within the last 5 years had also been overlook in the “introduction”. Such as

[1] Felski, A.; Zwolak, K., The Ocean-Going Autonomous Ship—Challenges and Threats. J. Mar. Sci. Eng., 2020, 8 (1), 41.

[3] Wang, L.; Wu, Q.; Liu, J.; Li, S.; Negenborn, R., State-of-the-Art Research on Motion Control of Maritime Autonomous Surface Ships. J. Mar. Sci. Eng., 2019, 7 (12) :438.

[7] Zhang, H.; Zhang, X.; Bu, R., Active Disturbance Rejection Control of Ship Course Keeping Based on Nonlinear Feedback and ZOH Component. Ocean Eng., 2021, 233, 109136.

[9] Dong, Y.; Wu, N.; Qi, J.; Chen, X.; Hua, C., Predictive Course Control and Guidance of Autonomous Unmanned Sailboat Based on Efficient Sampled Gaussian Process. J. Mar. Sci. Eng., 2021, 9 (12), 1420.

[20] Qin, H.;  Tan, P.;  Chen, Z.;  Sun, M.; Sun, Q., Deep Reinforcement Learning Based Active Disturbance Rejection Control for Ship Course Control. Neurocomputing, 2021. Available on line: https://doi.org/10.1016/j.neucom.2021.06.096.

[24] Raman-Nair, W.; Gash, R., Least Squares Identification of Linear Sway-Yaw Manoeuvring Coefficients and Drag-Area Parameters of Ships. Proceedings of the Institution of Mechanical Engineers Part M Journal of Engineering for the Maritime Environment, 2021, 235 (3), 809-815.

However some classical accademic literatures had also been reserved to increase the comprehension of the reviewed literatures. Such as

 

 

 

 

 

Reviewer 2 Report

Article is interesting, the subject is current and has useful value. In order to enhance the article quality, I suggest the following remarks be taken into account:

1. Main contribution of the paper should be clearly indicated in the Introduction. The authors should clearly indicate which in the presented idea is novel compared to the existing publications.
2. In order to be compared with other possible approaches, the authors should enrich literature review with relevant references. For example, as:
   • Borkowski P. „Inference engine in an intelligent ship course-keeping system” Computational Intelligence and Neuroscience vol. 2017, art. no. 2561383, 2017 (1-9)
   • Pend, X.; Jia, S.; Hu, Z. Nonlinear H-infinity inverse optimal output feedback control for ship course. Control Theory & Applications 2014, 31, 215–222.
   • Nicolau, V. Neuro-fuzzy system for intelligent course control of underactuated conventional ships, in Proceedings of the IEEE International Workshop on Soft Computing Applications, Hungary, 21-23 August 2007, pp. 95-101.
3. I suggest that for a better understanding of the paper content and for an easier implementation of the proposed algorithm it would be necessary to rewrite the Section 3 by including a flowchart of the algorithm and its algorithmic presentation with all the steps that need to be taken.
4. The authors are suggested to have Discussion section to investigate the weakness, strength, and potential enhancement of proposed scheme.

Author Response

Response to Reviewer 2 Comments

 

Point 1:

Main contribution of the paper should be clearly indicated in the Introduction. The authors should clearly indicate which in the presented idea is novel compared to the existing publications.

 

Response 1:

Thank you for the suggestions of the reviewers, the existing literatures about ship steering control had been reviewed, and the corresponding comments on these literatures had been written into the paper.

Especially the main contribution of the paper had been rewritten (in line 98-111) to address the innovation point of the paper: combined the EKF on-line identification technique with the CGS controller design methodology, a adatpive CGS ship steering controller is proposed to improve the ship course dynamci response control performance.

Also the limitations of the reviewed literatures are also descirbed, such as (1) the complexity structure of the controller and the poor dynamic response performance, or (2) the parameters have no definite physical meaning and might lead to poor stability and robustness of the controller. (in line 92-97.)

 

 

Point 2:

In order to be compared with other possible approaches, the authors should enrich literature review with relevant references. For example, as:

Borkowski P. „Inference engine in an intelligent ship course-keeping system” Computational Intelligence and Neuroscience vol. 2017, art. no. 2561383, 2017 (1-9)

Pend, X.; Jia, S.; Hu, Z. Nonlinear H-infinity inverse optimal output feedback control for ship course. Control Theory & Applications 2014, 31, 215–222.

Nicolau, V. Neuro-fuzzy system for intelligent course control of underactuated conventional ships, in Proceedings of the IEEE International Workshop on Soft Computing Applications, Hungary, 21-23 August 2007, pp. 95-101.

 

Response 2:

Thank you for the reviewer’s suggestion, the literatures of the paper had been enrished, and the latest literature within the last 5 years had been overlook in the “introduction”. Such as

[1] Felski, A.; Zwolak, K., The Ocean-Going Autonomous Ship—Challenges and Threats. J. Mar. Sci. Eng., 2020, 8 (1), 41.

[3] Wang, L.; Wu, Q.; Liu, J.; Li, S.; Negenborn, R., State-of-the-Art Research on Motion Control of Maritime Autonomous Surface Ships. J. Mar. Sci. Eng., 2019, 7 (12) :438.

[7] Zhang, H.; Zhang, X.; Bu, R., Active Disturbance Rejection Control of Ship Course Keeping Based on Nonlinear Feedback and ZOH Component. Ocean Eng., 2021, 233, 109136.

[9] Dong, Y.; Wu, N.; Qi, J.; Chen, X.; Hua, C., Predictive Course Control and Guidance of Autonomous Unmanned Sailboat Based on Efficient Sampled Gaussian Process. J. Mar. Sci. Eng., 2021, 9 (12), 1420.

[10] Peng, X. Y.; Jia, S. L.; Hu, Z. H., Nonlinear H-infinity Inverse Optimal Output Feedback Control for Ship Course. Control Theory and Applications, 2014, 31, 215-222.

[17] Borkowski, P., Inference Engine in an Intelligent Ship Course-Keeping System. Comput Intell Neurosci, 2017, 2017, 2561383.

[20] Qin, H.;  Tan, P.;  Chen, Z.;  Sun, M.; Sun, Q., Deep Reinforcement Learning Based Active Disturbance Rejection Control for Ship Course Control. Neurocomputing, 2021. Available on line: https://doi.org/10.1016/j.neucom.2021.06.096.

[24] Raman-Nair, W.; Gash, R., Least Squares Identification of Linear Sway-Yaw Manoeuvring Coefficients and Drag-Area Parameters of Ships. Proceedings of the Institution of Mechanical Engineers Part M Journal of Engineering for the Maritime Environment, 2021, 235 (3), 809-815.

 

Point 3:

I suggest that for a better understanding of the paper content and for an easier implementation of the proposed algorithm it would be necessary to rewrite the Section 3 by including a flowchart of the algorithm and its algorithmic presentation with all the steps that need to be taken.

Response 3:

Thank you for the suggestions of the reviewers, the structure of the Section 3 had been recognized, and the flowchart of the proposed ship steering adaptive CGS controller had been repainted according to the original figure 4. Such as

Figure 4. The concept of ship steering adaptive CGS controller based on EKF identification method.

Where the steps of the EKF on-line identification process is incorated into the whole ship steering adaptive CGS control process. Also the details of the EKF paramter identification technique are described in the Remark 2. (in line 218-225)

 

Point 4:

The authors are suggested to have Discussion section to investigate the weakness, strength, and potential enhancement of proposed scheme.

Response 4:

Thank you for the suggestions of the reviewers. The advantages and disadvantages of the paper had be rewritten in the conclusion and discussion part (in line 358-373).

The advantages of the proposed adaptive CGS controller is the better dynamic response and trajectories tracking performance due to the introduction the EKF on-line identification technique into the traditionl CGS controller design method, which had been addressed in the paper. (in line 358-365)

The disavantage of the proposed controller is violent ship steering rudder operation and more rudder control energy consumption due to the high sampling frequency of the EKF identification technique. (in line 366-369)

Furthermore, the potential proposed solution such as the ” event trigger mechanics” had also been suggested in the paper to reduce the steering operation frequency in the futur researches.(in line 371-372)

 

 

 

 

 

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

My suggestions provided in my original review have been incorporated in the manuscript. From my side the work is accepted in this new version.