Robust Near-Optimal Aerocapture Guidance Method Based on Saturation Function

Round 1

Reviewer 1 Report

The paper describes a Robust Near-Optimal Aerocapture Guidance Method Based on Saturation Function. The overall quality of the article is good however I have some points I would like to make:

1) It would be good if the authors provided more motivation and explanation as to why they chose this particular saturation function and control profile as shown in Equations 20-23. 

2) Also, I would like to see more discussions on the implications of using such a guidance method, for instance, what would happen with the control architecture in terms of stability/performance metrics. Given that most control architectures rely on linearized plant/actuator/guidance models, the impact of having a saturation function should be explored/discussed.

3) Some of the terms in equations are missing explanations, e.g. the subscripts in Equation 19.

4) Minor grammar issues should be fixed.

 

 

Author Response

Thank you very much for your comments, as well as the recognition of our research. My coauthors and I take your feedback seriously, and we have thought carefully about the suggestions. The main corrections are given below:

 

Point 1: It would be good if the authors provided more motivation and explanation as to why they chose this particular saturation function and control profile as shown in Equations 20-23.

Response 1: We chose this particular saturation function mainly for three reasons. First, it has a structure similar to the optimal bang-bang control, so the guidance method based on saturation function can realize near-optimal performance. Second, different from instantaneous and discontinuous switching in a bang-bang profile, the control magnitude’s switching in a saturation function profile is smoother and easier to adjust, which can improve the method’s robustness. Third, compared with the two-phase guidance scheme adopted by the comparison algorithm, the guidance method based on saturation function can be applied to the whole phase of aerocapture, making the guidance process more unified and continuous. Besides, as shown in Equation (23), we introduced a linear function into the control profile to prevent premature saturation of bank control, so that the guidance method can have more control margin to cope with uncertainties and disturbances. According to your kind suggestion, more motivation and explanation have been added in Subsection 3.1.

 

Point 2: I would like to see more discussions on the implications of using such a guidance method, for instance, what would happen with the control architecture in terms of stability/performance metrics. Given that most control architectures rely on linearized plant/actuator/guidance models, the impact of having a saturation function should be explored/discussed.

Response 2: We mainly evaluate and discuss the proposed guidance method in terms of stability/performance metrics through Monte Carlo simulations. According to the statistical results from simulations, the minimum total velocity increment from proposed method is very close to that from comparison method which is based on optimal bang-bang control, proving that the proposed method has near-optimal performance. Besides, the proposed method can provide the total velocity increment with a much smaller standard deviation, even in the scenarios with wide ranges of entry flight path angle and lift-to-drag ratio. Therefore, the proposed method is stable under uncertainties and disturbances, showing good robustness. The proposed numerical predictor-corrector guidance method predicts terminal states through numerical integration of differential equations of motion, so it doesn’t rely on linearized guidance models. And in the follow-up study, we will continue to consider these factors you mentioned carefully.

 

Point 3: Some of the terms in equations are missing explanations, e.g. the subscripts in Equation 19.

Response 3: We have supplemented the missing explanations of the terms in this paper’s equations. Thank you very much for your kind reminders.

 

Point 4: Minor grammar issues should be fixed.

Response 4: We are very sorry for some grammar issues in this paper. We have revised the whole manuscript carefully and tried to avoid any grammar or syntax error. We believe that the language is now acceptable.

Reviewer 2 Report

In this article, the authors have formulated a new numerical predictor-corrector guidance algorithm based on the saturation function profile. I support this article for publication in the Journal of Applied Sciences.

Author Response

Point: In this article, the authors have formulated a new numerical predictor-corrector guidance algorithm based on the saturation function profile. I support this article for publication in the Journal of Applied Sciences.

Response: Thank you very much for acknowledging our work.

Author Response File: Author Response.docx

Reviewer 3 Report

As an organization of the paper, we recommend:

-First the presentation of a nominal case after which the dispersion of the flight parameters.

 -Detail the guidance algorithm more than just a diagram.

 

In order that the approach leads to better results we suggest:

1 - Use two parameters for control: angle of attack and bank angle.

2- Use the attack angle for express the drag force and lift force.

Author Response

Thank you very much for valuable and helpful comments, as well as the important suggestions to our research. The main corrections in the paper and our responses are elaborated below:

 

Point 1: The presentation of a nominal case after which the dispersion of the flight parameters.

Response 1: Nominal cases have been presented before the dispersion of the flight parameters in Section 4. Thank you very much for your suggestion.

 

Point 2: Detail the guidance algorithm more than just a diagram.

Response 2: We are sorry for not giving a detailed description of the guidance algorithm. At the beginning of a guidance cycle, based on spacecraft’s current states and guidance profile, the longitudinal guidance law predicts the atmospheric exit state through numerically integrating the three-DOF dynamic equations. Then we can calculate the post-aerocapture orbit parameters and total velocity increment required to perform orbit insertion. If the orbit parameters and velocity increment don’t meet the mission requirements, we will correct the guidance parameter and update guidance profile. The longitudinal guidance system repeats the above process until the mission requirements are met, then the bank-angle magnitude is determined. As for the lateral channel, the lateral guidance law determines the bank-angle symbol by judging that if the post-reversal orbit inclination satisfies the mission requirement. Combining the outputs of both two channels, we can get the bank-angle command in current guidance cycle. According to the bank-angle command, we update spacecraft’s states through measurement in actual flight or integration of the dynamic equations in simulation. Then the first-order low-pass filter is used to estimate the dispersion effect and update aerodynamic profile. After that, we repeat the above steps in the next guidance cycle. We have supplemented the detailed introduction to the guidance algorithm in Subsection 3.3.

 

Point 3: Use two parameters for control: angle of attack and bank angle.

Response 3: Our spacecraft model is a capsule spacecraft. We usually only control its bank angle, while the angle of attack follows a predetermined profile considering trim flight, thermal protection system and so on. This can reduce the guidance algorithm’s complexity and make it easier to be applied online. These points are also mentioned in previous works (see Lu, P.; Cerimele, C.J.; Tigges, M.A.; Matz, D.A. Optimal aerocapture guidance.  Journal of Guidance, Control, and Dynamics 2015, 38, 553–565.). In order to enhance the credibility, corresponding supplementary explanations are added to the paper, and the Reference is given.

 

Point 4: Use the attack angle for express the drag force and lift force.

Response 4: In the aerocapture scenario, the spacecraft flies at a high Mach number. There is little change in the lift and drag coefficients, so they are considered to be constant along the trajectory (see Lockwood, M.K.; et al. Aerocapture systems analysis for a Titan mission. Technical report, NASA, 2006; Mazzaracchio, A. Flight-path angle guidance for aerogravity-assist maneuvers on hyperbolic trajectories. Journal of Guidance, Control, and Dynamics 2015, 38, 238–248.). And the method’s performance will not be greatly affected if we use the attack angle for expressing the drag force and lift force. In order to enhance the credibility, corresponding supplementary explanations are added at the beginning of Section 4, and the Reference is given.