Adaptive Trajectory Tracking Safety Control of Air Cushion Vehicle with Unknown Input Effective Parameters

Round 1

Reviewer 1 Report

This paper studies the trajectory tracking control problem of an Air Cushion Vehicle (ACV) with yaw rate error constraint, input effective parameters, model uncertainties and external wind disturbance. Firstly, based on the 4-DOF vector mathematical mode of ACV, the radial basis function neural network (RBFNN) is adopted to provide the estimation of model uncertainties and external wind disturbance.

(1)

But, the Ch2 is too long. The modelling process would not be needed because the aim of this paper is a control design.

The model is well known fact and too many related studies have been presented including some experiment results with real plants.

I recommend that the pages 4 to 9 should be shortened in 2 pages.

 

(2)

The stability analysis process is not clear.

The author tried to analysis the system stability for each motion not for total system dynamics.

 

It is clearly presented.

 

 

Author Response

Point 1: But, the Ch2 is too long. The modelling process would not be needed because the aim of this paper is a control design. The model is well known fact and too many related studies have been presented including some experiment results with real plants. I recommend that the pages 4 to 9 should be shortened in 2 pages.

Response 1: Thanks for your kind advice. We think modelling process is necessary to be retained. Because the pages 4 to 9 is not a separation modelling but a new vector form modelling. From review of the available literatures about the ACV，the scalar model of the ACV is mainly obtained by the idea of separation modeling. We summarized a vector form mathematical model which is similar to a normal full-drive surface ship. It not only can highlight the different characteristics between ACV and ordinary surface ships, but also promote the research method of surface ships to ACV. We think this is the first time to use a vector form similar to an ordinary surface ship, so a detailed derivation is given to prevent some readers from being unclear about the source.

Point 2: The stability analysis process is not clear. The author tried to analysis the system stability for each motion not for total system dynamics.

Response 2: Thanks for your comment. The stability of total system have been discussed in pager 13. We designed a Lyapunov function (49) which combined position error, surge speed error, yaw error, yaw rate error, RBFNN error and the error of filter. The stability analysis ensure all signals of the closed-loop system are uniformly ultimately bounded.

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

There are numerous grammar issues - including in each of the first two sentences.  However, I think I was able to understand well enough to make a useful review.

It is claimed that ACVs are "widely used".  I am not sure that is true.

Equation 2 is wrong (one should be "sup" and one should be "inf")

K should be L by normal nomenclature

Double "+" in equation 7

I have many issues with the model presented, to name a few:

• Calling the righting moment "grav" (it's really buoyancy)
• I think there sould be a jet damping effect so that there would be an "air momentum" term that is a function of r (yaw rate).  This is often called jet damping for jet engines - seems like there would be something similar here
• If v is in the body frame, and phi is the roll angle - then there should be a gravity term in the v_dot equation (if you roll right, then gravity will increase v)
• Drag is listed as a function of U^2 - which is always positive.  What if the vehicle is going backwards?  Doesn't seem like the correct unit vector has been applied to this force/moment
• The inputs should really be a rudder deflection (or thrust angle) and thrust - a torque is difficult to evaluate if it is reasonable here

Plots of results need to include plant inputs so the reader can see if they are reasonable.

Equation 24 should be explained.

Author Response

Point 1:There are numerous grammar issues - including in each of the first two sentences.  However, I think I was able to understand well enough to make a useful review.

Response 1: Thanks for your comment. We have checked the paper again and corrected the grammar issues as possible as we can. We also asked the native speakers to help us to improve the language expression.

Point 2: Thanks for your comment. We have changed the expression "widely used" in paragraph 1 and added some relevant references on ACVs applications

Response 2: Thanks for your comment. We add relevant references for ACV applications in the first paragraph of introduction. 

Point 3: Equation 2 is wrong (one should be "sup" and one should be "inf"),K should be L by normal nomenclature,Double "+" in equation 7

Response 3: Thanks for your advice. We have corrected the "sup" to "inf" in Equation 2. And we have deleted a "+" in equation 7.

Point 4:I think there should be a jet damping effect so that there would be an "air momentum" term that is a function of r (yaw rate).  This is often called jet damping for jet engines - seems like there would be something similar here

Response 4:Thanks for your kind advice. "Air momentum" term which project on the yaw DOF include a function of r. But we cant not get the specific form. Because according to the equation(5), we have I_{z}\dot{r}=N. In equation(7), N=N_{a}+N_{h}+N_{m}+N_{r}, we can see that the "air momentum" term is one part of N.

Point 5:If v is in the body frame, and phi is the roll angle - then there should be a gravity term in the v_dot equation (if you roll right, then gravity will increase v)

Response 5: Thanks for your thorough consideration. But we don't think that there should be a gravity term in the \dot{v} equation. Because gravity is always vertical downward, even if the center of gravity is shifted due to the roll angle. The \dot{v} is related to the horizontal force. The projection of gravity on the horizontal coordinate is not zero. But we think it will offsets the buoyancy projection on the horizontal coordinate.

Point 6:Drag is listed as a function of U^2 - which is always positive.  What if the vehicle is going backwards?  Doesn't seem like the correct unit vector has been applied to this force/moment.

Response 6：Thanks for your comment. The drags in 2.2.1, when the vehicle is going backwards, the coefficients, for example, C_xh, C_yh etc, are negative.

Point 7:Plots of results need to include plant inputs so the reader can see if they are reasonable.

Response 7:Thanks for your comment. We have added the plots of inputs that include the pitch angles of air propeller and the angles of air rudder in page 19. The pitch angle is between -25 to 40 degrees. And the rudder angle is between -30 to 30 degrees.

Point 8:Equation 24 should be explained.

Response 8: Thanks for your comment. I add a figure (Fig.3) to explain equation 24. It can be seen from equation(24), ψr∈ (−π,π]. When the ye!= 0 and xe= 0, we have arctan(ye/xe) → ±π/2. We defined ψr= ψd when ze= 0

Author Response File: Author Response.pdf