Adaptive Backstepping Nonsingular Terminal Sliding-Mode Attitude Control of Flexible Airships with Actuator Faults
Round 1
Reviewer 1 Report
I think the good start for the review will be a citation from (https://www.sciencedirect.com/science/article/abs/pii/S0376042110000618): Based on the existing research, there is no strong evidence that the flexibility effects have a significant impact on the flight characteristics of conventional modern airships.
It seems that the authors did a lot of work, unfortunately, in my opinion, they should rethink the strategy. The article describes a very complicated mathematical framework that is very hard to follow. The framework seems to be tailored specifically for airships, but they do not take into account (or at least they do not write about it) some important problems with airship control, which is e.g.: low quality of measurements or constraints of the actuation system. For other important problems, like the underactuation, the authors did not explain which degree of freedom is not actuated. According to the actuation model of the airship structure presented in Figure 1. The roll (phi) angle can be controlled, but the authors state that it is not. Without any explanation.
The results also are of poor quality, there is a lot of questions without answers, like what was the structure and parameters (and how were they been chosen) of the PID controller used for the comparison. Or even parameters for the proposed controller. Also what parameters of elasticity were used for the simulated model?
Finally, the results are presented only for altitude control, which is a great simplification of the problem of movement in three-dimensional space. And it is not clearly stated in the title or abstract.
My overall experience with this paper is that the authors did not spend enough time trying to understand the problems with the control of airships, and tried to connect some well-known methods to create some unique combination. Maybe the combination can have some advantages, but the authors failed to provide strong evidence of it. The conclusions are definitely too strong based on the presented results.
Author Response
1 I think the good start for the review will be a citation from (https://www.sciencedirect.com/science/article/abs/pii/S0376042110000618): Based on the existing research, there is no strong evidence that the flexibility effects have a significant impact on the flight characteristics of conventional modern airships.
Answer: In the reference of “Airship dynamics modeling: A literature review”, the authors propose that there are a few investigations on the fluid-structure interaction lighter-than-air (LTA) aircraft, and gives two reasons, one is the LTA fluid-structure interaction problem be complex, second is LTA aircraft fly at low speeds and the structural vulnerability and safety have been greatly improved for modern airships made of membrane structures, which make the fluid-structure interaction a less important issue in airship development. Here the authors think the fluid-structure interaction be a less important issue in airship development when the LTA aircraft flies at low speeds and small structural deformation. In fact, there are large deformation for the flexible stratospheric airship due to hull material with lower elastic moduli (unconventional composite materials) [1], and big difference of temperature change between day and night at stratospheric altitude, which make the flexible airship produce a big deformation, and the interaction between the flexibility and the aerodynamic forces should not be neglected. See Attachment Fig.1The High Platform II airship.
On the other hand, Bessert and Frederich analyzed the effects of deformation on the lift coefficients at angles of attack for the flexible CL-160 non-rigid airship using FEA package ABAQUS and CFD solver VSAERO, see Fig.2. Their analysis displayed strong effects of the geometric and material nonlinearities of the hull on the aerodynamic derivatives [2].
[1] Smith, M. S. and Rainwater, E. L., Applications of Scientific Ballooning Technology to High Altitude Airships, 3rd AIAA Annual Aviation Technology, Integration, and Operations Technical Forum, Denver, CO, November 17-19, 2003.
[2] Bessert N, Frederich O. Nonlinear airship aeroelasticity [J]. Journal of Fluids and Structures, 2005, Vol.21,No.8: 731-742.
2 It seems that the authors did a lot of work, unfortunately, in my opinion, they should rethink the strategy. The article describes a very complicated mathematical framework that is very hard to follow. The framework seems to be tailored specifically for airships, but they do not take into account (or at least they do not write about it) some important problems with airship control, which is e.g.: low quality of measurements or constraints of the actuation system.
Answer: Yes. For the problem of low quality of measurements for the attitude of the airship, it can be processed by one- or two-order filter for the sensor of the inertial measurement unit (IMU), so we don’t consider it because it’s easy implemented. And the actuation saturation is added to consider the constraints of the actuation system, that is, a model uncertainty d and the actuator saturation are introduced, so the system (10) can be modified as Eq.(33).where d denote model uncertainties such as aerodynamic coefficients and structural stiffness, sat() denotes saturation function.
Now we consider the input saturation problem, in order to analyze the effect of actuator saturation on the closed-loop dynamics, the actuator output is Eq.(46),
Furthermore, defining ∆u as the difference between the desired control input u and the actuator output, i.e., ∆u= ua− sat(ua), a saturation compensator is designed to deal with actuator saturation as follows Eq.(47),where Ks is control gain of the saturation compensator, and then the total control is Eq.(48). Since the actuator saturation has been considered in the original simulations, so the results are same.
3 For other important problems, like the underactuation, the authors did not explain which degree of freedom is not actuated. According to the actuation model of the airship structure presented in Figure 1. The roll (phi) angle can be controlled, but the authors state that it is not. Without any explanation.
Answer: The structure of the flexible airship is shown in Fig.1. There are four control surfaces including two rudders and two elevators in the tail fins, and two propellers are set up on each side of the hull. The gondola under the airship envelope houses the avionics system and flight control system and other payloads.
In this paper two underactuated cases are considered as follows: (Page 7)
Remark 1 There are two underactuated cases for the flexible airship. Case 1. the airship without lateral tilt angle of the propellers ((i.e. the thrust direction is fixed)) is underactuated in y-direction (that is, the lateral control force Tsy = 0), thus sway velocity v cannot be directly controlled. If wind is in the presence in this case, then the airship can align against the wind through yaw motion and reducing lateral forces requirement to a low and acceptable value，thus the lateral force input can vanish in stationary conditions.. Case 2. The airship works in Case 1 without ailerons or differential actuators (i.e., δeL = δeR, δrU = δrB, and the roll control moment MTx ≈ 0). Sway velocity v and bank angle φ cannot be directly controlled. In this case the disturbance of the roll moment resulted from wind can be attenuated by the airship roll damp, thus the roll moment input can vanish in stationary conditions.
4 The results also are of poor quality, there is a lot of questions without answers, like what was the structure and parameters (and how were they been chosen) of the PID controller used for the comparison. Or even parameters for the proposed controller. Also what parameters of elasticity were used for the simulated model?
Answer:
The structure of the PID controller is as Fig.3.
Parameters of the PID controller are selected to satisfy the requirements after several design iterations, see Table2. Parameters for the proposed BNTSM controller are as Table2,
where c1 and c2 are in Eq.(58), Eq.(63) and selected to satisfy the requirements in Section 3 after several design iterations. The damping ratio and undamped nature frequency of the command filter are selected as ζn =0.9, ωn =20 rad/s. Mode number N selects N = 2, Pe = 0.1 . A doublet command is predefined as the desired attitude.Parameters of elasticity are as follows: EI denotes bending stiffness with EI = πR3 ET0, E is the elastic modulus of the hull envelope and T0 is its thickness, R is the hull radius (on Page 4). u denotes elastic displacement. ET0 =433440(N/m) as in Table 1.
5 Finally, the results are presented only for altitude control, which is a great simplification of the problem of movement in three-dimensional space. And it is not clearly stated in the title or abstract.
Answer:
In the abstract: This paper studies on attitude tracking control of a flexible airship subjected to wind disturbances, actuator saturation and control surface faults.
Due to complex of interaction of structural and aerodynamic forces, the position tracking control problem will be studied in future work.
6 My overall experience with this paper is that the authors did not spend enough time trying to understand the problems with the control of airships, and tried to connect some well-known methods to create some unique combination. Maybe the combination can have some advantages, but the authors failed to provide strong evidence of it. The conclusions are definitely too strong based on the presented results.
Answer: First, trajectory tracking control for the airship within finite time is a hot topic recently [Ref.13]. However, most of them are for the rigid-body airship. However, the stratospheric airships are usually flexible airship, and to the best we know, there is no study on trajectory control with finite time constraint. Second, wind is one of the major factors affecting the trajectory tracking and hovering control for the airship [Ref.2, Ref.23], wind observer is introduced to reduce this effect. Finally, fault tolerant control is valuable objective because the actuators of the stratospheric airship work in the adverse environment for long endurance which make the actuator easily failed. Therefore Adaptive backstepping nonsingular terminal sliding-mode control of flexible airships with actuator faults is studied in this paper.
A fast nonsingular terminal sliding-mode (NTSM) combined with backstepping control is proposed for the problem. The benefits of this approach have NTSM merits of high robustness, fast transient response and finite time convergence, as well as backstepping control in terms of globally asymptotic stability. However, the major limitation of the backstepping NTSM is that its design procedure is dependent on the prior knowledge of the bound values of the disturbance and faults. To overcome this limitation, a wind observer is designed to compensate for the effect of the wind disturbances, a saturation compensator is designed to reduce actuator saturation effect, and an adaptive fault estimator is designed to estimate the faults of the control surfaces. Globally exponentially stability of the closed-loop control system is guaranteed by using Lyapunov stability theory. Finally, simulation results show the averaged tracking errors of the BNTSM controller are smallest, and then those by the BISMC design is smaller, and the PID controller provides worse tracking performances comparing with the BNTSM control and the BISMC. In the view of computational burden, the BNTSM controller is time consuming while the cost of the PID controller is the cheapest.
Ref.13 Yang, Y.N. A Time-specified Nonsingular Terminal Sliding Mode Control Approach for Trajectory Tracking of Robotic Airships, Nonlinear Dyn., 2018; 92, pp.1359–1367
Ref.2 Azinheira J.R., de Paiva E.C., Bueno S.S., Influence of Wind Speed on Airship Dynamics, J. Guid., Contr. and Dyn., 2002; 25(6), pp.1116–1124.
Ref.23 Zheng, Z.W., Zhu M., Shi D. L., Wu Z. , Hovering Control for a Stratospheric Airship in Unknown Wind, AIAA Guid., Nav., and Control Conf., AIAA SciTech Forum, National Harbor, MD, Jan., 2014,pp.1-16.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments
Overall Comments:
The paper presents a new control strategy: BNSTM, to the problem of attitude tracking of a flexible airship. This is a very well-written paper that is both rigorous and describes how it improves the state of the art. Some minor comments to improve the readership
Minor Comments
- The effort in this paper would be greatly appreciated if the authors explain why this controller is attributed with the terms: non-singular, and terminal. To help flesh these out, addressing the following questions might help:
- Do we typically expect singularities in a sliding mode controller?
- If so where, and how is this control law preventing them?
- What does terminal in this context mean?— This could be confused with a phenomenon where the control surfaces only act at the start and end of the tracking process.
- It appears from Figures 8 and 9, that the control surfaces are acting throughout the tracking process. So the authors need to explicitly clarify this.
- A nice-to-see feature with any paper on the sliding mode controller is to show how well the designed control law tracks the manifold surfaces. Specifically, can you show that the variable s is asymptotically approaching 0?
- The BISMC controller needs to be introduced before first using this acronym: What does BISMC mean?
- Equation 44, appears to have a typo: The authors talk about the sign(.) function in the description below but use the sgn() notation in the equation.
Author Response
Reviewer #2
The paper presents a new control strategy: BNSTM, to the problem of attitude tracking of a flexible airship. This is a very well-written paper that is both rigorous and describes how it improves the state of the art. Some minor comments to improve the readership
Answer: Thank you.
Minor Comments
1 The effort in this paper would be greatly appreciated if the authors explain why this controller is attributed with the terms: non-singular, and terminal. To help flesh these out, addressing the following questions might help:
- Do we typically expect singularities in a sliding mode controller?
Answer: No.
- If so where, and how is this control law preventing them?
Answer:
A non-singular terminal sliding mode (NTSM) surface or manifold is designed by using the fractional order derivative as Eq.(44). The sliding mode control law is as Eq.(66).
To prevent singularities in a sliding mode controller, all of the exponent terms in the control law of (66) must be positive.
- What does terminal in this context mean?— This could be confused with a phenomenon where the control surfaces only act at the start and end of the tracking process.
Answer: term of terminal means the tracking errors converge to zero or the system state converges the equilibrium point within finite time. So that is not the phenomenon where the control surfaces only act at the start and end of the tracking process.
- It appears from Figures 8 and 9, that the control surfaces are acting throughout the tracking process. So the authors need to explicitly clarify this.
Answer: From Figure 8 and 9 it can be seen that the pitch step input of 0.2 rad shows at 5sec and the tracking response converges the desired value at 10 sec (within 5 sec). Because the doublet command is a changing signal, the steady value of the tracking response also changes, so the overall tracking process is dynamic varying, but the response will fast converge when the command is fixed.
From Figure 10 it can be seen that the when the command changes at 5sec the elevator will change, and then the deflection of the control surface δe converges quickly to zero (equilibrium position) until the next command input.
2 A nice-to-see feature with any paper on the sliding mode controller is to show how well the designed control law tracks the manifold surfaces. Specifically, can you show that the variable s is asymptotically approaching 0?
Answer: Good suggestion. Fig.12 shows the response of sliding mode variable s, which are asymptotically approaching zero except for s(φ) due to underactuated roll motion. see Figure 12. Response of sliding mode variable s.
- The BISMCcontroller needs to be introduced before first using this acronym: What does BISMC mean?
Answer: BISMC means backstepping integral sliding mode control (BISMC), where the sliding surface s of the BISMC is defined as follows s= ramta1*z1 +ramta2*integ(z1)+z2
- Equation 44, appears to have a typo: The authors talk about the sign(.)function in the description below but use the sgn() notation in the equation.
Answer: Yes, we modified Eq.(44) as follows
sgn(.) is sign function.
Author Response File: Author Response.pdf
Reviewer 3 Report
The paper presents the properties of the Adaptive backstepping nonsingular terminal sliding-mode control method used on attitude tracking control of a flexible airship subjected to wind disturbances and selected failures of actuators. It should be emphasized that the authors do not describe details of the method properties related to fault tolerance. The paper only shows this feature for the selected faults case. A lot of information is consistent with the authors' previous papers, but this does not invalidate its publication. To make it easier to read, I suggest authors to make a list of the acronyms used. In the current version of the paper not all acronyms are correctly entered (eg BISMC) or they are presented in the wrong places (eg SMC is on line 58 and should be on line 52). For a more readable presentation of simulation results, the plots of the averaged tracking errors for a analysed methods should be added to the variable plots presented.
Author Response
Reviewer #3
1 The paper presents the properties of the Adaptive backstepping nonsingular terminal sliding-mode control method used on attitude tracking control of a flexible airship subjected to wind disturbances and selected failures of actuators. It should be emphasized that the authors do not describe details of the method properties related to fault tolerance. The paper only shows this feature for the selected faults case. A lot of information is consistent with the authors' previous papers, but this does not invalidate its publication.
Answer: Yes. The actuator faults for the airship have some kinds of stuck, float, loss of effect, and we set one kind of loss of effect because the actuator of the flexible airship runs long endurance, which does easily happen this fault in adverse environment. And the fault estimator of (72) is proposed in this paper because it has good adaptive capability.
2 To make it easier to read, I suggest authors to make a list of the acronyms used. In the current version of the paper not all acronyms are correctly entered (eg BISMC) or they are presented in the wrong places (eg SMC is on line 58 and should be on line 52).
Answer: BISMC means backstepping integral sliding mode control (BISMC), where the sliding surface s of the BISMC is defined as follows s = ramta1*z1+ramta2*integ(z1)+z2.
And the parameters are designed as Table2.
SMC has been modified on line 51. And the List of Acronyms are on page 20.
List of Acronyms:
BISMC Backstepping Integral Sliding Mode Control
BNTSM Backstepping Nonsingular Terminal Sliding Mode
CLFs Control Lyapunov Functions
CV Center of Volume
NTSM Nonsingular Terminal Sliding-Mode
SMC Sliding-Mode Control
RBFNN Radial Basis Function Neural Network
3 For a more readable presentation of simulation results, the plots of the averaged tracking errors for a analysed methods should be added to the variable plots presented.
Answer: Good suggestion. Since the longer simulation, the ET is large, so we only choose the maximal simulation time 20s here. We simulate from 0 to 5sec, 10sec, 15sec and 20sec for each controller with wind compensator and the results are as Fig.16 and Fig.17.
And we find the results are the same as original conclusion, that is, the reference signals of pitch and yaw angles are precisely tracked, but the averaged tracking errors of the BNTSM controller are smallest, and then those by the BISMC design is smaller, and the PID controller provides worse tracking performances comparing with the BNTSM control and the BISMC. In the view of computational burden, the BNTSM controller is time consuming while the cost of the PID controller is the cheapest. Therefore, we choose the table for comparison analysis for convenience.
Author Response File: Author Response.pdf
Reviewer 4 Report
The theoretical contributions should be stressed in detail in Introduction.
Advantages of the proposed algorithm upon the well-known algorithms should be stressed.
In introduction, it is not enough to state the current work. It should be expended and reconstructed. Including the motivation, the main difficulties, the main work and the improvements compared with previous related works should be emphasized in this section.
The methodologies that can study finite time control, that is, Event-triggered fractional-order sliding mode control technique for stabilization of disturbed quadrotor unmanned aerial vehicles, Barrier Function Adaptive Nonsingular Terminal Sliding Mode Control Approach for Quad-Rotor Unmanned Aerial Vehicles, and Desired tracking of delayed quadrotor UAV under model uncertainty and wind disturbance using adaptive super-twisting terminal sliding mode control, should be discussed in the Introduction part.
The importance of the problem considered in this paper should be further addressed.
The directions to further and improve the work should be added as future recommendation section after ‘conclusions’ section.
The types of software employed for solving the problem and also simulation experiments are unclear.
Please check carefully all notations and equations.
Author Response
Reviewers:
We appreciate your careful reading of our manuscript and valuable comments very much. As you will see we have carefully revised our manuscript as your suggestions. Your comments and our detailed replies are summarized as follows:
Review 4:
1 The theoretical contributions should be stressed in detail in Introduction.
Answer: Good suggestion.
The main contributions of the proposed scheme are summarized as follows.
(1) A backstepping nonsingular terminal sliding-mode control scheme is proposed for attitude tracking control of the flexible airship with actuator faults, actuator saturation and uncertainties of stiffness.
(2) A wind observer with an adaptive disturbance observer is designed to reject variable external bounded disturbances and cope with model parameter uncertainties.
(3)An anti-windup compensator based on proportion to saturation error is used to compensate actuator saturation.
(4)An adaptive fault estimator is incorporated into the BNTSM control to implement fault estimation and fault tolerant control.
2 Advantages of the proposed algorithm upon the well-known algorithms should be stressed.
Answer:
The proposed BNTSM control has advantages of high robustness, fast transient response and finite time convergence, and the globally asymptotic stability of the closed-loop system can be guaranteed. Furthermore, a wind observer and an adaptive fault estimator are designed to observe the wind disturbances and estimate the faults of the control surfaces, thus limitation of the backstepping nonsingular terminal sliding mode control dependent on prior knowledge is overcome.
3 In introduction, it is not enough to state the current work. It should be expended and reconstructed. Including the motivation, the main difficulties, the main work and the improvements compared with previous related works should be emphasized in this section.
Answer: Motivated by Li’s [21] and Hans’s work [25], the main work in this paper is a novel backstepping nonsingular terminal sliding mode (BNTSM) control scheme proposed for attitude tracking of the airship with unknown faults and disturbances and actuator saturation. In the proposed BNTSM control scheme, the nonsingular terminal sliding-mode technique and backstepping technique are integrated. The proposed BNTSM control has advantages of high robustness, fast transient response and finite time convergence, and the globally asymptotic stability of the closed-loop system can be guaranteed. Furthermore, a wind observer and an adaptive fault estimator are designed to observe the wind disturbances and estimate the faults of the control surfaces, thus limitation of the backstepping nonsingular terminal sliding mode control dependent on prior knowledge is overcome.
4 The methodologies that can study finite time control, that is, Event-triggered fractional-order sliding mode control technique for stabilization of disturbed quadrotor unmanned aerial vehicles, Barrier Function Adaptive Nonsingular Terminal Sliding Mode Control Approach for Quad-Rotor Unmanned Aerial Vehicles, and Desired tracking of delayed quadrotor UAV under model uncertainty and wind disturbance using adaptive super-twisting terminal sliding mode control, should be discussed in the Introduction part.
Answer: Good suggestion, we add them and discuss them in the introduction as follows
Mofid et al. proposed Super-twisting terminal SMC and Barrier Function terminal SMC to deal with quad-rotor unmanned aerial vehicles (UAVs) with delay input [14] and force the error dynamics to converge on a region near the origin in a finite time [15]. Event-triggered Fractional-order Sliding Mode Control Technique was proposed to stabilize the quadrotor UAV with external random/time-varying disturbances [16].(On Page 2)
14 Mofid O., Mobayen S., Zhang C. W., Esakki B., Desired Tracking of Delayed Quadrotor UAV under Model Uncertainty and Wind Disturbance using Adaptive Super-twisting Terminal Sliding Mode Control, ISA Transactions, doi.org/10.1016/j.isatra.2021.06.002, 2021, pp.1-17
15 Alattas K.A., Mofid O., Alanazi A.K., Abo-Dief H.M., Bartoszewicz A., Bakouri M. and Mobayen S., Barrier Function Adaptive Nonsingular Terminal Sliding Mode Control Approach for Quad-Rotor Unmanned Aerial Vehicles, Sensor, 2022, 22(3): pp.1-20
16 Pouzesh M., Mobayen S., Event-triggered Fractional-order Sliding Mode Control Technique for Stabilization of Disturbed Quadrotor Unmanned Aerial Vehicles, Aerospace Science and Technology, 2022, (121) 107337: pp.1-13
5 The importance of the problem considered in this paper should be further addressed.
Answer: We modified as follows
2.2. Fault Tolerant Trajectory Tracking Problem
Fault tolerant trajectory tracking problem is challenge for the flexible stratospheric airship because it’s a hard task to achieve precise trajectory tracking under the actuator faults, the main reason is that the interaction between fluid and structure should be considered.
6 The directions to further and improve the work should be added as future recommendation section after ‘conclusions’ section.
Answer: Good suggestion. We modified as follows
- 6. Future recomendation
Future work is to expand the control strategy into position control loop and velocity control loop for the flexible airship.
7 The types of software employed for solving the problem and also simulation experiments are unclear.
Answer: We modified as follows
Three scenarios of bounded wind disturbances, control surface faults, and variable stiffness of the flexible airship envelope are simulated to illustrate the BNTSM controller performances.
Scenario 1：Trajectory tracking control under unknown wind
This scenario will demonstrate attitude tracking performance by using the proposed BNTSM controller and the wind observer.
Scenario II: Trajectory tracking control under actuator faults with unknown wind
This scenario will demonstrate fault tolerant tracking performance by using the proposed BNTSM controller and the fault observer.
Scenario III: Trajectory tracking control under variable stiffness and unknown faults and winds
In this scenario we investigate the significance envelope flexibility has on the effect of rigid-body dynamics of the airship.
The software of Matlab and Simulink are employed to solve the problems.( On page 10).
8 Please check carefully all notations and equations.
Answer: Thank you, we check them.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Ad 1. I understand that in some publications the authors suggest that flexibility is important, but once again: 'there is no strong evidence for this'. So maybe the authors of this paper should verify this at the beginning.
Ad 5. It is my mistake, I overlooked the "attitude tracking" part. Still, the title of the paper is misleading, it is very good, that it is in the abstract, but the title is unacceptable.
Ad 2. For attitude-only control, the measurement problem is less harmful, but still exists. For filtering, there is a time delay that can have a big impact on the stability of the system. Also saturation is not the only limitation of the execution system.
Ad 3. Adding this remark do not explain how this underacutations influenced the research or its results.
Ad 4. The results are still of poor quality, and "several iterations" is unacceptable strategy for such small differences in results.
Ad 6. The answer provided by the authors is not connected with referenced review part. The conclusions are still definitely too strong for the presented results.
Author Response
Reviewers:
We appreciate your careful reading of our manuscript and valuable comments very much. As you will see we have carefully revised our manuscript as your suggestions. Your comments and our detailed replies are summarized as follows:
Reviewer #1:
Ad 1. I understand that in some publications the authors suggest that flexibility is important, but once again: 'there is no strong evidence for this'. So maybe the authors of this paper should verify this at the beginning.
Answer: Good question. First Selima Bennaceur showed the difference between flexible airship and rigid airship motions [Ref.1]. In figure 7 they superimpose total displacement along the X axis of the rigid airship and the flexible device. It is noticed that the flexible device continues to oscillate which proves the impact of flexibility on displacement. (please see Figs 7 and 8 in the attachment file).
The deformations (in figure 8) are about 0.20m what is more or less significant considering one has small deformations.
Second, we simulate the sky-500 model by elevator and rudder inputs, and the results are shown as Fig.3 and Fig.4 (Please see Figs 3 and 4 in the attached file).
It can be seen from Figs 3 and 4 that there are obvious difference between the responses of the rigid airship and flexible airship. Therefore, the interaction between fluid and structure could not be neglected.
Ref.1 Bennaceur S. ;Azouz, N.;Abichou A., An Efficient Modelling of Flexible Blimps: Eulerian Approach, Proceedings of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2007, Sep.2007, Las Vegas, Nevada, USA, pp.1-10
Ad 2. For attitude-only control, the measurement problem is less harmful, but still exists. For filtering, there is a time delay that can have a big impact on the stability of the system. Also saturation is not the only limitation of the execution system.
Answer: Yes. To reduce the measurement noise effect, we often add the low-pass filter, however, if the parameters of the filter are chosen improperly, it will produce big delay, even result in the system unstability. In this paper, we can use the command filter, i.e. a second-order lower pass filter as Eq.(37).
where denotes the filter damping ratio, ωn denotes the filter undamped nature frequency and set ζn =0.9, ωn =20 rad/s. This filter can be added to the outputs of attitudes and angular rates for the airship, see Fig.1(a). And the simulation results are as Fig.1(c).
Figure 1. The output filter influence on attitude tracking responses (see the attached file 1)
It can be seen from Fig.1(c) that the output responses have small time delay when the output filters are added in the control loop, but the output responses are smoother than those without filters. Of course, when the filter parameters are set improperly, the results will be worse.
Ad 3. Adding this remark do not explain how this underacutations influenced the research or its results.
Answer:
Remark 1 There are two underactuated cases for the flexible airship. Case 1. The airship without lateral tilt angle of the propellers ((i.e. the thrust direction is fixed)) is underactuated in y-direction (that is, the lateral control force Tsy = 0), thus sway velocity v cannot be directly controlled. If wind is in the presence in this case, then the airship can align against the wind through yaw motion and reducing lateral forces requirement to a low and acceptable value，thus the lateral force input can vanish in stationary conditions.. Case 2. The airship works in Case 1 without ailerons or differential actuators (i.e., δeL = δeR, δrU = δrB, and the roll control moment MTx ≈ 0). Sway velocity v and bank angle φ cannot be directly controlled. In this case the disturbance of the roll moment resulted from wind can be attenuated by the airship roll damp, thus the roll moment input can vanish in stationary conditions.
And Note that there is no aileron input for the flexible airship, so , that is, the first roll moment term is zero . (Line 457)
According to Remark 1, the airship works in Case 1 without ailerons or differential actuators, so there is no direct control input to produce roll moment. It can been seen from Figures 4 and 5 that the roll motion response is free oscillating and has not been controlled due to deficient directly roll moment under underatuated Case 2. (On page 12)
Ad 4. The results are still of poor quality, and "several iterations" is unacceptable strategy for such small differences in results.
Answer:
To be honest, the work for selection of the controller parameters is not easy. We first develop the backstepping controller for the flexible airship according to our previous work [Ref.1], because the controller form is almost same, and then we chose the backstepping control parameters of c1 and c2, we find these parameters will affect greatly the tracking errors.
Second, we add the sliding mode control, for the BISMC control, we refer our previous work [Ref.2], we find sliding mode control parameters of h, ς, and φs, which don’t obviously affect the tracking performances, but can improve the system adaptiveness when faults happen.
Finally, we develop the BNTSM controller, and it must satisfy the constraint for selecting the parameters of p, q with 1<p/q<2 and λ > p/q, so we refer the Ref.3 and determine them. The parameter β will greatly affect the closed-loop tracking performance, if we select a big value of β the result will be divergence, if we select a small one, there is no control effect, so we try on many times.
Ref.1 Liu, S. Q. ; Sang Y. G. Underactuated Stratospheric Airship Trajectory Control Using an Adaptive Integral Backstepping Approach, J. Aircraft, 2018;55(6), 2357-2371
Ref.2 Liu, S. Q. Sang Y. J., Whidborne J. F. ,2020, Adaptive sliding-mode-backstepping trajectory tracking control of underactuated airships, Aerospace Science and Technology, (97) pp 1-13
Ref.3 Yang, Y.N. A Time-specified Nonsingular Terminal Sliding Mode Control Approach for Trajectory Tracking of Robotic Airships, Nonlinear Dyn., 2018; 92, pp.1359–1367
Ad 5. It is my mistake, I overlooked the "attitude tracking" part. Still, the title of the paper is misleading, it is very good, that it is in the abstract, but the title is unacceptable.
Answer: Good suggestion. We modified the title” Adaptive backstepping nonsingular terminal sliding-mode attitude control of flexible airships with actuator faults”
Ad 6. The answer provided by the authors is not connected with referenced review part. The conclusions are still definitely too strong for the presented results.
Answer: We study on the Reference 19 carefully, the authors presented “ LTA aircraft fly at low speeds and the structural vulnerability and safety have been greatly improved for modern airships made of membrane structures, which make the fluid–structure interaction a less important issue in airship development. However, there has been growing interest in this problem over the last few years, partly because of the recent advances in computational capabilities which make it possible to solve the fluid–structure interaction problems, but also because of proposed new airship designs and materials. ”
“Fig. 10(a) shows the Sanswire Stratellite airship,designed by Sanswire-TAO [78] for missions in the lower stratosphere up to 18,288 m(60,000ft) altitude. The Stratellite is a segmented airship consisting of a sequence of buoyancy cells. Flight tests with the airship demonstrated large deformations of the hull which results from the relative displacement between the buoyancy cells. Therefore, the aerodynamics and flight dynamics models based on a rigid-body assumption, such as those reviewed in Sections 2 and 3, are not likely to be applicable to this very flexible airship.”
From above presentation, it can be seen that the authors make certain that the aerodynamics and flight dynamics models based on a rigid-body assumption is improper, the flexible airship must consider the interaction between fluid and structure although it is not important issue in the early airship development. The following example demonstrates the difference between rigid airship and flexible airship. Therefore our result is feasible.
The sky-500 model by a square wave input of elevator, and the results are as follows
Figure 1 Pitch response under the elevator input
It can be seen from Fig.1 that there are obvious difference between the responses of the rigid airship and flexible airship.
19 Li, Y. W.; Nahon, ; Sharf, I., Airship Dynamics Modeling: A Literature Review, Progr. Aerospace Sci., 2011;47, pp.217–239
Author Response File: Author Response.pdf
Reviewer 4 Report
The authors have answered the comments suitably.
