Adaptive Flight Path Control of Airborne Wind Energy Systems

Round 1

Reviewer 1 Report

This paper represents an interesting topic related to wind energy. Most of the paper is well written with clear description of methods and results. 

I have one major comment about the simulation results section. The author indicates that wind direction also affects the performance of the AWE system from the very beginning. However, the simulation only considers various wind speeds. Wind direction is not considered in the simulation. Without wind direction, are the simulation results still reliable and meaningful? It is critical to justify this issue.

A minor comment is that section number normally starts from 1 instead of 0.

Author Response

This paper represents an interesting topic related to wind energy. Most of the paper is well written with clear description of methods and results.

Response: Thank you.

I have one major comment about the simulation results section. The author indicates that wind direction also affects the performance of the AWE system from the very beginning. However, the simulation only considers various wind speeds. Wind direction is not considered in the simulation. Without wind direction, are the simulation results still reliable and meaningful? It is critical to justify this issue.

Response: The local changes in wind speed and direction in the time scale of seconds that we are refering to in line 116 of the (revised) manuscript are related to local turbulent fluctuations of the wind field. In references [12] and [13] the effect of such fluctuations on the operation of the system is analyzed by means of computational simulation. In our analysis we did not consider the effect of turbulence, which will be subject to a follow-up study. But next to turbulent fluctuations also the average wind velocity exhibits changes in magnitude and direction. It is generally assumed that these changes of the average wind velocity occur on a substantially larger time scale and are thus slow compared to the flight dynamics of the kites. We have added a corresponding remark to the manuscript at the bottom of page 5 of the (revised) manuscript. As consequence, the operation of the system can continuously be adjusted to these changes, e.g. by rotating the symmetry plane of the pumping cycle. This is the function of the supervisory control system. In a similar way also the elevation angle is adjusted by the supervisory control system.

A minor comment is that section number normally starts from 1 instead of 0.

Response: Thank you, we have corrected this.

Reviewer 2 Report

Very good paper. It is certainly scientifically relevant and could be of interest to a wide part of the wind energy community. The contributions are well-defined and clear throughout the paper. The methodology is mathematically rigorous, and the conclusions are supported by the results.

I just have some minor comments:

- Page 1, line 38: “The rated power of the generator is typically determining the installation” should be “The rated power of the generator typically determines the installation”.

- Last paragraph of introduction: “Section” is usually abbreviated with “Sec.”, not “Sect.”.

- Page 2, line 144: Period is missing after Eq, “…namely Eq. (1) assumes…”.

- Stand-alone equations should be followed by punctuation because they are part of the text.

- Caption of Fig. 3: the letters (a), (b) and (c) should be referred to subfigures, which are not present. Either add the letters in the figure or include the axes description in the main text.

- Page 6. Line 164: this seems to be a heading.

- Figure 5: The text in the white boxes is too small. Also, the resolution should be increased (like in Fig. 7).

- Is there a quantitative measure for assessing the actual figure-of-eight motion? This would be useful for comparing the different control algorithms. If this measure does not exist, could the authors define a new one that could be used in future studies?

Author Response

Very good paper. It is certainly scientifically relevant and could be of interest to a wide part of the wind energy community. The contributions are well-defined and clear throughout the paper. The methodology is mathematically rigorous, and the conclusions are supported by the results.

Response: Thank you.

I just have some minor comments:

- Page 1, line 38: “The rated power of the generator is typically determining the installation” should be “The rated power of the generator typically determines the installation”.

Response: Thank you, the reviewer's comment is modified in the (revised) manuscript (page 3, line 97).

- Last paragraph of introduction: “Section” is usually abbreviated with “Sec.”, not “Sect.”.

Response: We consistently follow Springer's "Guidelines for Contributions to Major Reference Works" which list "Sect." as abbreviation for "Section" (https://resource-cms.springernature.com/springer-cms/rest/v1/content/51958/data/v1)

- Page 2, line 144: Period is missing after Eq, “…namely Eq. (1) assumes…”.

Response: Thank you, this mistake is modified in the revised manuscript.

- Stand-alone equations should be followed by punctuation because they are part of the text.

Response: Thank you, all equations are followed by punctuation in the revised manuscript.

- Caption of Fig. 3: the letters (a), (b) and (c) should be referred to subfigures, which are not present. Either add the letters in the figure or include the axes description in the main text.

Response: Thank you, the figure has been revised from the ground up for the revised manuscript, does not use subfigures, and the information of the caption has been moved into the text.

- Page 6. Line 164: this seems to be a heading.

Response: Thank you, this mistake is modified in the new manuscript.

- Figure 5: The text in the white boxes is too small. Also, the resolution should be increased (like in Fig. 7).

Response: Thank you, the figure is regenerated as a vector file, also the size of the figure increased in the new manuscript.

- Is there a quantitative measure for assessing the actual figure-of-eight motion? This would be useful for comparing the different control algorithms. If this measure does not exist, could the authors define a new one that could be used in future studies?

Response: Thank you, a complete explanation for this point is added in the end of the two subsections 5.1 "Flight Condition I" and 5.2 "Flight condition II".

Reviewer 3 Report

In this paper, authors have numerically and experimentally compared the kite model to the identified model. Also, the pole placement is discrete space is adopted to have a stable closed-loop system robust to model uncertainties, which are due to unmeasured wind speed and changed shape of the kite. The system identification algorithm is applied to determine the parameters of a kite with variable-length tether used in a flight test of the 20 kW kite power system of TU Delft. Experimental data of this test were compared with the system identification results in real-time and significant changes were observed in the parameters of the dynamic model which heavily affect the resulting response.

In my opinion, this paper is of interest, especially having the experimental results included and compared. However, I have the following comments.

As you have claimed the closed-loop system is robust, please elaborate the uncertainty terms in the system model, and then show their corresponding effects. The pole placement is adopted to tune the controller gains. On the other hand, the presented system identification is used to identify the unknown parameters, in real-time. As this scheme is an online one, the authors should theoretically prove that the closed-loop system, i.e. equipped with system identification scheme, is stable. By that means, it is rather a standard approach to have an estimation scheme in the solution. But the stability is always proved considering the estimation scheme within the stability analysis, not separately. Please describe how the proposed controller is robust. As far as I know, in the discrete domain, to have a stable system, the poles must lie within a unit circle. However, one of the selected poles is -1.0771 which is outside of the unit circle, which is therefore unstable. Please let me know if this is the case. If so, please resolve this issue in the paper. In page 13, first line, the term LHS is used. I think it stands for the left-hand side. However, as it is not a well-known acronym please use left-hand side instead. In section 2, the operator or symbol (`) is used, which could lead to misunderstanding. Please use a better symbol and appropriately define it.

Author Response

In this paper, authors have numerically and experimentally compared the kite model to the identified model. Also, the pole placement is discrete space is adopted to have a stable closed-loop system robust to model uncertainties, which are due to unmeasured wind speed and changed shape of the kite. The system identification algorithm is applied to determine the parameters of a kite with variable-length tether used in a flight test of the 20 kW kite power system of TU Delft. Experimental data of this test were compared with the system identification results in real-time and significant changes were observed in the parameters of the dynamic model which heavily affect the resulting response.

In my opinion, this paper is of interest, especially having the experimental results included and compared. However, I have the following comments.

As you have claimed the closed-loop system is robust, please elaborate the uncertainty terms in the system model, and then show their corresponding effects.

Response: In Subsect. 2.1 we introduce a simplified kite system model, which is a single-input single-output (SISO) model that takes the relative steering action u_s on input and provides the course angle of the kite on output. The model is described by Eqs. (6), (7) and (8) of the (revised) manuscript. Additional parameters affecting this model are the instantaneous values of the azimuth and elevation angles and the apparent wind velocity. There are also a number of constants that have been determined experimentally for a specific kite (Hydra 14 m2). This simplified kite system model has been developed by co-author Uwe Fechner in the frame of his PhD research at TU Delft, for the specific purpose of flight controller development. We would like to stress that this model is not a dynamic (or quasi-steady) system model as it could be derived from the dynamic (or steady) force equilibrium at the kite, balancing aerodynamic, tether and gravitational forces with possible inertial force contributions. For this reason, we do not claim that this simplified system model gives a reasonably accurate representation of the flight dynamic behavior of the kite. It is, however, suitable for controller development and stability analysis, for which we use it in the manuscript.
In the following we compare the simplified kite system model with the analytical theory of tethered flight presented in Chapter 2 of the Springer textbook "Airborne Wind Energy". This chapter is cited in the manuscript and can be downloaded from https://doi.org/10.1007/978-3-642-39965-7_2. In the simplified kite system model we can formulate an expression for the tangential velocity v_k,tau of the kite by combining Eqs. (4), (6) and (7) of the (revised) manuscript. This expression is linearly dependent on the radius (tether length), elevation angle and apparent wind velocity. The exact (for m=0) expression of the tangential velocity v_k,tau is derived in Chapter 2 of the book, by combining Eqs. (2.10) and (2.20), which also includes Eqs. (2.21) and (2.22). As you can see this expression is a lot more complicated, containing trigonometric factors from elevation angle, azimuth angle and course angle, as well as the lift-to-drag ratio of the kite and the reeling factor f. It does however not include and influence of the tether length nor of the apparent wind velocity. For this we do have to realize that the simplified kite system model has been derived for constant tether length and for a specific kite with a given lift-to-drag ratio, so these values are implicitly covered by the fitting procedure to determine the model constants.
Including the above goes beyond the original objective of the paper and for this reason we are not including it in the manuscript. However, compared to the original version of the manuscript we have substantially improved the derivation of the simplified kite system model.

The pole placement is adopted to tune the controller gains. On the other hand, the presented system identification is used to identify the unknown parameters, in real-time. As this scheme is an online one, the authors should theoretically prove that the closed-loop system, i.e. equipped with system identification scheme, is stable. By that means, it is rather a standard approach to have an estimation scheme in the solution. But the stability is always proved considering the estimation scheme within the stability analysis, not separately. Please describe how the proposed controller is robust. As far as I know, in the discrete domain, to have a stable system, the poles must lie within a unit circle. However, one of the selected poles is -1.0771 which is outside of the unit circle, which is therefore unstable. Please let me know if this is the case. If so, please resolve this issue in the paper.

Response: We ave added the following explanation in the resubmitted manuscript:
-The characteristic equation in our model is polynomial with order three. We applied Jury's stability test and found all roots are located inside the unit circle as a condition for stability. Jury's stability test is similar to the Routh-Hurwitz stability criterion used for continuous time systems. Although Jury's test can be applied to characteristic equations of any order, its complexity increases for high-order systems.
-We found mistakes in Eqs. (49) and (51) of the (revised) manuscript, also the numerical values of the poles of the closed-loop TF in the z-form in line 285, that we have corrected. However, Eq. (52) is written correctly which is the combination of Eqs. (49) and (51).

In page 13, first line, the term LHS is used. I think it stands for the left-hand side. However, as it is not a well-known acronym please use left-hand side instead.

Response: we have written out left-hand side.

In section 2, the operator or symbol (`) is used, which could lead to misunderstanding. Please use a better symbol and appropriately define it.

Response: we have replaced this symbol.

Round 2

Reviewer 1 Report

The revision has addressed my comments.

Reviewer 3 Report

I appreciate the authors for addressing my comments. Now, I believe this paper can be accepted in the present form.