Fault-Tolerant Neuro Adaptive Constrained Control of Wind Turbines for Power Regulation with Uncertain Wind Speed Variation

Round 1

Reviewer 1 Report

This paper considered the faults as bounded uncertainties and an adaptive neural network controller is designed to achieve robust control. Generally speaking, this paper is not much interesting and badly written. It is very difficult to read the paper. Detailed comments are listed as follows:

Novelty of the paper is weak. Adaptive neural network has been widely used to cope with nonlinear system control for several decades. Thus, the proposed algorithm is not novel. This method is used for wind turbine control in this paper. However, only simulation results are given based on a well defined model. The simulation results are not convincing, because the unmodeled dynamics in real systems are not considered during algorithm design, which means we cannot say the proposed method is better than PID. Does system (25) define the desired operational mode? If it is, then it is strange to design a controller for the desired system but not for the real system. The symbols used in this paper is easy to be confused. There are so many symbols but they are not clearly defined. It is suggested to provide a symbol index before the text. In addition, some variables such as xt, w_{r,s} are not defined in the paper. ΔTa|ΔCp and Ta)β are bad symbols. d defined in (41) includes the term  ΔTa|ΔCp is state dependent, but it is treated as a bounded constant in the algorithm design. In Line 408. The reviewer cannot understand why G is bounded due to Ta)β, which is state-dependent. In Eq (46), \hat_ρf will converge to 0. How can it be used to estimate ρf, which is an unknown constant? In Section 2-4, symbols and equations should be more clear and easy for read.

Author Response

This paper considered the faults as bounded uncertainties and an adaptive neural network controller is designed to achieve robust control. Generally speaking, this paper is not much interesting and badly written. It is very difficult to read the paper.

Authors’ response:

We appreciate the comments from the reviewer. Your comments show that this paper has been carefully read for which we are grateful, because your comments have given us the opportunity to significantly improve the paper.

The response to your comments is as follows. This new version has been proofread by native English speakers, to improve its written English. Also, we have highlighted the contribution and novelties. Finally, the paper has been revised to let the readers easily read and understand.

The response to your comments is as follows. Also, any change in the paper, regarding to your comment, is addressed here and accordingly, is highlighted in the manuscript.

Detailed comments are listed as follows:

Novelty of the paper is weak. Adaptive neural network has been widely used to cope with nonlinear system control for several decades. Thus, the proposed algorithm is not novel.

Authors’ response:

The adaptive neural network application on nonlinear system, e.g. wind turbines, has been used for decade, as we reviewed the corresponding literature in the paper. However, as we clearly mentioned in the paper, the novelty of the algorithm is the constrained power control of the wind turbine, using BLF constrained control. We should inform the reviewer that this has not been applied on the wind turbines. On the other hand, to cope with the unknown wind speed variation, the Nussbaum type function has been utilized. Again, this is novel and has not been considered in the wind turbine control design. To address the novelties and contribution, see the lines 88-133, which are mentioned below.

Motivated by the aforementioned considerations the primary objective of this paper is to design the pitch actuator control of wind turbines under uncertain wind speed variation to constrain the rotor speed and the generated power within the safe-to-operate bounds. These bounds are defined in order to avoid the engagement of the mechanical brake. In this manner, the over speeding as well as the conservative power generation problems are resolved. The main idea consists of developing the BLF-based control to provide constrained behavior and further utilizing a Nussbaum-type function to cope with the unknown wind speed variation. The former is utilized to keep the generated power within the given desirable constraints, provided by the designer, and the latter is exploited to regulate the power without requiring the accurate wind speed measurement, observation or estimation.

With the adoption of BLF-based constrained control, the rotor speed and its variation are constrained, and consequently, the variation of generated power around the nominal power will not violate the predefined constraint. This guarantees the safe, desirable nominal power generation, and less mechanical brake engagement. The Nussbaum-type function is adopted to handle the unknown control direction problem, which is stemming from uncertain wind speed and consequent uncertain aerodynamic torque variation. Accordingly, the need for accurate wind speed measurement is avoided. The pitch actuator faults effects, including effectiveness loss, pitch angle bias, hydraulic leak, high air content in the oil, and pump wear, are compensated automatically via adaptive fault-tolerant controller design. Also, the effect of blade aerodynamic characteristic changes, due to debris build-up and erosion, is considered and mitigated. The fault information, including fault type, size and time, is estimated, which can be used for maintenance operations. Smooth pitch actuator saturation is designed to avoid harsh and fast pitch actuator saturation phenomenon which may increase the structural load on the wind turbine and performance degradation. Also, a neural network estimator is adaptively augmented in the proposed controller, to obtain the uncertain aerodynamic torque. The control design is fulfilled in the backstepping framework, utilizing the virtual control concept. In this regard, the repeated differentiation of virtual control is required, which increases the complexity of the designed controller order. DSC technique is used to eliminate this problem by introducing a first-order filter.

This method is used for wind turbine control in this paper. However, only simulation results are given based on a well-defined model. The simulation results are not convincing, because the unmodeled dynamics in real systems are not considered during algorithm design, which means we cannot say the proposed method is better than PID.

Authors’ response:

Regarding the simulation results, the unmodelled dynamics and the disturbances are considered, including pitch actuator saturation, blade aerodynamic characteristics change due to debris build up, pitch actuator dynamic change, bias, and effectiveness loss, and the pressure drop due to hydraulic oil leakage, high air content in the oil, and pump wear. Therefore, it is capturing the real wind turbine operation. Regarding the results, the proposed method is obviously better than the PID. Besides the illustrative figures, we have used the numerical criteria to investigate the results. Whether in fault free situation, or in the faulty situation the performance of the proposed controller is better than the PID, see the figures 6-9, 13-16, 19-22, 27 and 28, and tables 3, 5, 8 and 9.

Does system (25) define the desired operational mode? If it is, then it is strange to design a controller for the desired system but not for the real system.

Authors’ response:

To avoid this misunderstanding, we have clearly explained below equation (25), that this expression describes the wind turbine rotor dynamic behaviour in the desired operational mode, which takes into account possible pitch actuator dynamic changes. Also, smooth pitch angle saturation is included. Indeed, this is desired operational mode of wind turbine affected by disturbance, faults and saturation. It is rather a standard approach to represent the normal model affected by the faults, disturbance, uncertainty, and so on.

The symbols used in this paper is easy to be confused. There are so many symbols but they are not clearly defined. It is suggested to provide a symbol index before the text.

Authors’ response:

We reviewed the paper and made sure that all the symbols are well-defined. Also, we added a nomenclature table, for ease of readability.

In addition, some variables such as xt, w_{r,s} are not defined in the paper. ΔTa|ΔCp and Ta)β are bad symbols.

Authors’ response:

We made sure that all variables have been clearly defined. See lines 149, 166 and 167 for the mentioned variable. ΔTa|ΔCp and Ta)β are replaced by and , respectively.

d defined in (41) includes the term ΔTa|ΔCp is state dependent, but it is treated as a bounded constant in the algorithm design. In Line 408.

Authors’ response:

This has been clearly explained in lines 307-310. For your convenience it is mentioned below.

is due to , which is the result of the changes in the blade aerodynamic characteristics. The debris build-up and erosion occur slower than the mean time to the maintenance of the blades. So, all terms which are contributing to are assumed to be bounded, then is bounded as, , where is an unknown positive constant.

The reviewer cannot understand why G is bounded due to Ta)β, which is state-dependent.

Authors’ response:

This issue has been described in Remark 1. For your convenience it is mentioned below.

Remark 1. In Figure 4, it is evident that with . This means that, as the wind speed increases, by increasing pitch angle, the aerodynamic torque decreases.

In Eq (46), \hat_ρf will converge to 0. How can it be used to estimate ρf, which is an unknown constant?

Authors’ response:

We appreciate the reviewer for this helpful comment. Actually, this estimation is omitted in the revised version as the estimation will not be used in the controller structure. This is only used in the analysis of stability. This approach has been described in the following paper, which has been cited.

Lan, J.; Patton, R.J.; Zhu, X. Fault-tolerant wind turbine pitch control using adaptive sliding mode estimation. Renew Energy 2018, 116, 219-231.

This is clearly explained in the revised version, lines 417-420. For your convenience it is mentioned below.

It should be noted that this bound is only used to analyse the stability of the closed-loop system. Nevertheless, this will not be used in the designed control structure, as it is assumed to be unknown. So, the actual estimation will not be required in setting up and implementing the control scheme.

In Section 2-4, symbols and equations should be more clear and easy for read.

Authors’ response:

We considered the paper and made sure that all the symbols are well-defined. Also, we added a nomenclature table, for ease of readability.

We thank the reviewer for the helpful comments and for the opportunity to further improve the paper. We would like to thank the reviewer for the recommendations to our paper for publication and appreciate the time taken for the review process.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is well written, the concept is scientifically sound and described in good detail and the presentation of the state of the art is very good and provides a comprehensive analysis of the different projects and initiatives which constitute the background to the work.

However, in terms of how the methods are described,  it is not clearly explained how the RBF approximates the nonlinear dynamics of the wind turbine. Also the paper is scarce of information on the architecture of radial basis function neural network model, how the RBF neural network model is trained, on which reasons the number of hidden (RBF) units and unit centers for the RBF neural network have been selected, how the weights updating rules are obtained for optimization, information on the accuracy of the RBFNN, etc. More references on the RBFNN should be provided.

Author Response

The paper is well written, the concept is scientifically sound and described in good detail and the presentation of the state of the art is very good and provides a comprehensive analysis of the different projects and initiatives which constitute the background to the work.

Authors’ response:

We appreciate the comments from the reviewer. Your comments show that this paper has been carefully read for which we are grateful, because your comments have given us the opportunity to significantly improve the paper. The response to your comments is as follows. Also, any change in the paper, regarding to your comment, is addressed here and accordingly, is highlighted in the manuscript.

However, in terms of how the methods are described, it is not clearly explained how the RBF approximates the nonlinear dynamics of the wind turbine. Also the paper is scarce of information on the architecture of radial basis function neural network model, how the RBF neural network model is trained, on which reasons the number of hidden (RBF) units and unit centers for the RBF neural network have been selected, how the weights updating rules are obtained for optimization, information on the accuracy of the RBFNN, etc. More references on the RBFNN should be provided.

Authors’ response:

We appreciate the comments from the reviewer. Due to universal approximation capability of RBF over a compact set, in this paper it has been used to estimate the unknown aerodynamic torque. In the section 5.1, we have introduced the structure of RBF. For your convenience it is mentioned here.

The wind speed is uncertain as the wind speed is measured with an anemometer, usually placed at the back of the nacelle. Therefore, its measurement is affected by the turbulence generated by the rotor. So, the wind speed is considered as an uncertain disturbance. Accordingly, the aerodynamic torque is not accurately available. On the other hand, is contributing in the rotor dynamic response (25). So, should be estimated to be used in the proposed controller structure. In this paper, an RBF neural network is designed to estimate aerodynamic torque. To this end, is approximated as:

,

(26)

where, is the optimal weight vector, is the known basis functions vector, is the number of neural network nodes, , is the approximation error, and is selected as a Gaussian function given by [9]:

,

(27)

where, is the centre vector of the inputs, for . is the width vector of the Gaussian functions. is the approximation of provided by the RBF, described as:

,

(28)

The optimal weight vector, i.e. is defined as . It should be noted that is bounded as, , with unknown bound .

In the construction of the controller, the weights updating rules are defined in the adaptive manner, see (44). Therefore, in the Lyapunov stability analysis, it has been proved that the estimation error, i.e. , approaches to zero. The powerful point of this approach is that no offline training is required for the RBF, as the layer weights are being updated online.

Regarding the unit numbers and unit centers, we have numerically tuned them by trial and error approach, to cover the whole compact set of the variables, in which the aerodynamic torque is going to estimated. We also provided the new references on the RBF. For your convenience, they are mentioned here.

 

Jafarnejadsani, H.; Pieper, J.; Ehlers, J. Adaptive control of a variable-speed variable-pitch wind turbine using radial-basis function neural network. IEEE Trans Control Syst Technol 2013, 21, 2264-2272.

 

Shanzhi, L.; Haoping, W.; Yang, T.; AITOUCHE, A. A rbf neural network based mppt method for variable speed wind turbine system. IFAC-PapersOnLine 2015, 48, 244-250.

 

Habibi, H.; Nohooji, H.R.; Howard, I. Optimum efficiency control of a wind turbine with unknown desired trajectory and actuator faults. ‎J Renew Sustain Energy 2017, 9, 063305.

 

Rahimi, H.N.; Howard, I.; Cui, L. Neural impedance adaption for assistive human–robot interaction. Neurocomputing 2018, 290, 50-59.

Ge, S.S.; Hang, C.C.; Lee, T.H.; Zhang, T. Stable adaptive neural network control. Springer Science & Business Media: 2013; Vol. 13.

Ge, S.S.; Hong, F.; Lee, T.H. Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans Syst Man Cybern 2004, 34, 499-516.

 

We hope the reviewer's response will be positive in this new version of the paper. Please advise us if there is any further suggestion or if the reviewers are not satisfied.

We thank the reviewer for the helpful comments and for the opportunity to further improve the paper. We would like to thank the reviewer for the recommendations to our paper for publication and appreciate the time taken for the review process.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have clearly solved the reviewers' concerns. I recommend that this paper can be accepted now.