In wind energy research, airborne wind energy systems are one of the promising energy sources in the near future. They can extract more energy from high altitude wind currents compared to conventional wind turbines. This can be achieved with the aid of aerodynamic lift generated by a wing tethered to the ground. Significant savings in investment costs and overall system mass would be obtained since no tower is required. To solve the problems of wind speed uncertainty and kite deflections throughout the flight, system identification is required. Consequently, the kite governing equations can be accurately described. In this work, a simple model was presented for a tether with a fixed length and compared to another model for parameter estimation. In addition, for the purpose of stabilizing the system, fuzzy control was also applied. The design of the controller was based on the concept of Mamdani. Due to its robustness, fuzzy control can cover a wider range of different wind conditions compared to the classical controller. Finally, system identification was compared to the simple model at various wind speeds, which helps to tune the fuzzy control parameters.

Airborne wind energy (AWE) systems are very promising energy sources that use
flying devices. These devices can fly at high altitudes. Therefore, power can
be generated by harvesting stronger and more persistent wind. The kite system
is one of the AWE systems being developed. It consists mainly of two parts,
a flexible wing and a generator on the ground connected by a tether. To
capture as much power as possible from wind, the kite should fly at a high
crosswind speed. To satisfy this, control is applied to the kite to keep it
flying at high altitude, and perpendicular to the direction of the wind in an
optimized path

AWE systems can capture more energy with higher capacities, which is why they
are considered a good renewable energy system. The wind energy density at an
altitude of 10

Wind energy density ranges from 1400 to 4500

The power generation by AWE follows several concepts; however, in this paper we have only mentioned two different concepts. The first concept is based on the tension force in the tether. The crosswind-flying wing pulls the tether, which is wrapped around a drum on the ground connecting it to the generator, until the tether reaches its maximum length. Then, it is reeled back to the minimum length allowed based on the design limitations. The second concept depends on installing wind turbines mounted on the wing itself, which generates energy during crosswind flight. It sends the generated energy through the electrified tether to the ground. It is crucial for the kite system to control its motion for efficient and reliable operation.

The optimum trajectory for kite flight is one of the key control parameters
that can be decided by a flight path planner. To keep the kite on this
planned trajectory, a winch controller controls the tether length. The kite
flight has two main phases, as shown in Fig.

Working principle of the pumping kite power system

Many researchers have studied the control of the kite system

Neural network modeling was an idea that was analyzed, but the results were
not satisfactory. Quasi-static modeling was also considered for more accurate
controller implementation, but the results were not sufficient for validation

Experimental efforts for the autonomous take-off of the airborne systems were
carried out, however there are still some challenges to get fully autonomous
flight in different wind conditions. Moreover, a global controller that can
work under all conditions cannot be designed effectively for the commercial
products

Thus, alternative techniques are needed to stabilize the flight trajectory.
One technique is very promising for fixed short tethers, as it does not
require information about the wind field or the kite and still performs quite
well

The uncertainty of the kite's models
has recently been presented in

In this paper, the least square estimation (LSE) was used as a system identification to get a more accurate description for the steering dynamics of the kite in real time; the characteristics of the kite are varying with time because the wing is inflatable and flexible. Also, the wind speed can not be measured in real time, thus it is impossible to obtain the lift and drag forces during flight. This technique especially is used to identify the system parameters as it can calculate them analytically without iteration which means short calculation times and low chance of singularity in the solver.

The novelty of this work is to use an algorithm that is valid for any kite size and any tether length, so it can overcome the problems of the uncertainty. The LSE algorithm needs the steering values from the motors and the course angle from the sensors. Thus, no additional information is needed, such as the wind speed or the mathematical model of the kite, to identify the system that shall be controlled. Therefore, this paper tries to stabilize the kite using fuzzy control based on the LSE in real time.

This paper is divided into five main sections. The first section is the
introduction, which gives an overall view of
the previous research related to the paper's work. The second section shows
the mathematical model (Sect.

Different mathematical models have been used to derive the kite governing
equations. Some of these models considered the system as a kite connected
with two control tethers without considering the variation of the angle of
attack. These assumptions were considered to allow for an easier
implementation of the kite's dynamic states

Recent work considered the kite with a variable tether length and started to
derive mathematical models for this variation of the tether length.
A discretized tether model was derived during the reel-in and the reel-out
phases using the Lagrangian approach to obtain the governing equations.
Moreover, this model considered the segments of the tether as a rigid body
connected by spherical joints

Other research groups considered the tether model as a discretized tether
with point masses connected by springs to each other, and aerodynamic
analysis was performed using the vortex lattice method; however, the phases
of reeling-in and reeling-out were not mentioned in the analysis

Some studies on kite design are being conducted to assess the aerodynamic
characteristics. They applied the fluid-structure interaction method to study
the aero-elasticity of the kite since the kite consists of an inflatable wing

Recent work on kite modeling has been achieved at TU Delft by

This section is divided into three main subsections. The first subsection
presents the system model and gives a full description for the kite
kinematics framework (Sect.

As mentioned in the introduction, there are
different concepts to derive the mathematical model of the kite

To give a complete definition of the kite model, it is important to introduce
the different frames used in the derivation of the mathematical model of the
kite. The first frame is called the “Earth Centered–Earth Fixed”, and the
position of the kite and the ground station are measured there. These
measurements have to be converted into the “wind reference frame” as shown
in Fig.

Based on the given frames of the kite system, the given axes

To control the system using the classical control, the system should be
converted into a single input single output (SISO) model

Designing the FPP mainly depends on previous ordered positions that show the required flight path of the kite and the points that the kite should be steered toward. In the work presented in this paper, there are two points called attractor points, on the right and left sides of the wind window, to make the kite fly in a figure eight motion. The figure eight shape was chosen for different reasons: it gives the kite the chance to fly over the wind window to produce more power, by increasing the relative wind velocity. It also aids in smooth steering and reduces the overlapping that occurs if a circular motion is used.

Four-step flight path planner for flying a figure eight: First turn
left, then steer toward

Figure

This offset is needed to compensate for the time delay between the command to stop turning and the kite actually stopping. This value depends mainly on the rotational inertia of the kite but also on the speed of the steering actuators

.Finite sub-states of the figure-eight flight path planner.

Finite sub-state diagram showing the sub-state and the transitional
condition of the figure eight controller. This sub-state machine is active in
the state FIG-8 of the high-level controller. The states LAST-LEFT and
LAST-RIGHT are omitted for simplicity

To design the FPP, we need to define the inputs and the output for the
algorithm. The kite orientation

The FPP algorithm needs to obtain the values of

Schematic to show the turn rate law of the kite as a function of the
angular velocity and turn radius

As shown in Fig.

The kite's position can be controlled using the setting values of the
elevation, the azimuth and the normalized depower setting

Simulink is commercial
software developed by MathWorks. It is a graphical programming tool for
different aspects of engineering. However, it is used here to
represent the system's model and design the controller for a fixed sample
time. It mainly aims to save time for the user by replacing long code with
simple blocks to achieve the same requirements. Simulink is widely used in
automatic control and digital signal processing

The aim of this section is to identify the variation of the system parameters
during flight. The parameters must be updated in real time by analyzing the
history of the model's input (control action) and output data (course angle).
Least square estimation (LSE)

This figure shows that the system is SISO with the course angle required as an input, and the output is the measured course angle of the kite. Then, the error would be calculated from the difference between the input and measured course angle obtained from the sensors. Then, the error signal will be the input for the controller block (adaptive controller) to obtain the suitable control action.

The system identification block will use the control action results from the
controller block and the measured course angle as input and then begin
estimating the system's parameters (Eq.

Block diagram of the adaptive control system.

This algorithm has the advantage of quickly obtaining system parameter values
and has no singularity for any initial conditions, even if they are zeros.
The LSE uses the motor action

Initialize matrix

Calculate

Update

Repeat the loop for each time step.

Fuzzy logic control system.

In this section, the control strategy is detailed using Mamdani's fuzzy
algorithm

The computations of fuzzy control were calculated as hardware-in-the-loop
(HIL)

The kite system consists of an inflatable wing, and its shape changes with
time due to the force distribution on its surface. Thus, the mathematical
model of the kite cannot be fixed during the whole flight. Moreover, the wind
speed varies during the flight, and there is no accurate way to assess it in
real time to calculate the force distribution on the kite's surface

Due to all these difficulties, the need for robust control such as fuzzy control to stabilize the kite is very important. Therefore, choosing the fuzzy logic controller is a good choice to satisfy these requirements because it is strong in stabilizing nonlinear systems and can address systems with inaccurate mathematical models. However, the fuzzy logic controller is difficult to implement on small-sized commercial microcontrollers since it requires many calculations that are difficult to implement on microcontrollers fixed on the kite's surface. Therefore, sending the sensor data to the ground station by wireless communications and performing the calculation using a ground station is a good choice to obtain the control action. This step causes a delay due to the transmission time, which is considered in the model and calculation.

Mamdani's model consists of three stages to stabilize the kite system,
including fuzzification
(Sect.

The main membership of fuzzification and defuzzification.

The process arranges the inputs of the fuzzy logic control to obtain the
fuzzy set membership values in the various input universes of discourse

The range of the error was estimated based on the
error of the classical control in Sect.

This is the second stage of the fuzzy logic algorithm. It consists of
“if-statements”

This style of fuzzy logic control is called the Mamdani rule. Choosing the
rule base of the fuzzy logic control depends on the designer's experience
with the system. The designer of the rule bases chooses them based on the
mathematical model of the system. From the experience of the kite system, the
rule bases are chosen as follows:

This is the last stage of the fuzzy logic control. It is the process of
converting the set of inferred fuzzy signals chosen from the fuzzy output, as
mentioned in the rule base (Sect.

This section shows the result of the system identification
(Sect.

Two flight conditions were tested in this simulation. The difference between
the two flight conditions is the wind speed. The wind speed is modeled as
shown in Figs.

In the first flight condition, the kite model was affected by the wind speed
given in Fig.

As mentioned in Sect.

In the second flight condition, the wind speed was changed as given in
Fig.

This paper presented a technique to identify the kite's parameters and controller that would be robust enough to stabilize the kite in real time when other classical controls cannot satisfy this. Using the least square estimation algorithm for system identification helps to present a complete definition for the kite's parameters in real time. The variation of the kite's parameters comes from the changes in wind speed and direction, the change in the aerodynamic coefficients, and the change in the kite's shape (as it consists of an inflatable wing).

The kite model is mainly non-linear. Therefore, the choice of fuzzy control
is suitable for such systems. Additionally, the computations of fuzzy control
were calculated as HIL. When deriving the system identification equations,
the model was considered as a discrete linear model with a short sample time.
The results of the system identification were compared with the classical
model for different wind speeds, as shown in
Figs.

The wind field data and the model implementation code could be made available in the framework of a cooperation agreement. Please contact the corresponding author for further information.

The kite is moving in two directions (spherical coordinates).

The law states that the turn rate of the kite about its yaw axis is
a function of the steering deflection of the actuator

The steering value of the motor

Comparison between the estimated turn rate and the measured turn rate for the 25

An empirical relationship is achieved in

Fitted turn rate law parameters of the Hydra kite

All authors declare that there is no support from any organization for the submitted work. There are have been no financial relationships with any organizations that might have an interest in the submitted work in the previous three years. There are no other relationships or activities that could have influenced the submitted work.

Roland Schmehl was supported by the H2020-ITN project AWESCO funded by the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 642682. Edited by: Joachim Peinke Reviewed by: two anonymous referees