# An Improved Uncertainty and Disturbance Estimator-based Speed Control for Grid-Connected Pumping Kite Wind Generator

Mouaad Belguedri, Abdeldjabar Benrabah, Farid Khoucha, Mohamed Benbouzid, Khelifa Benmansour

► To cite this version:

Mouaad Belguedri, Abdeldjabar Benrabah, Farid Khoucha, Mohamed Benbouzid, Khelifa Benmansour. An Improved Uncertainty and Disturbance Estimator-based Speed Control for Grid-Connected Pumping Kite Wind Generator. Control Engineering Practice, 2024, 143, pp.105795. hal-05340333

HAL Id: hal-05340333

https://hal.univ-brest.fr/hal-05340333v1

Submitted on 31 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# An Improved Uncertainty and Disturbance Estimator-based Speed Control for Grid-Connected Pumping Kite Wind Generator

Mouaad Belguedriª, Abdeldjabar Benrabahª, Farid Khouchaª, Mohamed Benbouzidᵇᶜ, Khelifa Benmansourᵈ

## Abstract

Pumping kite generator systems (KGS) represent a novel and exciting concept for future wind energy harvesting at higher altitudes where the wind is more reliable, stable, and highly predictable. The configuration of such systems generally employs a flying tethered kite attached to a generator/motor and connected to the grid using a power electronic interface. This work aims to enhance control system efficiency and increase the generated power by improving the speed control of the generator. To this end, an uncertainty and disturbance estimator (UDE) based speed controller is developed to deal with the challenges presented by this new technology, particularly periodical variation of the rotational speed reference in maximum power point tracking. The practicality and effectiveness of the proposed UDE-based control method are demonstrated through simulation and experimental results. It is shown that the proposed control strategy offers improved tracking performance and robustness against model uncertainties and external disturbances.

**Keywords:** Pumping kite generator, uncertainty and disturbance estimator, synchronous machine, robust control.

## 1. Introduction

Recently, a new class of wind energy converters has been conceived under the name of kite wind generators or power kites. To overcome conventional wind turbines limitations, these new technologies employ controlled tethered power kites in order to harness the high-altitude, stronger, and more stable wind, with more competitive cost (Fagiano et al., 2009).

The technical challenge of this new concept is how to transmit wind energy to the ground. One solution is to drive a ground-based synchronous machine (SM) using tethered kites. The power kite tether is rolled around a drum linked to an electrical drive positioned on the ground level. Through this phase, the wind force on the kite unrolls the tether leading to the rotation of the drum and the electric drive that will operate as a generator. When the tether reaches its maximum length, the machine operates in a motor mode to retrieve the kite, consuming a small percentage of the generated power.

Recently, wind power kite generators have been undergone a lot of research and demonstrations that principally focused on the aerodynamic aspect, i.e., aerodynamic characteristics of tethered wings (Schmidt et al., 2019), aerodynamic performance (Akberali et al., 2021, Yan and Zhang, 2022), flight path tracking control (Zempoalteca-Jimenez et al., 2021, Costello et al., 2017), automatic flight control (Bari and Khan, 2020, Todeschini et al., 2021), power optimization (Berra and Fagiano, 2021, Stuyts et al., 2014). However, the configuration and control of the electrical part have not been fully investigated.

Although this new wind turbine technology operates in a less disturbed environment than the traditional wind generator, the

complexity of its aerodynamic characteristics made it very difficult, if not impossible, to obtain an accurate modeling of the system. Moreover, the optimal reeling-out speed is generally time- and space-varying in the traction phase because of the path of the kite and the wind speed (Berra and Fagiano, 2021). In fact, in this phase, the instantaneous optimal value of the tether reeling speed is 1/3 of the wind speed component along the tether direction (Argatov and Silvennoinen, 2010, Fagiano and Milanese, 2012), which results in a periodical variation of the rotational speed reference in maximum power point tracking (MPPT) control. These challenges make the standard control laws very limited in order to maximize the harvested energy. Therefore, the use of advanced control techniques for speed control is inevitable.

In (Ahmed et al., 2013), the rotational speed of a grid-connected closed-orbit KGS has been controlled using a proportional-integral (PI), although its robust performance remains unaddressed. Meanwhile, the industry relies on manual tuning of PID/PI controllers, following a trial-and-error approach based on the empirical experience of plant operators. Nevertheless, this process represents a considerable challenge for operators, who have to accurately tune multiple parameters to achieve satisfactory performance (Sun et al., 2019). In (Mademlis et al., 2018), the problem of the periodical variation of rotational speed and shaft torque has been introduced in MPPT control of a tidal undersea Kite system. A PI control loop with active damping has been applied for generator speed control. However, the tracking performance has been poor for the fast kite speed motion. In (Saberi and Rezaie, 2022), a finite-control-set model predictive control with adaptive cost function and a terminal sliding mode disturbance observer have been

<footnote>ªEcole Militaire Polytechnique, UER ELT, 16111 Algiers, Algeria</footnote>

<footnote>ᵇUniversity of Brest, UMR CNRS 6027 IRDL, 29238 Brest, France</footnote>

<footnote>ᶜShanghai Maritime University, Shanghai, Pudong 201306, China</footnote>

<footnote>ᵈUniversity of Medea, Medea, Algeria</footnote>
used to control the speed of PMSG attached to a KGS.
Nevertheless, the speed reference was considered constant.

<table><thead><tr><th>Nomenclature</th><th></th></tr></thead><tbody><tr><td>F</td><td>Total force acting on the kite</td></tr><tr><td>F<sub>grav</sub></td><td>Gravity force</td></tr><tr><td>F<sub>app</sub></td><td>Apparent force</td></tr><tr><td>F<sub>aer</sub></td><td>Aerodynamic force</td></tr><tr><td>F<sub>trac</sub></td><td>Tether traction force</td></tr><tr><td>W<sub>e</sub></td><td>Effective wind speed</td></tr><tr><td>W<sub>0</sub></td><td>Wind speed</td></tr><tr><td>W<sub>a</sub></td><td>Kite speed</td></tr><tr><td>F<sub>L</sub></td><td>Lift force</td></tr><tr><td>F<sub>D</sub></td><td>Drag force</td></tr><tr><td>A</td><td>Kite surface</td></tr><tr><td>ρ</td><td>Air density</td></tr><tr><td>C<sub>L</sub></td><td>Lift coefficient</td></tr><tr><td>C<sub>D</sub></td><td>Drag coefficient</td></tr><tr><td>E</td><td>Aerodynamic efficiency coefficient of the kite</td></tr><tr><td>r̂<sup>trac</sup></td><td>Kite speed along the cable direction</td></tr><tr><td>θ</td><td>Polar angle</td></tr><tr><td>φ</td><td>Azimuth angle</td></tr><tr><td>r̂<sup>trac</sup><sub>opt</sub></td><td>Optimal kite speed along the cable direction</td></tr><tr><td>J</td><td>Equivalent moment of inertia</td></tr><tr><td>D</td><td>Equivalent viscous damping coefficient,</td></tr><tr><td>ω<sub>r</sub></td><td>Machine rotor speed</td></tr><tr><td>ω<sub>ref</sub></td><td>Machine rotor speed reference</td></tr><tr><td>ω<sub>m</sub></td><td>Reference state</td></tr><tr><td>p</td><td>Pole pair number</td></tr><tr><td>φ<sub>m</sub></td><td>Flux linkage</td></tr><tr><td>i<sub>sq</sub></td><td>Q-axis stator current</td></tr><tr><td>α</td><td>Reference model bandwidth</td></tr><tr><td>β</td><td>Filter bandwidth</td></tr><tr><td>UDE</td><td>Uncertainty and disturbance estimator</td></tr><tr><td>SM</td><td>Synchronous machine</td></tr><tr><td>MPPT</td><td>Maximum power point tracking</td></tr><tr><td>KGS</td><td>Kite generator system</td></tr><tr><td>PI</td><td>Proportional-integral</td></tr><tr><td>MSC</td><td>Machine-side converter</td></tr><tr><td>GSC</td><td>Grid-side converter</td></tr></tbody></table>

Several advanced control strategies have been developed aiming to enhance speed control performance and efficiency of electrical drive, e.g., internal model control (Ping et al., 2021, Sebaa et al., 2017), sliding-mode control (Zhao et al., 2023, Zhang et al., 2012), adaptive backstepping control (Karabacak and Eskikurt, 2011) and Adaptive Fuzzy Control (Li and Gu, 2012, Zheng et al., 2021). These approaches have demonstrated their effectiveness in enhancing control performance in certain aspects, such as achieving faster transient responses and greater resilience against parameters mismatch and external torque disturbances. However, this improvement often comes at the cost of increased controller complexity.

In this work, the uncertainty and disturbance estimator (UDE) based speed controller is proposed to deal with the previous issues. The UDE-based control algorithm is based on uncertainty and disturbance estimation using an appropriate

filter. It was proposed in (Zhong and Rees, 2004) as an alternative to the time-delay control (TDC). The UDE-based control has been applied in several practical applications in linear and nonlinear systems such as piezoelectric stage (Ren et al., 2019), chaotic systems (Yi et al., 2020), quadrotors (Lu et al., 2020, Qian and Liu, 2019), robotic systems (Dong and Ren, 2017), tidal stream turbines (Yin and Zhao, 2019), grid-tied inverters (Ye and Xiong, 2017, Wu et al., 2019), electrical drives (Ren et al., 2016b, Li et al., 2019, Fu et al., 2020) and conventional variable-speed wind turbine (Ren and Zhong, 2013). In these contexts, it has been showing excellent performance over the years (Wang et al., 2020). In (Ren et al., 2016a), the design of the reference system and the filter has been addressed for different cases of the reference signal, step signal and sinusoidal signal separately. However, for KGS control, there is a compromise between imposing the desired dynamic of the system (rising time) in transition phases between traction and retraction phases, and the tracking performance (static error) in traction phases. Therefore, the control law has to guarantee a good tracking performance of the periodical speed reference in MPPT control for optimal energy extraction in generation phases, while maintaining a stable dynamic during transition phases. Due to its ability to decouple system dynamics from tracking performance (Ren et al., 2016a), the UDE-based control is a particularly suitable approach. By effectively separating these aspects, it offers a convincing solution that improves control accuracy and contributes to overall system stability.

The main contribution of this paper lies in developing an UDE-based speed control strategy suitable for open-orbit KGS. Moreover, an adequate reference model system is proposed to deal with the problem of periodical variation of rotational speed reference and increase tracking performance in order to maximize the power provided by the system.

The remainder of this paper is structured as follows: First, the power kite system is modeled in Section 2. The problem of disturbances and uncertainties of KGSs and periodical variation of rotational speed reference is presented in Section 3. The UDE-based speed control strategy is presented in Section 4. The feasibility and validity of the proposed control method are verified by simulation and experimental tests in Section 5. Finally, conclusions are drawn in Section 6.

## 2. Power Kite Generator Modeling

Fig. 1 shows the simplified structure of a kite generator system operating in the open-orbit/pumping mode adopted in this paper. The concept is to extract energy from high-altitude winds by controlling the kite to fly with high crosswind speed and transform the mechanical energy transmitted by a tether to drive a ground-based electric generator. The kite flies in a lying eight-orbits, rising in altitude and generating energy until the tether reaches its maximum length, so the recovery phase starts by reeling in the tether and consuming energy (Ahmed et al., 2011). In this work, only the generation phase is considered.

The forces acting on the kite are:

$$F=F_{grav}+F_{app}+F_{aer}+F_{trac} \quad (1)$$
<figure><img src="image_2.png" /><figcaption>Fig. 1. Simplified kite generator system operating in pumping mode.</figcaption></figure>

where $F_{grav}$ is the gravity force, $F_{app}$ is the apparent force and $F_{aer}$ is the aerodynamic force, which depends on the effective wind speed $W_e$ given by

$$ \overline{W_e} = \overline{W_0} - \overline{W_a} \quad (2) $$

Where $W_0$ is the wind speed and $W_a$ is the kite speed.

The aerodynamic force has two components: lift force $F_L$ and drag force $F_D$ expressed by (Ahmed et al., 2011)

$$ F_L = \frac{1}{2} \rho A C_L |\overline{W_e}|^2 \quad (3) $$

$$ F_D = \frac{1}{2} \rho A C_D |\overline{W_e}|^2 \quad (4) $$

where $A$ is the kite surface, $\rho$ is the air density, $C_L$ is the lift coefficient and $C_D$ is the drag coefficient.

For simplicity, the inertial and apparent forces are assumed to be negligible with respect to the aerodynamic forces. In addition, the tether weight and drag force are also neglected. The tether traction force $F_{trac}$ is obtained using the same method applied in (Fagiano et al., 2009, Ahmed et al., 2011). It is given by:

$$ F_{trac} = \frac{1}{2} \rho A C_L E^2 \left( 1 + \frac{1}{E^2} \right)^{3/2} |\overline{W_{e,r}}|^2 \quad (5) $$

where $W_{e,r}$ is the effective wind speed along the cable direction and $E$ is the aerodynamic efficiency coefficient of the kite ($E=C_L/C_D$).

Assuming that the wind speed vector is aligned with the X axis, then $W_{e,r}$ is expressed as

$$ W_{e,r} = W_0 \sin(\theta) \cos(\varphi) - \dot{r}_{trac} \quad (6) $$

where $\dot{r}_{trac}$ is the kite speed along the cable direction, $\theta$ and $\varphi$ are the polar angle and the azimuth angle, respectively.

Moreover, the generated power can be given by

$$ P_{trac} = \frac{1}{2} \rho A C_L E^2 \left(1 + \frac{1}{E^2}\right)^{3/2} (W_0 \sin(\theta) \cos(\varphi) - \dot{r}_{trac})^2 \dot{r}_{trac} \quad (7) $$

To find the instantaneous optimal value of the tether's reeling speed, the derivative of $P_{trac}$ is computed with respect to $\dot{r}_{trac}$ as

$$ \frac{dP_{trac}}{d\dot{r}_{trac}} = \frac{1}{2} \rho A C_L E^2 \left(1 + \frac{1}{E^2}\right)^{3/2} \left[-2(W_0 \sin(\theta) \cos(\varphi) - \dot{r}_{trac})\dot{r}_{trac} + (W_0 \sin(\theta) \cos(\varphi) - \dot{r}_{trac})^2\right] \quad (8) $$

Then, by setting the derivative to zero and solving for $\dot{r}_{trac}$, two critical points are found. One of them ($W_0 \sin(\theta) \cos(\varphi)$)

makes the power equal to zero, so the instantaneous optimal value of the tether reeling speed is:

$$ \dot{r}_{trac} = \frac{W_0 \sin(\theta) \cos(\varphi)}{3} \quad (9) $$

<figure><img src="image_3.png" /><figcaption>Fig. 2. KGS optimal reeling speed.</figcaption></figure>

Fig. 2 shows the optimal reeling speed of the tether that should be pursued by the system to guarantee a maximum power extraction from the kite.

### 3. Problem Formulation

The KGS power electronic conversion system consists of a SM, a machine-side converter (MSC), a DC link, a grid-side converter (GSC), and an inductive filter as shown in Fig. 3.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Global diagram of the conversion system.</figcaption></figure>

The MSC is used to adjust the current and torque of the SM to ensure MPPT control. Meanwhile, the GSC control aims to maintain a constant DC-link voltage and control the power flow exchanged with the grid.

During power kite operation, the traction force of the tether is transformed through a drum and a gearbox to a mechanical torque applied on the SM that can be expressed by

$$ C_m = \frac{F_{trac}}{K_g} \quad (10) $$

where $F_{trac}$ is the traction force of the tether described in (5) and $K_g$ is the gearbox factor multiplied by the drum's diameter. The torque in (10) depends on the effective wind speed, which is affected by turbulences and unpredictable conditions (Ren and Zhong, 2013), and depends also on the accurate position of the kite. Therefore, it would be considerably challenging to create precise model of the dynamic characteristics of the KGS. Moreover, conventional controllers, such as PI, are designed by imposing a first- or a second- order response to the closed loop system, which is satisfying for a step reference. However, for a reference with a periodical variation, as in the case of KGS (Fig. 2), the system would be incapable of tracking the reference, as demonstrated in Fig. 4, causing a decrease in the generated
power. One solution is tuning the controller parameters to be higher for faster dynamic. However, that will affect the system stability, increase the control effort and can also introduce more overshoot without reaching sufficient tracking performances. In this paper, an UDE-based control scheme is proposed to deal with the previously stated issues.

<figure><img src="image_5.png" /><figcaption>Fig. 4. First- and second- order system response to a reference with periodic variation.</figcaption></figure>

# 4. KGS UDE-based Robust Control

## 4.1. UDE-based Control Law

The mechanical motion of the SM is characterized by the following equation:

$$J \dot{\omega}_r(t) = C_m(t) - C_g(t) - D \omega_r(t) \quad (11)$$

where J is the equivalent moment of inertia of the rotating systems, D is the equivalent viscous damping coefficient, $\omega_r$ is the machine rotor speed, and $C_g$ is the generator load torque defined as

$$C_g(t) = \frac{3}{2} p \varphi_m^i \dot{sq}(t) \quad (12)$$

where p is the pole pair number, $\varphi_m$ is the flux linkage, and $\dot{sq}$ is the q-axis stator current.

Putting $x(t) = \omega_r(t)$ as the state and $u(t) = i_{sq}(t)$ as the control input, (11) can be rewritten as

$$\dot{x}(t) = Ax(t) + Bu(t) + u_d(t) \quad (13)$$

where $A = -D/J$ is the known state vector, $B = -\frac{3}{2} p \varphi_m/J$ is the control vector, and $u_d(t)$ represent the external disturbances and the unknown state vector.

For the reference model, the response of a linear time-invariant (LTI) system is used.

$$\dot{x}_m(t) = A_m x_m(t) + B_m c(t) \quad (14)$$

where $c(t) = \omega_{ref}(t)$ is the desired state vector, $A_m = -\alpha$ and $B_m = \alpha$ for a response of a decoupled first-order system with bandwidth $\alpha$.

For the error state between $x(t)$ and $x_m(t)$ to converge to zero, the control action $u(t)$ can be given by

$$u(t) = B^{-1} [A_m x(t) + B_m c(t) - Ax(t)] - B^{-1} u_d(t) \quad (15)$$

According to (Zhong and Rees, 2004), $u_d(t)$ can be estimated using the system states, the control signal, and a strictly proper low-pass filter $g_f(t)$ with unity steady-state gain and broad enough bandwidth as

$$\hat{u}_d(t) = u_d(t) * g_f(t) \quad (16)$$

where “*” denotes the convolution operator.

Following the design procedures used in (Ren et al., 2016b), expressing $u_d(t)$ from (13) and combining (15) and (16) result in

$$u(t) = B^{-1} [A_m x(t) + B_m c(t) - Ax(t) - \{\dot{x}(t) - Ax(t) + Bu(t)\}] * g_f(t) \quad (17)$$

So the UDE-based control law can be written as

$$u(t) = B^{-1} [L^{-1} \left\{ \frac{1}{1-G_f(s)} \right\} (A_m x_m(t) + B_m c(t)) - Ax(t) - L^{-1} \left\{ \frac{sG_f(s)}{1-G_f(s)} \right\} x(t)] \quad (18)$$

where $G_f(s)$ is the Laplace transform of $g_f(t)$, and $L^{-1}\{\cdot\}$ is the inverse Laplace transform operator.

Using a first-order low-pass filter with bandwidth $\beta$, the UDE-based control law (18) can be rearranged in the s-domain form as

$$U(s) = B^{-1} [(A_m X_m(s) + B_m C(s)) - AX(s) + (\beta I - A_m)E(s) - \frac{\beta}{s}A_m E(s)] \quad (19)$$

From (19), the proportional and integral gains can be simply expressed as $K_p = \alpha + \beta$ and $K_i = \alpha\beta$.

## 4.2. Stability analysis

By applying Laplace transform, (13) can be rewritten as

$$sX(s) = AX(s) + BU(s) + U_d(s) \quad (20)$$

Expressing $U(s)$ from (19), (20) becomes:

$$sX(s) = AX(s) + [(A_m X_m(s) + B_m C(s)) - AX(s) + (\beta I - A_m)E(s) - \frac{\beta}{s}A_m E(s)] + U_d(s) \quad (21)$$

After rearranging (21), the control output can be derived as

$$X(s) = C(s) \frac{\alpha}{s+\alpha} \frac{s}{s^2+(\alpha+\beta)s+\alpha\beta} + U_d(s) \frac{s}{s^2+(\alpha+\beta)s+\alpha\beta} \quad (22)$$

$$X(s) = C(s) \frac{\alpha}{s+\alpha} G(s) + U_d(s) G(s) \quad (23)$$

From (22), it is clear that the stability of the closed-loop control depends only on the values of the bandwidth $\alpha$ and $\beta$. The poles are $-\alpha$ and $-\beta$. Therefore, the system is stable if and only if $\alpha > 0$ and $\beta > 0$.

It can also be seen from Fig. 5 and 6, that increasing $\alpha$ and $\beta$ results in more expanded stability margin and faster tracking speed.
<figure><img src="image_6.png" /><figcaption>Fig. 5. G(s) Bode plot with $\beta=100$.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. G(s) Bode plot with $\alpha=5$.</figcaption></figure>

### 4.3. Design of the Reference System

Independently of UDE-based control, reference models have played an essential role in the field of systems control. They find application in adaptive control systems, where online parameter adjustment is performed to guide a plant to track a specified reference model, either through an open-loop configuration that operates without exploiting information from the plant and the controller, or through a closed-loop configuration that actively incorporates feedback from the plant to adapt the reference trajectory (Gibson et al., 2012). Moreover, reference models have seen extensive application in various advanced control methodologies, including reference tracking model predictive control (Köhler et al., 2018), fuzzy logic control (Hušek and Cerman, 2013, Ndubisi, 2008) and neural model reference control (Voloşencu, 2021, George et al., 2010).

Within the context of UDE-based control, the reference model assumes a significant role alongside the filter. Previous works have addressed the design of the reference system and the filter, considering diverse scenarios of the reference signal, including tracking step signals and sinusoidal signals (Ren et al., 2016a). Furthermore, the introduction of a nonlinear reference model has been discussed in (Lu et al., 2020).

In this paper, the linear time-invariant system represented in (14) is used. Where the parameter $\alpha$ typically plays a crucial

role in determining the desired system response for standard control scenarios, such as a step reference input (as illustrated in Fig. 8(a)). However, the dynamics of KGS present a unique challenge. The reference control $\omega_{ref}$ is not constant but exhibits periodic variations, as seen in the context of maximum power point tracking (MPPT) control (Fig. 2). Consequently, selecting $\alpha$ based only on the dynamic characteristics of the system raises a specific issue. The reference state $\omega_m$ inevitably deviates from the reference $\omega_{ref}$, as illustrated in Fig. 8(b). This misalignment of $\omega_m$ with respect to $\omega_{ref}$ can be problematic, as the system state $\omega$ should ideally track the reference state $\omega_m$ and not the reference $\omega_{ref}$ itself. Consequently, this misalignment can degrade the system tracking performance.

To achieve this alignment using the conventional UDE-based control, a significantly larger $\alpha$ is required, which alters the system dynamics to match the periodic variations of $\omega_{ref}$. However, this approach presents inherent drawbacks and has several undesirable consequences: higher control effort, negative impact on the system response to sudden changes in the speed set point or the external disturbances and the system stability can be compromise.

In order to address this challenge and those discussed in Section 3, an adaptive reference model is proposed. This adaptive model exploits the two degrees of freedom inherent in the UDE-based control framework, which allows the independent design of the reference model and the filter. This separation effectively dissociates the reference model from tracking performance, offering a unique advantage.

In the proposed approach, two parameters are used:

* A fixed parameter $\alpha_0$, chosen to meet the desired specifications of the closed-loop control system, such as settling time. $\alpha_0$ primarily governs system dynamics during transition phases, and deteriorments with the filter bandwidth $\beta$ the control effort and system stability.

* An adjustable parameter $\alpha$, is introduced exclusively in the model reference system to adapt $\omega_m$ as a function of $\omega_{ref}$ and $\omega_{mes}$.

The adaptation mechanism works as follows:

* When the difference between $\omega_{ref}$ and $\omega_{mes}$ exceeds a predetermined threshold $K$, it implies the system is in a transition phase. So, $\alpha$ takes on the value of $\alpha_0$. This configuration ensures that the system reacts like a first-order system (Fig. 8(a)) while delivering the required performance.

* If the difference between $\omega_{ref}$ and $\omega_{mes}$ is less than the threshold $K$, $\alpha$ gradually increases to $\alpha_{max}$ with an increment $k$. This gradual adjustment enables the reference state to effectively follow the reference command, as shown in Fig. 8(c).

This adaptive mechanism significantly improves tracking performance, particularly during generation phases of the KGS, when the reference speed exhibits periodic variations. Importantly, this improvement is achieved without compromising system dynamics, stability or control effort since the controller parameters depend only on $\alpha_0$ and $\beta$, the same as in conventional UDE-based control developed in 4.1: $K_p=\alpha_0+\beta$ and $K_i=\alpha_0\beta$.
The α-tuning methodology, shown in Fig. 7, demonstrates the functioning of this adaptive reference model within the control scheme.

<figure><img src="image_8.png" /><figcaption>Fig. 7. Flowchart of the proposed method for adjusting α.</figcaption></figure>

Therefore, incorporating the adaptive reference model into the modified UDE-based control scheme (as shown in Fig. 9) offers a robust solution to the challenges posed by KGS operation, particularly in scenarios involving periodic reference variations. This approach improves tracking performance while preserving system stability and dynamics, ultimately enhancing the effectiveness of KGS control strategies.

<figure><img src="image_9.png" /><figcaption>Fig. 8. First-order reference model response to reference command. (a) To step reference command with α = 7. (b) To variable reference command with α = 7. (c) To variable reference command with α = 1000.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 9. Block diagram of the modified UDE-based speed control system.</figcaption></figure>

# 5. Simulation and Experimental Results

## 5.1. Parameters tuning

The tuning process of the UDE-based control method is fundamentally guided by its inherent two-degree-of-freedom structure.

The parameter α of the reference system determines the set-point response of the system. The selection of α involves careful consideration of the practical constraints and limitations of the machine, including factors such as maximum torque, inertia and electrical constraints. The aim is to ensure that α gives satisfactory performance within these restraints.

On the other hand, the filter bandwidth β determine the disturbance response. A broader bandwidth, allows the passage of wider range of frequency components associated with disturbances and uncertainties, leading to a more robust control effort (Zhong et al., 2011). However, it is important to note that an excessively broad bandwidth can lead to the amplification of high-frequency noises, which may deteriorate the control signal (Ren et al., 2016a). Consequently, selecting β involves a compromise between achieving robust disturbance rejection and mitigating the effects of measurement noises.

In order to establish appropriate values for these parameters, a practical tuning approach involving a trial-and-error methodology has been employed. Specifically, α is set to the value of 5, guided by the desired set-point response of the system. Then, the value of β is chosen based on a trade-off between achieving accurate tracking performance and mitigating the negative impact of measurement noises. In this particular case, the optimal value of β has been set at 200.

For the modified UDE-based control, the values of α₀ and β are maintained consistent with those employed in the conventional UDE-based control, which are 5 and 200, respectively. α_max is chosen large enough so that the reference state can accurately track the reference command in the generation phase when it is periodically variable. Therefore, it is set to 1000. The increment k is set to 0.001 to ensure a smooth transition between the two phases. The threshold K is set at 5 to separate the phases described in section 4.3.

The proposed UDE-based control strategy is compared with the conventional Integral-proportional (IP) speed regulator, represented in Fig. 10.

<figure><img src="image_11.png" /><figcaption>Fig. 10. Block diagram of the IP controller.</figcaption></figure>

The IP controller is used instead the PI controller to avoid the introduction of a zero in the closed loop transfer function (Ane and Loron, 2006). The IP controller parameters are obtained by synthesizing the closed loop system with a response of a second-order system of the following canonical form

$$H(p) = \frac{1}{1 + \frac{2m}{\omega_n}p + \frac{1}{\omega_n^2}p^2} \quad (24)$$

Then, the controller parameters are given as

$$K_p = \frac{2D}{3p\varphi_m}(2m\tau_m\omega_n - 1) \quad \text{and} \quad \tau_i = \frac{3K_p p\varphi_m}{2D\tau_m\omega_n^2}.$$

where τ_m=J/D, ω_n and m are the natural frequency and the damping ratio respectively.

In order to establish a fair comparison, ω_n and m are chosen for the PI controller and the UDE-based controller to obtain almost identical responses. Consequently, ω_n and m are set to 10.5 and 1.1, respectively. Fig. 11 shows the speed response to step reference using each controller.
<figure><img src="image_12.png" /><figcaption>Fig. 11. Step reference speed response.</figcaption></figure>

The Integral-proportional (IP) regulator shown in Fig. 12 is used in the DC-link regulation. With: $K_{pv}=2.02e^{-4}$, $K_{iv}=10$.

<figure><img src="image_13.png" /><figcaption>Fig. 12. Block diagram of the $V_{dc}$ controller.</figcaption></figure>

For the dq-current control loops, a synchronous-frame proportional-integral (PI) control method is used for both machine and grid current control. The following parameters are used:

* For machine current control: $K_p=0.075$, $K_i=2.5$.

* For grid current control: $K_p=0.25$, $K_i=6.25$.

## 5.2. Simulation Results

To evaluate the performance of the proposed UDE-based control, simulations have been carried out in the MATLAB/Simulink environment based on the system shown in Fig. 3.

The mean absolute error (MAE) is used here to compare the tracking performance of the controllers. The MAE is calculated as

$$MAE = \frac{1}{n} \sum_{i=1}^{n} |\omega_{ref}(i) - \omega_{mes}(i)| \quad (25)$$

The parameters of the power kite generator and the power conversion system used in the simulation are listed in Table 1.

Fig. 13 shows the rotor speed responses for speed reference given by the MPPT control of each controller for a wind speed of 7 m/s. It can be observed that the modified UDE-based control strategy can offer better tracking performance than the IP controller and the conventional UDE-based controller. Fig. 13(b) shows the impact of the misalignment of $\omega_m$ with respect to $\omega_{ref}$ on the conventional UDE-based controller; even though the system state $\omega_{mes}$ tracks perfectly the reference state $\omega_m$, the latter follows the reference command $\omega_{ref}$ with a delay that downgrades the tracking performance. Fig. 13(c) shows that for the modified UDE-based controller, the reference state $\omega_m$ and the reference command $\omega_{ref}$ are almost identical, which results in better tracking performance. Table 2 illustrates the MAEs of different controllers, it can be seen that the modified UDE-based controller exhibits the best tracking performance over the other two controllers and reduces significantly the rotor speed error.

<figure><img src="image_14.png" /><figcaption>Fig. 13. Simulation results of the machine speed response. (a) With IP controller. (b) With conventional UDE-based controller. (c) With modified UDE-based controller.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. 14. q-axis current response of the SM. (a) With IP controller. (b) With conventional UDE-based controller. (c) With modified UDE-based controller.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 15. d-axis current response of the SM. (a) With IP controller. (b) With conventional UDE-based controller. (c) With modified UDE-based controller.</figcaption></figure>
The q-axis current of the SM is regulated to its reference given by the speed controllers output, as can be seen in Fig. 14. Similarly, the d-axis current is maintained at its reference $i_{dref}=0$, as shown in Fig. 15.

<table><caption>Table 1: Kite Generator System Parameters</caption><thead><tr><td>Parameters</td><td>Value</td></tr></thead><tbody><tr><td>Kite's area</td><td>4 m<sup>2</sup></td></tr><tr><td>Air density</td><td>1.225 kg/m<sup>3</sup></td></tr><tr><td>Lift coefficient</td><td>1</td></tr><tr><td>Drag coefficient</td><td>0.33</td></tr><tr><td>gearbox factor*drum diameter</td><td>33.33</td></tr><tr><td>Minimum tether length</td><td>100 m</td></tr><tr><td>SM excitation If</td><td>2.5 A</td></tr><tr><td>Pole pair number</td><td>2</td></tr><tr><td>System total inertia</td><td>0.03 kg m<sup>2</sup></td></tr><tr><td>Viscous damping</td><td>0.005 N.m.s</td></tr><tr><td>Machine inductance</td><td>6 mH</td></tr><tr><td>Machine resistance</td><td>0.2 Ω</td></tr><tr><td>DC-link capacitance</td><td>4700 μF</td></tr><tr><td>Grid-side filter inductance</td><td>20 mH</td></tr><tr><td>Grid-side filter resistance</td><td>0.5 Ω</td></tr><tr><td>Carrier frequency</td><td>10 kHz</td></tr><tr><td>Sampling time</td><td>10<sup>-6</sup> s</td></tr></tbody></table>

<table><caption>Table 2: MAE of Different Controllers</caption><thead><tr><td></td><td>IP</td><td>UDE</td><td>UDEm</td></tr></thead><tbody><tr><td>MAE</td><td>8.69</td><td>10.94</td><td>1.12</td></tr></tbody></table>

In order to assess the effectiveness of the proposed controller, the mechanical power error has been calculated by comparing the theoretical optimal system power with the actual power generated using each controller. This error is expressed as

$$E=P_{theo}-P_{mes} \quad (26)$$

The results in Fig. 16 show that the proposed modified UDE speed controller clearly performs better than the other controllers regarding reducing the error between the theoretical and actual generated power. Specifically, the error was found to be smaller when employing the proposed controller, indicating the impact of speed control on the system power efficiency.

Fig. 17 provides the DC-link voltage response for a reference of 400V with the IP controller. The later demonstrates periodic oscillation around the designated reference due to cyclic variations in the power flow generated by the KGS in the generation phase, which can be seen through periodic changes in the magnitude of grid currents shown in Fig. 18.

<figure><img src="image_17.png" /><figcaption>Fig. 16. Difference between theoretical and generated mechanical powers.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 17. DC-link voltage response.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 18. Grid current response.</figcaption></figure>

To investigate the controller's response to sudden changes in the speed reference, the wind speed was changed from 7m/s to 9m/s at $t=12s$. The results, shown in Fig. 19, demonstrate that the proposed UDE-based controller effectively maintains a stable speed transition consistent with the desired dynamic response, while ensuring accurate tracking of the periodically variable speed reference.

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /><figcaption>Fig. 19. System response to speed reference changing. (a) Speed response with the modified UDE-based controller. (b) q-axis current response.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Fig. 20. Speed response under inertia mismatch. (a) Using IP controller. (b) Using the proposed UDE-based controller.</figcaption></figure>

The controller is also evaluated with respect the machine parameters uncertainty. For this purpose, the equivalent moment of inertia of the rotating systems *J* is used since it directly influences the control scheme. In this test, the machine is operating in motor mode.

Fig. 20(a) and 20(b) illustrate the rotor speed response for a step reference of 400 rpm with different value of the equivalent moment of inertia: *J* = *J*₀, *J* = 0.5*J*₀, *J* = 1.5*J*₀. Where *J*₀ is its actual value. It can be seen that the proposed UDE-based control is more immune to parameters mismatch and can guarantee the same transient response even when mismatch occurs.

## 5.3. Experimental Results

A wind kite testbed has been built (Fig. 21) to emulate the real behavior of a KGS, and a test bench has been adopted to evaluate practically the control performance of the proposed controller. The structure of the experimental platform is shown in Fig. 22, which consists of a DC machine supplied by a buck converter to emulate the behavior of the wind kite turbine in the generation phase, a SM connected to the grid via a back-to-back converter and an inductive filter. A dSPACE DS1104 platform is used to implement the control algorithms. NEMICON Encoder HES-20-2MD with a resolution of 2000 P/R is used to measure the rotor position and speed, which explain the wiggle of rotational speed in experimental results. The designed system parameters are listed in Table 3.

The performances of the proposed modified UDE-based control strategy have been verified by implementing experimental tests. The DCM is controlled to emulate the KGS for a wind speed of 7 m/s, which results in the variable mechanical torque shown in Fig. 23 applied on the SM.

It is clear from Fig. 24 that the modified UDE-based control strategy exhibits superior tracking performance compared to the IP controller and the conventional UDE-based controller. Additionally, it can be noted from Table 4 that the proposed controller displays the most effective tracking performance of all three controllers with the lowest MAE.

<table><caption>Table 3: Kite Generator System Parameters in experimental validation</caption><thead><tr><td>Parameters</td><td>Value</td></tr></thead><tbody><tr><td>Kite's area</td><td>4 m<sup>2</sup></td></tr><tr><td>Air density</td><td>1.225 kg/m<sup>3</sup></td></tr><tr><td>Lift coefficient</td><td>1</td></tr><tr><td>Drag coefficient</td><td>0.33</td></tr><tr><td>gearbox factor*drum diameter</td><td>33.33</td></tr><tr><td>Minimum tether length</td><td>100 m</td></tr><tr><td>SM excitation If</td><td>2.5 A</td></tr><tr><td>Pole pair number</td><td>2</td></tr><tr><td>System total inertia</td><td>0.03 kg m<sup>2</sup></td></tr><tr><td>Viscous damping</td><td>0.005 N.m.s</td></tr><tr><td>Machine inductance</td><td>4.5 mH</td></tr><tr><td>Machine resistance</td><td>0.2 Ω</td></tr><tr><td>DC-link capacitance</td><td>4700 μF</td></tr><tr><td>Grid-side filter inductance</td><td>20 mH</td></tr><tr><td>Grid-side filter resistance</td><td>0.5 Ω</td></tr><tr><td>Carrier frequency</td><td>10 kHz</td></tr><tr><td>Sampling time</td><td>0.0003 s</td></tr></tbody></table>

<figure><img src="image_23.png" /><figcaption>Fig. 21. Experimental test bench.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Fig. 22. Conversion system diagram of the grid-connected KGS emulator.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Fig. 23. Mechanical torque applied on the SM.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>Fig. 24. Experimental results of the machine speed response. (a) With IP controller. (b) With conventional UDE-based controller. (c) With modified UDE-based controller.</figcaption></figure>

<table><caption>Table 4: MAE of Different Controllers</caption><thead><tr><th></th><th>IP</th><th>UDE</th><th>UDEm</th></tr></thead><tbody><tr><th>MAE</th><td>8.65</td><td>10.63</td><td>2.67</td></tr></tbody></table>

The outstanding performance of the proposed method results in a noticeable increase in the power generated by the system, as shown by the minimized error between the generated power and the theoretical optimal power of the kite shown in Fig. 25.

<figure><img src="image_27.png" /><figcaption>Fig. 25. Experimental result highlighting the difference between theoretical and generated mechanical power.</figcaption></figure>

Fig. 26(a) and 26(b) illustrate experimental robustness test results against parameter uncertainties regarding the equivalent moment of inertia. They clearly demonstrate the superior resilience of UDE-based control to parameter mismatch, ensuring consistent transient response even under various degrees of mismatch.

<figure><img src="image_28.png" /><figcaption>Fig. 26. Speed response under inertia mismatch. (a) Using IP controller. (b) Using the proposed UDE-based controller.</figcaption></figure>

## 6. Conclusion

In this paper, the grid connection of a pumping kite generator system was considered. Due to the nature of KGSs, even with stable aerodynamic conditions, the rotation speed reference and the mechanical torque are variable because of the lying eight-trajectory form. Hence, conventional controllers cannot offer satisfactory tracking performance. To address this issue, the UDE-based control strategy was proposed for the control of the SM rotor speed. Moreover, a modified model reference based on a first-order system has been proposed to overcome the limitations of the conventional UDE-based control, particularly to enhance tracking performance for periodic speed reference in the case of MPPT control while maintaining the same control effort and without downgrading system stability.

The superior performances of the proposed control strategy were demonstrated through simulation and experimental validation compared to conventional UDE and IP controllers. The improvement in speed regulation has, as expected, a significant impact on the overall efficiency and power generation capacity of the KGS, which was proven by simulation and experimental tests.

Although the proposed control strategy has been tested with an open-orbit KGS, it can be easily applied for all systems with a periodically changing reference.

In future research, particular attention will be given to the complete analysis of the recovery phase of the KGS. Furthermore, while the proposed methodology demonstrated robust stability, using a first-order model system led to certain limitations with respect to response time optimization. Consequently, future efforts will be directed towards exploring more advanced model systems, aiming to achieve a refined balance between stability and response time. In addition, DC bus voltage oscillations, triggered by variations in the kite's power output, emerged as a major challenge to ensure smooth system operation. Therefore, developing an efficient control strategy for the GSC will be also investigated to effectively mitigate the impact of these voltage oscillations.

## References

* Ahmed, M., Hably, A. & Bacha, S. Power maximization of a closed-orbit kite generator system. 2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011. IEEE, 7717-7722.
Ahmed, M. S., Hably, A. & Bacha, S. 2013. Kite generator system modeling and grid integration. *IEEE Transactions on Sustainable Energy*, 4, 968-976.

Akberali, A. F. K., Kheiri, M. & Bourgault, F. 2021. Generalized aerodynamic models for crosswind kite power systems. *Journal of Wind Engineering and Industrial Aerodynamics*, 215, 104664.

Ane, T. & Loron, L. Easy and efficient tuning of PI controllers for electrical drives. *IECON 2006-32nd Annual Conference on IEEE Industrial Electronics*, 2006. IEEE, 5131-5136.

Argatov, I. & Silvennoinen, R. 2010. Energy conversion efficiency of the pumping kite wind generator. *Renewable Energy*, 35, 1052-1060.

Bari, S. & Khan, M. U. Sliding mode control for autonomous flight of tethered kite under varying wind speed conditions. 2020 17th International Bhurban Conference on Applied Sciences and Technology (IBCAST), 2020. IEEE, 315-320.

Berra, A. & Fagiano, L. An optimal reeling control strategy for pumping airborne wind energy systems without wind speed feedback. 2021 European Control Conference (ECC), 2021. IEEE, 1199-1204.

Costello, S., François, G. & Bonvin, D. 2017. Real-time optimizing control of an experimental crosswind power kite. *IEEE Transactions on control systems technology*, 26, 507-522.

Dong, Y. & Ren, B. 2017. UDE-based variable impedance control of uncertain robot systems. *IEEE Transactions on Systems, Man, and Cybernetics: Systems*, 49, 2487-2498.

Fagiano, L. & Milanese, M. Airborne wind energy: an overview. 2012 American Control Conference (ACC), 2012. IEEE, 3132-3143.

Fagiano, L., Milanese, M. & Piga, D. 2009. High-altitude wind power generation. *IEEE Transactions on Energy Conversion*, 25, 168-180.

Fu, X., He, H., Xu, Y. & Fu, X. 2020. A strongly robust and easy-tuned current controller for PMSM considering parameters variation. *IEEE Access*, 8, 44228-44238.

George, M., Basu, K. P. & Chiat, A. T. W. 2010. Model reference controlled separately excited DC motor. *Neural Computing and Applications*, 19, 343-351.

Gibson, T., Annaswamy, A. & Lavretsky, E. Improved transient response in adaptive control using projection algorithms and closed loop reference models. AIAA Guidance, Navigation, and Control Conference, 2012. 4775.

Hušek, P. & Cerman, O. 2013. Fuzzy model reference control with adaptation of input fuzzy sets. *Knowledge-Based Systems*, 49, 116-122.

Karabacak, M. & Eskikurt, H. I. 2011. Speed and current regulation of a permanent magnet synchronous motor via nonlinear and adaptive backstepping control. *Mathematical and Computer Modelling*, 53, 2015-2030.

Köhler, J., Müller, M. A. & Allgöwer, F. 2018. Nonlinear reference tracking: An economic model predictive control perspective. *IEEE Transactions on Automatic Control*, 64, 254-269.

Li, J., Wang, S., Gao, J. & Fang, Y. PID-type Sliding Mode Control for Permanent Magnet Synchronous Motor Based on Uncertainty and Disturbance Estimator. 2019 Chinese Automation Congress (CAC), 2019. IEEE, 3506-3511.

Li, S. & Gu, H. 2012. Fuzzy adaptive internal model control schemes for PMSM speed-regulation system. *IEEE Transactions on Industrial Informatics*, 8, 767-779.

Lu, Q., Ren, B. & Parameswaran, S. 2020. Uncertainty and disturbance estimator-based global trajectory tracking control for a quadrotor. *IEEE/ASME Transactions on Mechatronics*, 25, 1519-1530.

Mademlis, G., Liu, Y., Chen, P. & Singhroy, E. Generator speed control and experimental verification of tidal undersea kite

systems. 2018 XIII International Conference on Electrical Machines (ICEM), 2018. IEEE, 1531-1537.

Ndubisi, S. 2008. A fuzzy model reference learning controller for synchronous generator terminal voltage control. *European Journal of Scientific Research*, 24, 378-386.

Ping, Z., Li, Y., Song, Y., Huang, Y., Wang, H. & Lu, J.-G. 2021. Nonlinear speed tracking control of PMSM servo system: A global robust output regulation approach. *Control Engineering Practice*, 112, 104832.

Qian, L. & Liu, H. H. 2019. Path-following control of a quadrotor UAV with a cable-suspended payload under wind disturbances. *IEEE Transactions on Industrial Electronics*, 67, 2021-2029.

Ren, B., Dai, J. & Zhong, Q.-C. 2019. UDE-based robust output feedback control with applications to a piezoelectric stage. *IEEE Transactions on Industrial Electronics*, 67, 7819-7828.

Ren, B. & Zhong, Q.-C. UDE-based robust control of variable-speed wind turbines. *IECON 2013-39th Annual Conference of the IEEE Industrial Electronics Society*, 2013. IEEE, 3818-3823.

Ren, B., Zhong, Q.-C. & Dai, J. 2016a. Asymptotic reference tracking and disturbance rejection of UDE-based robust control. *IEEE Transactions on Industrial Electronics*, 64, 3166-3176.

Ren, J., Ye, Y., Xu, G., Zhao, Q. & Zhu, M. 2016b. Uncertainty-and-disturbance-estimator-based current control scheme for PMSM drives with a simple parameter tuning algorithm. *IEEE Transactions on Power Electronics*, 32, 5712-5722.

Saberi, S. & Rezaie, B. 2022. Robust adaptive direct speed control of PMSG-based airborne wind energy system using FCS-MPC method. *ISA transactions*, 131, 43-60.

Schmidt, E., De Oliveira, M. D. L. C., Da Silva, R. S., Fagiano, L. & Neto, A. T. 2019. In-flight estimation of the aerodynamics of tethered wings for airborne wind energy. *IEEE Transactions on Control Systems Technology*, 28, 1309-1322.

Sebaa, M., Hassaine, S. & Ogab, C. 2017. Robust Control Method for PMSM Based on Internal Model Control with Speed and Load Torque Estimator. *International Journal on Electrical Engineering & Informatics*, 9.

Stuyts, J., Horn, G., Vandermeulen, W., Driesen, J. & Diehl, M. 2014. Effect of the electrical energy conversion on optimal cycles for pumping airborne wind energy. *IEEE Transactions on Sustainable Energy*, 6, 2-10.

Sun, L., Zhang, Y., Li, D. & Lee, K. Y. 2019. Tuning of active disturbance rejection control with application to power plant furnace regulation. *Control Engineering Practice*, 92, 104122.

Todeschini, D., Fagiano, L., Micheli, C. & Cattano, A. 2021. Control of a rigid wing pumping Airborne Wind Energy system in all operational phases. *Control Engineering Practice*, 111, 104794.

Voloşencu, C. 2021. Study of the Angular Positioning of a Rotating Object with Neural Model Reference Control. *WSEAS Transactions on Computers*, 20, 234-238.

Wang, Y., Ren, B. & Zhong, Q.-C. 2020. Bounded UDE-based controller for input constrained systems with uncertainties and disturbances. *IEEE Transactions on Industrial Electronics*, 68, 1560-1570.

Wu, Y., Ye, Y., Zhao, Q., Cao, Y. & Xiong, Y. 2019. Discrete-time modified UDE-based current control for $S LCL S$-type grid-tied inverters. *IEEE Transactions on Industrial Electronics*, 67, 2143-2154.
Yan, C. & Zhang, H. 2022. Analysis of the work performance of the lift mode crosswind kite power system based on aerodynamic parameters. *Energy Reports*, 8, 40-52.

Ye, Y. & Xiong, Y. 2017. UDE-based current control strategy for LCCL-type grid-tied inverters. *IEEE Transactions on Industrial Electronics*, 65, 4061-4069.

Yi, X., Guo, R. & Qi, Y. 2020. Stabilization of chaotic systems with both uncertainty and disturbance by the UDE-based control method. *IEEE Access*, 8, 62471-62477.

Yin, X. & Zhao, X. 2019. Composite hierarchical pitch angle control for a tidal turbine based on the uncertainty and disturbance estimator. *IEEE Transactions on Industrial Electronics*, 67, 329-339.

Zempoalteca-Jimenez, M.-A., Castro-Linares, R. & Alvarez-Gallegos, J. 2021. Trajectory Tracking Flight Control of a Tethered Kite Using a Passive Sliding Mode Approach. *IEEE Latin America Transactions*, 20, 133-140.

Zhang, X., Sun, L., Zhao, K. & Sun, L. 2012. Nonlinear speed control for PMSM system using sliding-mode control and disturbance compensation techniques. *IEEE transactions on power electronics*, 28, 1358-1365.

Zhao, K., Jia, N., She, J., Dai, W., Zhou, R., Liu, W. & Li, X. 2023. Robust model-free super-twisting sliding-mode control method based on extended sliding-mode disturbance observer for PMSM drive system. *Control Engineering Practice*, 139, 105657.

Zheng, Y., Zhao, H., Zhen, S. & Sun, H. 2021. Fuzzy-set theory based optimal robust constraint-following control for permanent magnet synchronous motor with uncertainties. *Control Engineering Practice*, 115, 104911.

Zhong, Q.-C. & Rees, D. 2004. Control of uncertain LTI systems based on an uncertainty and disturbance estimator. *J. Dyn. Sys., Meas., Control*, 126, 905-910.

Zhong, Q. C., Kuperman, A. & Stobart, R. 2011. Design of UDE-based controllers from their two-degree-of-freedom nature. *International Journal of Robust and Nonlinear Control*, 21, 1994-2008.