Modified ADRC for position lower-knee exoskeleton system: Rehabilitation case

Nasir Ahmed Alawad; Amjad J. Humaidi; Muhammed M. Muslim

doi:10.1556/1848.2024.00922

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International Review of Applied Sciences and Engineering

Volume/Issue:: Accepted Manuscript / Online First

Modified ADRC for position lower-knee exoskeleton system: Rehabilitation case

Authors:

Nasir Ahmed Alawad

Nasir Ahmed Alawad Department of Computer Engineering, Faculty of Engineering, Mustansiriyah University, Baghdad, Iraq

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nasir.awad@uomustansiriyah.edu.iq

Amjad J. Humaidi

Amjad J. Humaidi Control and Systems Engineering Department, University of Technology, Baghdad, Iraq

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amjad.j.humaidi@uotechnology.edu.iq https://orcid.org/0000-0002-9071-1329

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Muhammed M. Muslim

Muhammed M. Muslim Control and Systems Engineering Department, University of Technology, Baghdad, Iraq

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muhammed.m.muslim@uotechnology.edu.iq

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Online Publication Date:: 10 Jan 2025

Publication Date:: 10 Jan 2025

Article Category:: Research Article

DOI:: https://doi.org/10.1556/1848.2024.00922

Keywords:: ADRC; lower extremity; trajectory tracking; rehabilitation; exogenous disturbances; transfer function approach; tracking differentiator

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Abstract

The goal of this study is to develop a linear disturbance rejection control (ADRC) based on transfer-function approach. The proposed control strategy is applied to control the angular position of knee joint for rehabilitation purpose. The Extended State Observer (ESO) is the core of ADRC strategy and the performance of all ADRC controllers are assessed based on tracking and estimations errors due to controller and observer, respectively. The transfer-based approach of ADRC (TFADRC) is characterized by simplicity and direct control design. A comparison study in performance between conventional linear ADRC (CLADRC) and TFADRC approach has been made. The results based on numerical simulation showed that the proposed approach gives better tracking performance compared to conventional one. Based on Root Mean Square of Error (RMSE) metric, the TFADRC gives less tracking error (0.0205 rad) under load disturbances than that based on CLADRC (0.0547 rad). Moreover, better noise rejection capability can be obtained by TFADRC as compared to the conventional one. However, the price of better performance gained by TFADRC is to actuate higher level of control signal compared to its counterpart.

Abstract

1 Introduction

Han [1, 2] proposed the ADRC twenty years ago, and it has received increasing study attention over the years. It is a hybrid of current control theory's state observer and traditional PID control. The ADRC distinguishes itself from other control systems by not only estimating plant uncertainties and external disruptions in the ESO, but also effectively adapting to them in the controlled loop. Different works have addressed the relation of ADRC and transfer functions from differing viewpoints in recent years [3] on the control scheme characteristics of ADRC, [4] with a PID analysis, [5] on the internal model control (IMC) demonstration of ADRC, [6] and [7] on a transfer function illustration and a heuristic combining additional plant models, and perhaps even [8] on the reverse way, incorporating linear controllers with ADRC.

To ensure compatibility with established traditional procedures in practical applications, [9] proposed altering the ADRC to a one-degree of freedom (1DOF) error-based transfer function, employing an extended error-driven design rigorously demonstrated here through singular perturbation theory. An interrupted DC–DC buck converter is used in the experimental analysis of the used method. The driving themes pursued in this article [10] include retaining the original 2DOF properties of ADRC and giving appropriate continuous- and discrete-time transfer function approximations.

The suggested technique allows a user to simply make a compromise between the undershoot and the reaction time, utilizing the frequency response method, in [11] employing transfer function analysis, leading to a solution for tuning the ADRC for non-minimum phase systems. In [12] a LADRC controller with a transfer function to an energy inverter is introduced to increase predictive analysis and noise rejecting, with experiments and calculations used to verify the performance of the proposed scheme. Compared to the traditional extended state observer ESO framework, the differential concept of the summation disturbance can efficiently raise the ESO observation bandwidth and obtain the influence of rapid compensation for whole disturbance, but it will also magnify the high-frequency noise, so the differences between the observer's efficiency and its sensitivity to noise must be resolved.

Finally, a good answer will have substantial consequences in industrial applications if ADRC can be simply implemented in such transfer function blocks. All extant implementations of ADRC in the research use a two-degree-of-freedom approach, in which the ESO captures disturbance information and cancels it with a portion of the control signal in the inner loop, allowing the controller to respond with the modified plant in cascade integral equation. The contribution of this paper can be highlighted in the following points:

An improved ADRC was built by modifying the ESO for traditional ADRC depending on transfer function approach by applying classical control theory.
One degree was used for controller design depending on desired trajectory response related to closed-loop poles location.
The proposed controller satisfied the stability criterion by using pole-placement technique.

2 Exoskeleton modelling system

The exoskeleton knee system must be able to produce varied and efficient movement because it is developed to be used in daily tasks. For hardware resources required to perform the calculations, one right leg seems to have a hip holder, a motor driver, a lower leg grabber, and two (position, current) sensor systems [13, 14], as illustrated in Fig. 1a. Users wear the knee gadget to aid with the movements of their lower limb when sitting. There is only a single active DOF (flexion/extension) in the knee joint. Figure 1b depicts the system for actuating the leg at the joint region for physical rehabilitation.

Fig. 1.

(a) Prototype for knee exoskeleton and (b) knee motion mechanism

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

The nonlinear dynamic in this work for the knee exoskeleton and individual model with a single joint is found using the Euler-Lagrange method. The nonlinear dynamic modeling of this system can be explained as follows [14–16]:

J \ddot{θ} = τ_{h} + τ - f_{s} s g n \dot{θ} - τ_{g} \cos θ - f_{v} \dot{θ}

(1)

where

θ

represents an angle of the joint of the knee joining the actual position of full extension and the shank, while

\dot{θ}

and

\ddot{θ}

standard for the joint of the knee angular velocity and acceleration, respectively. The torque imparted to the knee exoskeleton system at the knee degree is denoted by

f_{s}

J

f_{v}

τ_{g}

, τ, and

τ_{h}

, which are viscous friction coefficient, solid friction coefficient, gravity torque, actuation torque, and the human torque disturbance, respectively.

3 Conventional linear ADRC (CLADRC)

The CLADRC algorithm for single-input single-output systems are described in detail. As shown in Fig. 2, the CLADRC loop is formed by three blocks [14–18].

Tracking differentiator (TD): It is applied to create transient profile $r_{1}$ for the reference $\tilde{r}$ and its derivatives $\dot{r_{1}}$ , $\ddot{r_{1}}, \dots$ , $r_{1}^{(n)}$ .
Extended State Observer (ESO): It calculates the system states $z_{1}, z_{2}, \dots, z_{n}$ as well as the new state $z_{(n + 1)}$ that includes the non-modeled dynamics and perturbations.
Controller: For the disturbance-free plant, it gives a state feedback control law $u_{o}$ . As a result, the system's input control signal $u = \frac{(u_{o} - z_{n + 1})}{b_{o}}$ is established to operate on the true plant and reject the disturbance information. $b_{o}$ is a gain variable.

Fig. 2.

CLADRC structure

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

The CLADRC process needs the system order (

n

) as well as the nominal value of its critical gain

b_{o}

. Moreover, if the process exhibits open-loop stability, a low-order LADRC may be employed, and closed-loop stability can be achieved through effective parameter estimation of the CLADRC [19]. Since the system order is n = 2 and there is an extra state

z_{3}

, the third order CLADRC was chosen as the control method for the knee position control system in this study. Rewrite Equation (1) to state-space form:

\ddot{y} = f (.) + b_{o} u

(2)

where

f (.)

is total disturbances (internal and external).

f (.) = - τ_{g} \cos θ - f_{s} s g n \dot{θ} - f_{v} \dot{θ} + τ_{h}

(3)

Define states as:

{\dot{x}}_{1} = x_{2} = \dot{θ}

{\dot{x}}_{2} = x_{3} + b_{o} u

(4)

{\dot{x}}_{3} = \dot{f}

y = x_{1} = θ

For the system given by Equation (4), the suggested observer dynamics structure is given by

\dot{x} = A x + b_{o} B u + E f

y = C x

(5)

where A = [\begin{array}{c} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}], B = [\begin{array}{c} 0 \\ b_{o} \\ 0 \end{array}], E = [\begin{array}{c} 0 \\ 0 \\ 1 \end{array}], c = [\begin{array}{c} 1 & 0 & 0 \end{array}]

(6)

As a result, a third order ESO is constructed in the same way as for the system, employing a linear Luenberger-like estimator, as follows:

\dot{z} = A z + B u + β (y - \hat{y})

(7)

\hat{y} = C z

where

z = {[z_{1} z_{2} z_{3}]}^{T}

is the estimates vectors of

y

\dot{y}

, and

f

, respectively and the observer error

e = y - z_{1}

.The observer gains:

β = [β_{1} β_{2} β_{3}] = [3 w_{o} 3 w_{o}^{2} w_{o}^{3}]

(8)

w_{o}

is the observer bandwidth. With estimate of

x_{3} \approx f,

the following control law is obtained from the ESO:

u = \frac{(u_{0} - z_{3})}{b_{o}}

(9)

where

u_{o}

is the output of the PD controller.

u_{o} = K_{p} (r - {\hat{z}}_{1}) + K_{d} (\dot{r} - {\hat{z}}_{2})

(10)

K_{p}

and

K_{d}

are proportional and derivative gains, respectively and the controller gains values are given by

k_{p} = ω_{c}^{2}

k_{d} = 2 ω_{c}

.[2], where

ω_{c}

is the control loop bandwidth. Let the relationship between the two bandwidths be

w_{o} = 4 ω_{c}

. [2]. The TD is an essential element of the ADRC. Because the derivative is present in the ADRC structure, it avoids jump reactions and softens them out. In this study, we used an optimized TD [20]:

\begin{array}{c} {\dot{v}}_{1} = v_{2} \\ {\dot{v}}_{2} = - 1.73 λ v_{2} - λ^{2} (v_{1} - r) \end{array}

(11)

Here,

v_{1}

is the desired trajectory and

v_{2}

is its derivative. The value of

λ

is evaluated and the result is chosen to satisfy the transient profile information space. The input signal's “tracking differentiator” is therefore indicated by

v_{2}

4 Transfer function ADRC approach (TFADRC)

Because the CLADRC design has been reduced to a linear form, it is now simple to apply classical control theory to transfer function time domain analysis and design [21]. To perform a transfer function domain analysis, we must first convert the ESO to a transfer function. Figure 3 shows the diagram of the ADRC design with state feedback. The corresponding two-degree-of-freedom transfer function type of this design is illustrated in Fig. 3, where H(s) is the pre-filter transfer function and C(s) is the controller transfer function.

Fig. 3.

The equivalent transfer function structure of CLADRC

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

From Fig. 3, the

P (s)

represents the exoskeleton system,

C (s)

is the controller and

H (s)

is the prefilter. To find the last two blocks, which represent TFADRC, rewrite Equation (7) as:

\dot{z_{1}} = z_{2} + β_{1} (y - z_{1})

\dot{z_{2}} = z_{3} + b_{o} u + β_{2} (y - z_{1})

(12)

\dot{z_{3}} = β_{3} (y - z_{1})

Substitute Equation (10) in Equation (9) and rewrite as:

u = \frac{K_{p} (r - z_{1}) + K_{d} (\dot{r} - z_{2}) - z_{3}}{b_{o}}

(13)

Substituting Equation (13) into Equation (12), the result formula can be as follows:

\dot{z_{1}} = z_{2} + β_{1} y - β_{1} z_{1}

\dot{z_{2}} = K_{p} r - K_{d} z_{2} + β_{2} y - (β_{2} + K_{p}) z_{1}

(14)

\dot{z_{3}} = β_{3} y - β_{3} z_{1}

Taking the Laplace form to Equation (14) and solving to calculate the states (

z_{1}

z_{2}

z_{3}

)

z_{1} = \frac{b s}{s^{3} + β_{1} s^{2} + β_{2} s + β_{3}} u + (\frac{β_{1} s^{2} + β_{2} s + β_{3}}{s^{3} + β_{1} s^{2} + β_{2} s + β_{3}} y

(15)

z_{2} = \frac{b (s^{2} + β_{1} s)}{s^{3} + β_{1} s^{2} + β_{2} s + β_{3}} u + \frac{(β_{2} s^{2} + β_{3} s)}{s^{3} + β_{1} s^{2} + β_{2} s + β_{3}} y

(16)

z_{3} = \frac{- b β_{3}}{s^{3} + β_{1} s^{2} + β_{2} s + β_{3}} u + \frac{β_{3} s^{2}}{s^{3} + β_{1} s^{2} + β_{2} s + β_{3}} y

(17)

Substituting Equations (15)–(17) in Equation (13) and reorganizing terms, U is rewritten as:

U (s) = - \frac{1}{s} \frac{(β_{1} K_{p} + β_{2} K_{d} + β_{3}) s^{2} + (β_{2} K_{p} + β_{3} K_{d}) s + β_{3} K_{p}}{b [s^{2} + (β_{1} + K_{d}) s + β_{1} K_{d} + β_{2} + K_{p}} Y (s) + K_{p} (\frac{s^{3} + β_{1} s^{2} + β_{2} s + β_{3}}{b s [s^{2} + (β_{1} + K_{d}) s + β_{1} K_{d} + β_{2} + K_{p}]} R (s)

(18)

Equation (18) can be written as two parts:

U (s) = - C (s) Y (s) + C (s) H (s) R (s)

(19)

C (s) = \frac{1}{s} \frac{(β_{1} K_{p} + β_{2} K_{d} + β_{3}) s^{2} + (β_{2} K_{p} + β_{3} K_{d}) s + β_{3} K_{p}}{b [s^{2} + (β_{1} + K_{d}) s + β_{1} K_{d} + β_{2} + K_{p}]}

(20)

H (s) = \frac{K_{p} (s^{3} + β_{1} s^{2} + β_{2} s + β_{3})}{(β_{1} K_{p} + β_{2} K_{d} + β_{3}) s^{2} + (β_{2} K_{p} + β_{3} K_{d}) s + β_{3} K_{p}}

(21)

The transfer functions can be easily calculated using linear system theory. Equation (20) and Equation (21) show the corresponding transfer functions for a third order ADRC with state feedback. The output trajectory is bounded, and the entire behavior response is stable in this study because the P(s) is stable and the overall disturbances $f (.)$ is differentiable.

5 Computer simulation and discussion

Assume a healthy 33-year-old male who weighs 75 kg and measures 1.73 m tall in this task. A person in a sitting position wearing a lower limb exoskeleton as shown in Fig. 1 and specified settings for this system are depicted [22]: $J = 0.8 k g . m^{2}$ , $f_{s} = 0.75 N . m$ , $f_{v} = 1.25 N . m . \sec . {r a d}^{- 1}$ and $τ_{g} = 6.25 N . m$

To validate the effectiveness of the proposed control strategy (TFADRC) for rehabilitation system, computer simulations were run in the MATLAB/Simulink environment. If the settling time of suggested system is given by (

τ_{s} = 0.4 \sec

), then one can have [2, 23]:-

w_{c} = \frac{10}{τ_{s}}

(22)

All values ( $β_{1} β_{2} β_{3}$ , $K_{p}$ , $K_{d}$ ) accordingly can be calculated. The reference signal is represented by $r = - 0.785 \sin (1.75 π t)$ .

For comparative study, various performance metrics are utilized, including the Integral Square Error (ISE), Integral of the Absolute Magnitude of Error (IAE), Integral Absolute of the Control Signal (IAU), Integral Square of the Control Signal (ISU), and Root Mean Square Error (RMSE) [24–26]. The study evaluated three cases, without disturbance, applied constant load during the training and finally applied Gaussian noise at the output position.

5.1 Without disturbance

This section uses a TFADRC controller and compared with CLADRC. The trajectories response can both track the target signal precisely without overshooting and under the same bandwidth for observers, as shown in Fig. 4. TFADRC, on the other hand, has a faster transient reaction. Figure 5 shows the trajectory tracking errors for both the TFADRC and CLADRC controllers. Many different performance metrics are used to assess tracking performance. According to Table 1, the RMSE for the TFADRC and CLADRC controllers is (0.0004) and (0.0039), respectively. This suggests that the TFADRC control is more accurate than the CLADRC control. As demonstrated in Fig. 6, the control efforts for CLADRC are higher than those for TFADRC, but with limited maximum torque ( $\pm 10 N . m)$ .

Fig. 4.

Time response comparison between TFADRC and CLADRC without disturbance

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

Fig. 5.

Tracking error comparison between TFADRC and CLADRC without disturbance

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

Table 1.

The performance of CLADRC and TFADRC without disturbance

Method	RMSE (rad.)	ISE (rad.)	IAE (rad.)	IAU (N.m)	ISU (N.m)
CLADRC	0.0039	$1 * 10^{- 4}$	0.0311	28.35	121.1
TFADRC	0.0004	$1.8 * 10^{- 6}$	0.0023	29.37	119.8

Fig. 6.

Comparison between required torque of TFADRC and CLADRC without disturbance

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

5.2 With constant load disturbance

The effort of user is considered using $τ_{h} \neq 0$ or 0.5 N m for payload introduced at the start of the flexion/extension cycle (at time = 2 s), which is applied at the output knee position movement. Control techniques are evaluated using a specified trajectory that illustrates flexion and extension movements, under the control strategies. The trajectories' tracking performance is shown in Fig. 7. The figure shows that the responses due to controllers could successfully track the desired trajectory. However, TFADRC approach has better load rejection capability than that based on CLADRC. Figure 8 depicts the difference in knee position between the desired and actual locations. The TFADRC control approach achieves the least tracking error in comparative experiments, demonstrating its effectiveness and superiority. Figure 9 depicts the control efforts ( $τ_{c})$ or $u (t)$ required for both control systems. The comparative experimental results indicate that the CLADRC control method necessitates the least control effort for the controller (ISU) and exhibits the greatest reduction in chattering within the control signal index (IAU) when juxtaposed with TFADRC. However, the presence of a saturation limiter in the CLADRC controller results in increased vibration compared to TFADRC, as detailed in Table 2.

Fig. 7.

Comparison between time response of TFADRC and CLADRC with load disturbance

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

Fig. 8.

Comparison between tracking error of TFADRC and CLADRC with load disturbance

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

Fig. 9.

Comparison between the required torque of TFADRC and CLADRC with load disturbance

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

Table 2.

The performance indices for CLADRC and TFADRC with load disturbance

Method	RMSE (rad.)	ISE (rad.)	IAE (rad.)	IAU (N.m)	ISU (N.m)
CLADRC	0.0547	0.0298	0.1238	25.1	115.2
TFADRC	0.0205	0.0041	0.0193	23.9	213.9

5.3 With noise disturbance

Because practical work is comprised of numerous mechanical and electrical components, all of which are impacted by external noises, it must be examined as a universal platform. Consider Gaussian noise with a variation of 0.0001 and a mean value of 0. Figure 10 depicts the trajectory tracking performance; all position responses appear to follow the expected trajectory, but with minor vibration. Figure 11 illustrates the disparity in knee positions between the actual and intended positions. The TFADRC control approach achieves the least tracking error in comparative experiments, demonstrating its usefulness and superiority. Figure 12 displays the control efforts to investigate the required control torque ( $τ_{c}$ ) or $u (t)$ for both control schemes. The comparative experimental results indicate that the CLADRC control method necessitates the least control effort for the ISU controller and exhibits the most significant reduction in chattering within the control signal index (IAU) when contrasted with TFADRC, as detailed in Table 3.

Fig. 10.

Time response comparison between TFADRC and CLADRC with Gaussian noise disturbance

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

Fig. 11.

Tracking error comparison between TFADRC and CLADRC with Gaussian noise disturbance

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

Fig. 12.

Comparison between required torque of TFADRC and CLADRC with Gaussian noise disturbance

Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00922

Table 3.

The performance of CLADRC and TFADRC with Gaussian noise disturbance

Method	RMSE (rad.)	ISE (rad.)	IAE (rad.)	IAU (N.m)	ISU (N.m)
CLADRC	0.0064	0.00041	0.0511	64.52	534.9
TFADRC	0.0033	0.00010	0.0264	91.84	1,331

One challenging problem in the proposed controller is how to be implemented in real-time environment such that the exoskeleton device can replace the exercising physicians. The solution is either to use FPGA format or other embedded system design formats [27–32].

6 Conclusion

The purpose of this study is to develop a TFADRC control strategy to actuate lower-limb exoskeleton robot to help in rehabilitating disabled persons. The proposed TFADRC approach has been verified via computer simulation. Then, the results obtained by this control design have been compared to those obtained by CLADRC. The results showed that the proposed TFADRC is more stable with higher rejection capabilities against disturbances and noises as compared to conventional ADRC. Based on Root Mean Square of Error (RMSE) metric, the TFADRC gives less tracking error (0.0205 rad) under load disturbances than that based on CLADRC (0.0547 rad). Moreover, better noise rejection capability can be obtained by TFADRC as compared to the conventional one. However, the price of better performance gained by TFADRC is to actuate higher level of control signal compared to its counterpart. In spite of considerable simplifications in the TFADRC control scheme, the total disturbance is successfully compensated without affecting nominal performance. This research can be expanded in the future by introducing other control schemes to be applied for the rehabilitation robot and compared in performance to the proposed controller [33–47].

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International Review of Applied Sciences and Engineering

Print ISSN:: 2062-0810

Online ISSN:: 2063-4269

Editorial Board

Mohammad Nazir AHMAD, Institute of Visual Informatics, Universiti Kebangsaan Malaysia, Malaysia

Murat BAKIROV, Center for Materials and Lifetime Management Ltd., Moscow, Russia

Nicolae BALC, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Umberto BERARDI, Toronto Metropolitan University, Toronto, Canada

Ildikó BODNÁR, University of Debrecen, Debrecen, Hungary

Sándor BODZÁS, University of Debrecen, Debrecen, Hungary

Fatih Mehmet BOTSALI, Selçuk University, Konya, Turkey

Samuel BRUNNER, Empa Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland

István BUDAI, University of Debrecen, Debrecen, Hungary

Constantin BUNGAU, University of Oradea, Oradea, Romania

Shanshan CAI, Huazhong University of Science and Technology, Wuhan, China

Michele De CARLI, University of Padua, Padua, Italy

Robert CERNY, Czech Technical University in Prague, Prague, Czech Republic

Erdem CUCE, Recep Tayyip Erdogan University, Rize, Turkey

György CSOMÓS, University of Debrecen, Debrecen, Hungary

Tamás CSOKNYAI, Budapest University of Technology and Economics, Budapest, Hungary

Anna FORMICA, IASI National Research Council, Rome, Italy

Alexandru GACSADI, University of Oradea, Oradea, Romania

Eugen Ioan GERGELY, University of Oradea, Oradea, Romania

Janez GRUM, University of Ljubljana, Ljubljana, Slovenia

Géza HUSI, University of Debrecen, Debrecen, Hungary

Ghaleb A. HUSSEINI, American University of Sharjah, Sharjah, United Arab Emirates

Nikolay IVANOV, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

Antal JÁRAI, Eötvös Loránd University, Budapest, Hungary

Gudni JÓHANNESSON, The National Energy Authority of Iceland, Reykjavik, Iceland

László KAJTÁR, Budapest University of Technology and Economics, Budapest, Hungary

Ferenc KALMÁR, University of Debrecen, Debrecen, Hungary

Tünde KALMÁR, University of Debrecen, Debrecen, Hungary

Milos KALOUSEK, Brno University of Technology, Brno, Czech Republik

Jan KOCI, Czech Technical University in Prague, Prague, Czech Republic

Vaclav KOCI, Czech Technical University in Prague, Prague, Czech Republic

Imre KOCSIS, University of Debrecen, Debrecen, Hungary

Imre KOVÁCS, University of Debrecen, Debrecen, Hungary

Angela Daniela LA ROSA, Norwegian University of Science and Technology, Trondheim, Norway

Éva LOVRA, Univeqrsity of Debrecen, Debrecen, Hungary

Elena LUCCHI, Eurac Research, Institute for Renewable Energy, Bolzano, Italy

Tamás MANKOVITS, University of Debrecen, Debrecen, Hungary

Igor MEDVED, Slovak Technical University in Bratislava, Bratislava, Slovakia

Ligia MOGA, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Marco MOLINARI, Royal Institute of Technology, Stockholm, Sweden

Henrieta MORAVCIKOVA, Slovak Academy of Sciences, Bratislava, Slovakia

Phalguni MUKHOPHADYAYA, University of Victoria, Victoria, Canada

Balázs NAGY, Budapest University of Technology and Economics, Budapest, Hungary

Husam S. NAJM, Rutgers University, New Brunswick, USA

Jozsef NYERS, Subotica Tech College of Applied Sciences, Subotica, Serbia

Bjarne W. OLESEN, Technical University of Denmark, Lyngby, Denmark

Stefan ONIGA, North University of Baia Mare, Baia Mare, Romania

Joaquim Norberto PIRES, Universidade de Coimbra, Coimbra, Portugal

László POKORÁDI, Óbuda University, Budapest, Hungary

Roman RABENSEIFER, Slovak University of Technology in Bratislava, Bratislava, Slovak Republik

Mohammad H. A. SALAH, Hashemite University, Zarqua, Jordan

Dietrich SCHMIDT, Fraunhofer Institute for Wind Energy and Energy System Technology IWES, Kassel, Germany

Lorand SZABÓ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Csaba SZÁSZ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Ioan SZÁVA, Transylvania University of Brasov, Brasov, Romania

Péter SZEMES, University of Debrecen, Debrecen, Hungary

Edit SZŰCS, University of Debrecen, Debrecen, Hungary

Radu TARCA, University of Oradea, Oradea, Romania

Zsolt TIBA, University of Debrecen, Debrecen, Hungary

László TÓTH, University of Debrecen, Debrecen, Hungary

László TÖRÖK, University of Debrecen, Debrecen, Hungary

Anton TRNIK, Constantine the Philosopher University in Nitra, Nitra, Slovakia

Ibrahim UZMAY, Erciyes University, Kayseri, Turkey

Andrea VALLATI, Sapienza University, Rome, Italy

Tibor VESSELÉNYI, University of Oradea, Oradea, Romania

Nalinaksh S. VYAS, Indian Institute of Technology, Kanpur, India

Deborah WHITE, The University of Adelaide, Adelaide, Australia

International Review of Applied Sciences and Engineering
Address of the institute: Faculty of Engineering, University of Debrecen
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2023
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International Review of Applied Sciences and Engineering
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International Review of Applied Sciences and Engineering
Language	English
Size	A4
Year of Foundation	2010
Volumes per Year	1
Issues per Year	3
Founder	Debreceni Egyetem
Founder's Address	H-4032 Debrecen, Hungary Egyetem tér 1
Publisher	Akadémiai Kiadó
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
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ISSN	2062-0810 (Print)
ISSN	2063-4269 (Online)