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  • 1 Department of Electrical Engineering, College of Engineering, University of Baghdad, Al-Jadriyah, , 10001, Baghdad, , Iraq
  • | 2 Department of Computer Engineering Techniques, Al-Rasheed University College, Baghdad, 10001, , Iraq
Open access

Abstract

This paper deals with the disturbance rejection, parameter uncertainty cancelation, and the closed-loop stabilization of the water level of the four-tank nonlinear system. For the four-tank system with relative degree one, a new structure of the active disturbance rejection control (ADRC) has been presented by incorporating a tracking differentiator (TD) in the control unit to obtain the derivate of the tracking error. Thus, the nonlinear-PD control together with the TD serves as a new nonlinear state error feedback. Moreover, a sliding mode extended state observer is presented in the feedback loop to estimate the system's state and the total disturbance. The proposed scheme has been compared with several control schemes including linear and nonlinear versions of ADRC techniques. Finally, the simulation results show that the proposed scheme achieves excellent results in terms of disturbance elimination and output tracking as compared to other conventional schemes. It was able to control the water levels in the two lower tanks to their desired value and exhibits excellent performance in terms of Integral Time Absolute Error (ITAE) and Objective Performance Index (OPI).

Abstract

This paper deals with the disturbance rejection, parameter uncertainty cancelation, and the closed-loop stabilization of the water level of the four-tank nonlinear system. For the four-tank system with relative degree one, a new structure of the active disturbance rejection control (ADRC) has been presented by incorporating a tracking differentiator (TD) in the control unit to obtain the derivate of the tracking error. Thus, the nonlinear-PD control together with the TD serves as a new nonlinear state error feedback. Moreover, a sliding mode extended state observer is presented in the feedback loop to estimate the system's state and the total disturbance. The proposed scheme has been compared with several control schemes including linear and nonlinear versions of ADRC techniques. Finally, the simulation results show that the proposed scheme achieves excellent results in terms of disturbance elimination and output tracking as compared to other conventional schemes. It was able to control the water levels in the two lower tanks to their desired value and exhibits excellent performance in terms of Integral Time Absolute Error (ITAE) and Objective Performance Index (OPI).

1 Introduction

A Four-tank system is one of the most important industrial and chemical processes that contain several manipulated variables, strongly interacting, controlled variables, parameters uncertainties, and nonlinear dynamics. Therefore, due to all of these reasons, the need to find suitable multivariable control techniques increases over time. A Four-tank system is a laboratory process that was originally proposed by Karl Henrik Johansson [1–3]. It becomes one of the popular case studies that show various behaviors, one of these behaviors is the effect of multivariable zeros in both linear and nonlinear models.

The Four-tank system is a multi-input multi-output (MIMO) system and a good motivation to find a new technique to solve multivariable control problems. In the present time, many researchers show different control techniques to solve these problems. The main control techniques that are used with the four-tank system are Decoupled PI controller [4], Fuzzy-PID [5], second-order sliding mode control [6], IMC-based PID [7]. In [8], various control schemes are used such as gain scheduling controller, a linear parameter varying controller, and input-output feedback linearization. J-Han in [9] proposed a new technique to eliminate the disturbance and uncertainty for SISO and MIMO systems, this technique is called active disturbance rejection control. It consists of tracking differentiator (TD), an extended state observer (ESO), and nonlinear state error feedback. Each part of ADRC has a function to accomplish; TD provides a derivative to get fast tracking, ESO estimates and rejects the total disturbance which contains plant uncertainties, exogenous disturbances, and system dynamics. In [10], the authors demonstrated the stability of the ADRC for ball and beam system. The results showed an effective performance for both ADRC and ESO. In [11], the author reported the importance of choosing the bandwidth of the observer. A large value of observer bandwidth increases noise sensitivity, and a lower value slows down the estimation convergence. Therefore, it must be selected carefully. In [12], the author proposed a new configuration for the four-tank system, a new control strategy for a class of controllers such as PID, LADRC, and ADRC. This control strategy depends on tracking error to measure the controlled target. The experiment and simulation results examined an improvement in output tracking and disturbance suppression. The authors in [13, 14] proposed an improved version for the nonlinear ESO and nonlinear state error feedback control to reduce the chattering phenomena and actuator saturation. In [15], the authors introduced the model predictive control with the linear model of the four tanks system to stabilize and optimize the input and the output. Authors of [16] proposed an Adaptive Pole Placement Controller (APPC) and a robust Adaptive Sliding Mode Controller (ASMC) to improve the robustness and rapidity of various industrial processes such as the four tanks system. In [17], the authors proposed a decentralized model predictive controller with the nonlinear model of the four tanks system to ensure the bound of the linearizing error by converting the system into a class of subsystems which in turn was converted into an n-number of robust tubes. In [18], the author has introduced a controller design based on a neural network. Although all the above studies proposed an excellent and accurate controller for the four-tank system but still there two drawbacks in their work. Firstly, some of the above studies used the linearized model of the four-tank system except for [3, 6, 12, 17, 18]. As a result, the controller was incapable to follow the nonlinear dynamics of the system, especially in the practical implementation. Secondly, exogenous disturbance and parameter uncertainties were not taken into consideration. Motivated by the above studies, this paper considers parameter uncertainties and exogenous disturbances in the control design of the four-tank system. Moreover, a new nonlinear controller with a tracking differentiator was also used to control the nonlinear model of the four-tank system. This combination will form the proposed ADRC for the four-tank system with a unit relative degree that gives an excellent, smooth, and fast output response with reduced sensitivity to the noise due to the adoption of the TD with nonlinear PID (NLPID) controller. The contribution of this paper lies in the following. A new nonlinear controller has been proposed by integrating the nonlinear PID controller with the tracking differentiator (TD). The TD replaces the traditional differentiator needed in the derivative part of the PID control design; thus, a new nonlinear PID controller with less sensitivity to the measurement noise is obtained. This new nonlinear PID controller has been integrated with the sliding mode extended state observer (SMESO) to form an improved active disturbance rejection control. Moreover, the genetic algorithm has been used to tune the parameters. A new performance index has been proposed to tune the parameters of the proposed nonlinear PID controller and the SMESO. A new multi-objective performance index is used in the minimization process, which includes the integral time absolute error, the absolute of the control signals, and the square of the control signals for both channels.

The rest of the paper is organized as follows: Section 2 presents the modeling of the four-tank system. Section 3 presents the proposed ADRC with a unit relative degree system. Section 4 presents the convergence of SMESO. Section 5 illustrates simulation results and discussion of the results, finally section 6 presents the conclusion of the work.

2 Modeling of the four-tank system

As shown in Fig. 1, the four-tank system consists of two pumps, a source tank, two valves, and four water tanks. Pump A extracts the water from the source tank and pours it into tank 1 and tank 4. Symmetrically, pump B extracts the water from the source tank and pours it into tank 2 and tank 3. Then the output flow of the pumps is divided into two by using three-way valves. Valve1 separated the spilled water into tank 1 by a fraction γ1 and to tank4 by a fraction (1 – γ1). In the same way, tank 2 and tank 3 are fed from pump B, and by Valve2 the water distributed to tank2 by a fraction γ2 and to tank 3 by a fraction (1 – γ2). By gravity action, the liquid in tank3 flows into tank 1 and then from tank 1 returns to the source tank. Symmetrically, the liquid in tank4 flows into tank 2 and then returns to the source tank. The water level in tank1 and tank 2 is controlled by the two pumps, the flow of the water to tank1 is γ1k1u1 and for tank 4 is (1 – γ1)k1u1, similarly for the flow of the water to tank 2 is γ2k2u2 and for tank3 is (1 – γ2)k2u2. In this paper, h3 is considered as the internal dynamics of is h1, symmetrically h4 is the internal dynamics of h2. So there are two disturbances, the first is the flow from the upper tank to the lower tank and the second one is the flow rate. The fraction (γ1,γ2) specifies the position of multivariable zeros which operate the system in minimum phase or non-minimum phase, in other words, these multivariable zero depend on the position of valves, 1<γ1+γ2<2 minimum phase and for non-minimum phase 0<γ1+γ2<1. In this paper, the system operates in minimum phase mode. According to Bernoulli equation and Mass balance, the nonlinear model of the four-tank system is the following [1]:
h˙1=a1A12gh1+a3A12gh3+γ1k1A1(u1+d1)
h˙2=a2A22gh2+a4A22gh4+γ2k2A2(u2+d2)
h˙3=a3A32gh3+(1γ2)k2A3u2
h˙4=a4A42gh4+(1γ1)k1A4u1
y1=kch1
y2=kch2
where Aj the cross-sectional area of is tankj, aj is the cross-section area of the outlet hole, hj is the water level in tankj,j={1,,4}. u1andu2 are the voltages applied to pump A and pump B respectively, g is the acceleration of gravity and kc is a calibrated constant, k1 and k2 are pump proportionality constants, k1u1 and k2u2 are the water flow rate generated by pump A and pump B respectively, d1 and d2 are the exogenous disturbances by the flow rate. We assume that the water flow generated by pump A and pump B is proportional to its applied voltages (u1and u2).
Fig. 1.
Fig. 1.

Schematic diagram of the four-tank system

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

3 Proposed active disturbance rejection control with a unit relative degree

J. Han [9], introduced an excellent method during the last decade to deal with the disturbances and uncertainties of the nonlinear system. This method is known as Active Disturbance Rejection Control (ADRC). The term active in ADRC means that ADRC estimates/cancels the total disturbance (parameter uncertainties, external disturbance, system dynamics, and any unknown or unwanted dynamics) in an online manner, which shows the effectiveness of ADRC. Generally, ADRC consists of three essential elements, tracking differentiator (TD), Nonlinear State Error Feedback controller (NLSEF), and the Extended State Observer (ESO).

In general, for a system with a unit relative degree or relative degree one (ρ=1) there is no need to use tracking differentiator (TD) because the ESO estimates two states, z1 is the system state and z2 is the generalized disturbance. So, the TD is combined with the nonlinear state error feedback (NLSEF) controller to constitute a new control structure for the ADRC. The general form of the proposed ADRC with relative degree one is shown in Fig. 2 below. It is illustrated that instead of the reference signal r(t), the error signal e˜(t) is using as an input to TD to obtain a smooth signal of the error and its derivative which in turn is used in the NLSEF to get the required control output u0(t). Furthermore, ESO will convert the system into a chain of integrators by estimating and canceling the total disturbance in an online fashion. Finally, after connecting the circuit using Matlab/Simulink, GA is used as an optimization technique to find optimal and suitable values for the parameters of TD, NLSEFC, and ESO. The proposed ADRC consists of a TD, an NLSEF, and a nonlinear ESO (NLESO) and it is explained as follows.

Fig. 2.
Fig. 2.

The proposed relative degree one (ρ=1) ADRC

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

3.1 Tracking differentiator (TD)

The use of a tracking differentiator has been increased in the last decade, to avoid set point jump, provide fast output tracking, and extract an accurate differentiated signal from the reference one that was not ideal in the classical (ordinary) differentiation [9, 19]. It is necessary to provide a transient profile to reduce the effect of peaking and chattering phenomena, achieving high control performance and high robustness against noise. The proposed method shows that it is not impossible to use TD with systems that have a unit relative degree. The equations of the proposed TD are expressed as follows:
e˜˙1=e˜2
e˜˙2=R2(e˜1e˜1+|e˜1e˜|)Re˜2
where e˜1 is the tracking error and its equal to e˜1=rz1, e˜2 is the derivative and e˜ is the input to the tracking differentiator and R is the parameter chosen to speed up or slow down the transient profile. In the next subsection, we will introduce the proposed controller and how we used the proposed TD with the nonlinear controller for systems with a unit relative degree.

3.2 Nonlinear TD-NLPID controller

NLPID is the modified version of the traditional PID controller. It is evolved to achieve fast process, high robustness, and stability and can handle the strong nonlinearity of the nonlinear systems, which the traditional PID controller fails to do. The main aim of the proposed controller is to treat the error function and its integration and derivative as a nonlinear function and thus satisfy the rule “small error large gain, large error small gain”. The NLPID equations are expressed as follows,
uNLSEFi=ui1+ui2+uintegreatori
ui1=(k11i+k12i1+exp(μi1e˜i12))|e˜i1|αi1sign(e˜i1)
ui2=(k21i+k22i1+exp(μi2e˜˙i12))|e˜˙i1|αi2sign(e˜˙i1)
uintegratori=(ki1+exp(μie˜i1dt2))|e˜i1dt|αisign(e˜i1dt)
u0i=δtanh(uNLSEFiδ)
where k11i,k12i,k21i,k22i,ki,μi1 and μi2,αi1,αi2 are tuning design parameters and e˙˜i1=e˜i2. Moreover, αi1 αi2 < 1 to ensure the error functions |e˜i1|αi1, |e˜˙i1|αi2 are sensitive to small error values [14, 20], and to satisfy the rule “small error large gain, large error small gain” [9]. The parameter δ is a positive coefficient that would make “tanh” function between the sector [+ δ, –δ] instead of [+,]. In other words, “tanh” function will limit the control signal by δ which in turn cancels the high-frequency components, reduces the chattering in the control signal, and provides energy-saving [21, 22]. The new structure of the nonlinear controller that consists of an NLPID controller and a TD that is used to control the water level of the two lower tanks shows an excellent response and control. The main aim of the proposed controller for a system with a unit relative degree is that instead of using ordinary differentiation, we can use the benefits of the TD to get filtered error and its derivative and thus excluding higher values of the ordinary differentiation caused by noise. The stability analysis and design details of the NLPID controller can be referred to in [14].

3.3 Sliding mode extended state observer (SMESO)

The nonlinear ESO (NLESO) is more efficient and accurate than linear ESO (LESO) because the NLESO solves the problem of slow convergence and peaking phenomenon that exists in LESO [23, 24]. The SMESO estimates the total disturbance, system's state and converts the system into a chain of integrators. The SMESO is given by the following equations:
zi1=zi2+b0iui+βi1ki(ei1)ei1
zi2=βi2ki(ei1)ei1
ki(ei1)=kαi|ei1|αi1+kβi|ei1|βi
where i=1,2, ei1=hizi1,ei and zi1 are the estimated error and the estimated state of hi respectively. ki(ei1) is a nonlinear function [13], αiandβi are positive tuning parameters that must be less than 1. kαiandkβi Are the nonlinear function gains and they are tuning parameters too. βi1andβi2 Are the observer gain parameters and they are selected such that the characteristic polynomial s2+βi1s+βi2 is Hurwitz [11], and for simplicity s2+βi1s+βi2=(s+ω0i)2, where ω0i is SMESO bandwidth and it would be the only tuning parameter. Thus, βi1=2ω0i and βi2=ω0i2. The proposed ADRC with the nonlinear model of the four-tank system is shown in Fig. 3. Figure 3, represents the detailed form of Fig. 2. Four tanks system has two inputs (u1,u2) and two output (h1,h2). The reference signal (r1,r2) represents the desired value of the water level in tank1 and tank2 respectively. As mentioned previously, for the system with a unit relative degree, there is no need for the TD. So, we can use it to generate the error e˜11 and its derivative e˜12 for the 1st subsystem and e˜21,e˜22 for the 2nd subsystem. Then, the estimated total disturbance will be canceled from the control signal of each subsystem (u01,u02) to generate the required control law, ui=(u0izi2/b0i),i=1,2. The state-space model and stability analysis of SMESO are presented in detail in [13].
Fig. 3.
Fig. 3.

Proposed ADRC with the nonlinear model of the four-tank system with unit relative degree (ρ=1)

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

4 Convergence of the SMESO

In this section, we will introduce the convergence of the Sliding Mode Extended State Observer (SMESO) using Lyapunov stability theorem.

For 1st subsystem, the error dynamics are stated in the following. Firstly, (1) is rewritten as:
h˙1=f1+b01d1+b01u1
Let
h12=f1+b01d1
Now, sub. (18) In (17) yields,
h˙1=h12+b01u1
Now differentiate (17) to get,
h˙12=f˙1+b01d˙1
{h˙1=h12+b01u1h˙12=f˙1+b01d˙1
where h12 is the generalized disturbance, f1 is the system dynamics and parameter uncertainty and d1 is the exogenous disturbance.
Now, for the SMESO1 of the 1st channel, Eq. (14), (15) can be rewritten as
{z˙11=z12+b01u1+β11k1(e11)e11z˙12=β12k1(e11)e11
From (5), and sub kc=1,h1 can be found as
{h1=y/kch12=f1+b01d1
The estimated error for subsystem1 can be written as
{e11=h1z11e12=h12z12
where e11 and e12 are the estimated errors, z11 is the estimated state of h1, z12 is the estimated total disturbance of the 1st channel. Now differentiating (24) yields,
{e˙11=h˙1z˙11e˙12=h˙12z˙12
where e˙11 and e˙12 are the error dynamics for the 1st subsystem. Sub. (21), (22) in (25), yields,
{e˙11=β11k1(e11)e11+e12e˙12=β12k1(e11)e11+h˙12
In state-space form, (26) can be rewritten as
[e˙11e˙12]=[β11k1(e11)1β12k1(e11)0][e11e12]+[01]h˙12
So, the general form of the error dynamics is
e˙i=Aiei+h˙i2
where i refers to the subsystem number which is either 1 or 2, Ai=[βi1ki(ei1)1βi2ki(ei1)0],e˙i=[e˙i1e˙i2] and ei=[ei1ei2]. Now to check that whether the estimated error converges to zero as t, i.e., the SMESO is asymptotically stable. To achieve that, Lyapunov stability is used [25]. Let us choose the Lyapunov function as VSMESOi=12eiTei. Then,
V˙SMESOi=eiTe˙iV˙SMESOi=[ei1ei2][βi1ki(ei1)1βi2ki(ei1)0][ei1ei2]+h˙i2
Assume that h˙i2 converges to zero as t (which is the case for constant exogenous disturbances) [13], then,
V˙SMESOi=[ei1ei2][βi1ki(ei1)1βi2ki(ei1)0][ei1ei2]

The quadric form V˙SMESOi=eiTQie˙i is asymptotically stable if Qi is a negative definite matrix. Then, according to [25], the system is asymptotically stable when the following conditions are satisfied,

  1. VSMESOi is positive definite, VSMESOi(ei)>0forei0,i=1,2.

  2. V˙SMESOi(ei)<0forei0, i = 1, 2.

Now to check the negative definiteness of Qi, Routh stability criteria can be used to find the stability limits of matrix Qi. Firstly, compute the characteristic equation for matrix Qi,
|λIQi|=0,|λ+βi1ki(ei1)1βi2ki(ei1)λ|=0
λ2+βi1ki(ei1)λ+βi2ki(ei1)=0
where i =1, 2. Then from Routh stability criteria, one gets,
1βi2ki(ei1)
βi1ki(ei1)0
βi1βi2ki(ei1)20βi1ki(ei1)=βi2ki(ei1)0

βi1ki(ei1)>0,ki(ei1)>0. Then Qi is negative definite if the nonlinear gain ki(ei1) satisfies ki(ei1)>0. We conclude that the SMESO is asymptotically stable.

5 Simulation results and discussion

5.1 Simulation results

The proposed ADRC for the Four-tank nonlinear model is designed and simulated using Matlab/Simulink. The parameters of the Four-tank model are shown in Table 1. The simulations include comparing the proposed scheme with four different schemes. The Genetic Algorithm is used in the paper as an optimization technique [26, 27], and [28], to tune the parameters of the NLPID controller, SMESO, and TD of all schemes including the proposed one. In addition, to measure the performance of the entire system, a useful multi-Objective Performance Index (OPI) has been used in this work. It measures the effectiveness of the proposed scheme and it is expressed as follows
OPI=w1OPI1+w2OPI2
where OPI1andOPI2 represent the objective performance index for the first and second subsystems respectively, w1andw2 are weighting factors. To treat the two subsystems equally likely, w1andw2 are set to 0.5. Both OPI1andOPI2 are expressed as
{OPI1=W1ITAE1N11+W2UABS1N12+W3USEQ1N13OPI2=W1ITAE2N21+W2UABS2N22+W3USEQ2N23
where W1,W2andW3 are the weighting factors that satisfy W1+W2+W3=1. According to that, they are set to W1 = 0.4, W2 = 0.2 and W3 = 0.4. N11,N12,N13,N21,N22andN23 are the nominal values of the individual objective functions, which are included in the OPI to ensure that the individual objectives have comparable values and are treated equally likely by the tuning algorithm. Thus, their values are set to N11 = 1.814362, N12 = 4389.201, N13 = 305.59, N21 = 1.77746, N22 = 4332.233, and N23 = 285.2937. Table 2 shows the description and mathematical representation of the performance indices.
Table 1.

Sample parameters of the Four-tank system

ParameterValueUnit
h116cm
h213cm
h39.5cm
h46cm
γ10.7unitless
γ20.6unitless
k13.33cm3/volt.sec
k23.35cm3/volt.sec
a10.071cm2
a20.056cm2
a30.071cm2
a40.056cm2
A128cm2
A232cm2
A328cm2
A432cm2
kc1volt/cm
g981cm/sec2
Table 2.

Description and mathematical representation of performance

PIDescriptionMathematical representation
ITAEIntegral time absolute error0tft|e(t)|dt
UABSIntegral absolute of the control signal0tf|u(t)|dt
USEQIntegral square of the control signal0tfu(t)2dt

The Five schemes that were simulated in this work are listed as follows,

  1. Scheme1: (LADRC). Linear State Error Feedback (LSEF) [9] + LESO.

The LESO is expressed as follows,
{z˙i1=zi2+b0iui+βi1(ei1)z˙i2=βi2(ei1)

The parameters of Eq. (30) are already previously in this work.

  • 2. Scheme2: (NLADRC). Nonlinear State Error Feedback (NLSEF) [9] + LESO of Eq. (30).

The NLSEF is given by
{fal(e˜i1,α1i,δ1i)={e˜i1/(δi11αi1),xδi1|e˜i1|αi1sign(e˜i1),x>δi1fal(e˜i2,αi2,δi2)={e˜i2/(δi21αi2),xδi2|e˜i2|αi2sign(e˜i2),x>δi2
{{u01=fal(e˜11,α11,δ11)+fal(e˜12,α12,δ12)u02=fal(e˜21,α21,δ21)+fal(e˜22,α22,δ22){u1=(u01z12)/b01u2=(u02z22)/b02
where i=1,2, e˜i1=rizi1, ei2 are the tracking error and its derivative respectively, α11, α12, α21, α22, δ11, δ12,δ21 and δ22 are positive tuning parameters.

The simulated results for each scheme are given next. The tuned parameters of both the controller and the observer of each scheme (1, 2, 3, and 4) are given in Tables 3 7.

Table 3.

Parameters of scheme 1

ParameterValueParameterValue
kp118.6300kd23.0500
ki10.0002β1186.2600
kd12.5300β121860.2
kp226.6550β2131.8200
ki20.0024β22253.1281
Table 4.

Parameters of scheme2

ParameterValueParameterValue
α10.7763β11298.6900
δ10.0140β122230.4
α20.4167β21349.0100
δ21.8958β222993.1
Table 5.

Parameters of scheme3

ParameterValueParameterValue
α110.6190δ220.7441
δ110.0238R300
α120.7115β11326.1200
δ120.9276β122658.9
α210.5813β21270.2800
δ210.0814β221826.3
α220.9905--
Table 6.

Parameters of scheme4

ParameterValueParameterValue
k1116.2650k2127.0400
k1211.4124k2220.0142
μ118.5790μ225.6130
α110.6812α220.6625
Table 7.

Parameters of scheme4

ParameterValueParameterValue
β11266.4000kβ10.6713
β121774.2β10.2221
β21327.6800kα20.8579
β222684.4α20.6265
kα10.3675kβ20.6812
α10.9733β20.7062

The values of the parameter for the proposed scheme are listed in Tables 8 and 9.

Table 8.

The parameters of the proposed scheme (NLSEF part)

ParameterValueParameterValueParameterValue
k11110.6800k10.7124k2222.1384
k1212.3826μ17.9420μ223.5100
μ115.7050α10.5705α220.7073
α110.5773k21110.5285k20.5773
k1122.3715k2211.1070μ21.5810
k1220.8844μ213.4640α20.2948
μ120.2240α210.6184δ37.4430
α120.5189k2122.5620R100
Table 9.

Parameters values of the proposed scheme (SMESO part)

ParameterValueParameterValue
β11294.8600kβ10.7648
β122173.6β10.8946
β21218.1000kα20.5705
β221189.2α20.7124
kα10.1095kβ20.5773
α10.6964β20.7942

The water level of tank1 and tank2 are shown in Figs 45. The results show that the output response of the proposed scheme is faster, smoother, and without overshooting as compared to that of the other schemes. It takes about less than 2s to reach the steady-state (desired value), while a longer settling time is clearly shown in the output response of the other schemes. Figures 6 and 7 show the output response in the existence of the disturbance for the 1st subsystem at t = 40s and the 2nd subsystem at t = 60s. The results show that scheme1, scheme2 scheme3, and scheme4 when applying disturbance for 1st subsystem at t = 40s exhibit an output response with an undershoot which reaches nearly 0.1265%, 0.375%, 0.1875%, 0.125% respectively of the steady-state value and last about 1.2 s for scheme1, 2.1s for scheme2, 1s for scheme3 and 0.5s for scheme4 until the output response reaches its steady state. The same for 2nd subsystem, at t = 60s the, output response exhibits an undershoot which reaches nearly 0.307%, 0.315%, 0.305%, 0.153% of its steady-state value for scheme1, scheme2 scheme3, and scheme4 respectively and last about 1.9 s for scheme1, 1.92s for scheme2, 1.5s for scheme3 and 0.5s for scheme4 until it reaches its steady-state, while our proposed scheme rejects the disturbance very quickly.

Fig. 4.
Fig. 4.

Water level in tank1

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

Fig. 5.
Fig. 5.

Water level in tank2

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

Fig. 6.
Fig. 6.

A disturbance is applied for 1st subsystem at t = 40s

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

Fig. 7.
Fig. 7.

A disturbance is applied for 2nd subsystem at t = 60s

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

Figures 8 and 9 show the control signal for the 1st subsystem and the 2nd subsystem. The proposed scheme shows chattering free, whilescheme2 shows chattering in the control signal. This proves that the proposed scheme is better than other schemes.

Fig. 8.
Fig. 8.

The control signal for the 1st subsystem

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

Fig. 9.
Fig. 9.

The control signal for the 2nd subsystem

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

To observe the effect of the system parameter uncertainty on the four tanks model, the value of the outlet hole a1 is varied by (Δa1=2%). Figure 10 show the response of the water level of tank1 while applying the uncertainties. (a) with uncertainty (Δa1=+2%). (b) with uncertainty (Δa1=2%). It is observed that the proposed scheme can handle the uncertainties with high performance, which shows the effectiveness of the SMESO.

Fig. 10.
Fig. 10.

The water level in tank 1 with uncertainty in the outlet hole a1

Citation: International Review of Applied Sciences and Engineering 2022; 10.1556/1848.2021.00352

5.2 Discussions

From the presented results, it is clearly shown that with the proposed scheme, the water level arrives at its steady-state (desired value) in a shorter time as compared to other schemes used in the comparison and without overshooting or undershooting. Even when a disturbance is applied to the system (at t = 40 disturbance applied to the 1st subsystem and at t = 60 disturbance applied to the 2nd subsystem), the disturbance does not affect the system's output due to the excellent estimation of the SMESO to the total disturbance which is canceled from the input channel via the SMESO. Moreover, when the parameter uncertainty of Δa1=2% is applied to the system, the variation in the outlet hole a1 does not affect the system output. The inclusion of the SMESO in the feedback loop reduced the peaking phenomenon that was visible when using the LESO (e.g., scheme1, scheme2, scheme3). Moreover, the control signal of the proposed scheme shows a reduction in chattering due to the adoption of the new nonlinear controller as compared to the other schemes. The new NLPID controller is nonlinear and satisfies the rule “small error large gain, large error, small gain” which works by producing a chattering-free control signal. Table 10 shows the simulated results of the performance indices after GA tuning for all the schemes that are applied in this work including the proposed one. Table 11 lists the complete abbreviations used in this paper. As shown in Table 10, the proposed scheme shows an improvement for the transient response, in other words, ITAE1andITAE2 are reduced by 50.4% and 40.31% respectively as compared to the other schemes. Finally, the proposed scheme achieves the best OPI, ITAE1andITAE2 among all the other schemes.

Table 10.

Simulation Results for the Four Tanks System

Schemes/PIscheme 1scheme 2scheme 3scheme 4Proposed scheme
ITAE15.04485310.7318107.3613442.6097882.501022
ITAE27.51426913.4633536.3961272.6842292.642392
UABS113115.098625976.413223649.1137472518.4805362480.090176
UABS216124.00159501021.529276618.4596312695.5036332684.961943
USEQ116194.33653554.01567827.778464678.346693666.768796
USEQ220840.56193946.70016561.123995658.756634705.609611
OPI23.219069072.4811631.6888431.5780221.537139

Now we will show the effectiveness of our proposed method compared with other methods as follows:

  1. In [6], Figs 2 and 3 shows that the water level reaches the steady-state (desired value) in about 13 s, while in our proposed scheme, it is observed that the water level reaches the desired value in less than 2 s with smooth fast response. Moreover, when the disturbance is applied, the system of [6], Figs 8 and 9 shows a noticeable overshoot and undershoot. This proves the robustness of our proposed scheme.

  2. In [12], Fig. 4 (a, b) shows that the water level for both tank1 and tank2 rises with rising time tr=25 s and tr=15 s for ADRC and LADRC respectively. While the water level using our proposed scheme rises faster with rising time tr=0.667944 s and tr=0.742405 s for tank1 and tank2 respectively without any noticeable oscillations. In addition, the system of [12] under the disturbance recovered to the desired value after 10 and 1s for ADRC and LADRC respectively, while our proposed method rejects the disturbance very quickly.

  3. In [15], the linearized model of the four tanks system is used. Figure 4 shows the response of the two lower tanks (tank1 and tank2) that rises with rising time tr=1.3 s. When the disturbance is applied, the response is not smooth enough. On the other hand, our proposed scheme shows a fast, smooth response with rising time tr=0.667944 s and tr=0.742405 s for tank1 and tank2 respectively.

  4. In [16], Table 6 shows the performance indices for both tank1 and tank2. It is observed that the system of [16] has ITAE1=8.0567107 and ITAE2=2.7820108 for ASMC controller. While our proposed scheme has ITAE1= 2.501022 and ITAE2=2.642392 for tank1 and tank2 respectively. This proves the effectiveness of our scheme.

  5. In [17], Fig. 10 shows a noticeable overshoot in the response of tank2, while our proposed scheme shows a smooth response with fast convergence. In this research, the effect of disturbance and parameter uncertainties have not been taken into consideration.

6 Conclusions

This work proposes a control scheme, i.e., (TD+NLPID) that is applied to the nonlinear model of the four-tank system which achieves the following:

  • It produces fast-tracking, makes the system less sensitive to noise and reduces the chattering that is produced by other schemes in the control signal, which subsequently increases energy consumption.

  • The proposed control scheme TD+NLPID reduces the noise in the closed-loop system, which is amplified when using ordinary derivatives in traditional PID control or LSEF control. The SMESO is not just cancelling the disturbance and estimate system's states, but, also reduces the peaking, a natural phenomenon in the LESO-based control schemes. This is due to the adoption of a nonlinear error function that is used in the design with asymptotic convergence.

  • The proposed TD-NLPID control scheme solves the main aims of this paper with excellent results and performance for a system that has a unit relative degree, strong nonlinearities, MIMO coupling interacting, multivariable zeros that make the system operate in two modes (minimum and non-minimum phase).

  • An extension to the current work includes the H/W implementation of the proposed TD-NLPID control scheme on a real four-tank system platform using one of the recent stand-alone computing systems like Arduino or Raspberry PI. Furthermore, applying other control techniques on the four-tank system and comparing the obtained results with that of this work [29–35].

Table 11.

List of abbreviations used in this paper

AbbreviationDefinition
TDTacking Differentiator
OPIObjective Performance Index
ITAEIntegral Time Absolute Error
UABSIntegral Absolute of the control signal (IAU)
USEQIntegral Square of the control signal (ISU)
MIMOMulti-Input Multi-Output system
ADRCActive Disturbance Rejection Control
LESOLinear Extended State Observer
LPIDLinear proportional-Integral- Derivative
LSEFLinear State Error Feedback
NLESONonlinear Extended State Observer
SMESOSliding Mode Extended State Observer
NLSEFNonlinear State Error Feedback
NLPIDNonlinear Proportional -Integral-Derivative
hjThe water level of tank j
γ1, γ2Ration of the flow in the valves
k1, k2Pump proportionality constant
ajThe cross-section area of the outlet hole of tank j
AjThe cross-section area of the tank j
kcThe calibrated constant
gGravity constant
ASMCAdaptive Sliding Mode Controller
APPCAdaptive Pole Placement Controller

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  • [1]

    K. H. Johansson , “The Quadruple-Tank Process-A multivariable laboratory process with an adjustable zero,” IEEE Control Syst. Technol, vol. 8, no. 3, pp. 456465, 2000. Available: https://doi.org/10.1109/87.845876.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [2]

    K. H. Johansson , A. Horch , O. Wijk , and A. Hansson , “Teaching multivariable control using the quadruple-tank process,” in Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), Phoenix, AZ, USA, (1), 1999, pp. 807812. https://doi.org/10.1109/CDC.1999.832889.

    • Search Google Scholar
    • Export Citation
  • [3]

    K. H. Johansson and J. L. R. Nunes , “A multivariable laboratory process with an adjustable zero,” in Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), Philadelphia, Pennsylvania, (4), 1998, pp. 20452049. https://doi.org/10.1109/ACC.1998.702986.

    • Search Google Scholar
    • Export Citation
  • [4]

    C. Ramadevi and V. Vijayan , “Design of decoupled PI controller for quadruple tank system,” Int. J. Sci. Res. (IJSR), vol. 3, no. 5, pp. 318323, 2014.

    • Search Google Scholar
    • Export Citation
  • [5]

    S. N. Deepa and A. Raj , “Modeling and implementation of various controllers used for quadruple- tank,” in International Conference on Circuit, Power and Computing Technologies (ICCPCT), Nagercoil, India, 2016, pp. 15. https://doi.org/10.1109/ICCPCT.2016.7530245.

    • Search Google Scholar
    • Export Citation
  • [6]

    V. Chaudhari , B. Tamhane , and S Kurode , “Robust liquid level control of quadruple tank system-second order sliding mode,” IFAC Pap. On-Line, vol. 53, no. 1, pp. 712, 2020. Available: https://doi.org/10.1016/j.ifacol.2020.06.002.

    • Crossref
    • Search Google Scholar
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    K. Divya , M. Nagarajapandian , and T. Anitha , “Design and implementation of controllers for quadruple tank system,” Int. J. Adv. Res. Edu. Technol. (IJARET), vol. 4, no. 2, pp. 158165, 2017.

    • Search Google Scholar
    • Export Citation
  • [8]

    A. Abdullah and M. Zribi , “Control schemes for a quadruple tank process,” Int. J. Comput. Commun. Control, vol. 7, no. 4, pp. 594604, 2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [9]

    J. Han , “From PID to active disturbance rejection control,” IEEE Trans. Ind. Elect., vol. 56, no. 3, pp. 900906, 2009. Available: https://doi.org/10.1109/TIE.2008.2011621.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [10]

    J. Li , X. Qi , Y. Xia , and Z. Gao , “On asymptotic stability for nonlinear ADRC based control system with application to the ball-beam problem,” 2016 American Control Conference (ACC), pp. 47254730, 2016. Available: https://doi.org/10.1109/ACC.2016.7526100.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [11]

    Z. Gao , “Scaling and bandwidth-parameterization based controller tuning,” in Proceedings of the 2003 American Control Conference, 2003, pp. 4989-4996. https://doi.org/10.1109/ACC.2003.1242516.

    • Search Google Scholar
    • Export Citation
  • [12]

    X. Meng , H. Yu , J. Zhang , T. Xu , and H. Wu , “Liquid level control of four-tank system based on active disturbance rejection technology,” Measurement, no. 175, 2021. Available: https://doi.org/10.1016/j.measurement.2021.109146.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [13]

    I. K. Ibraheem and W. R. Abdul-Adheem , “Improved sliding mode nonlinear extended state observer-based active disturbance rejection control for uncertain systems with unknown total disturbance,” Int. J. Adv. Comput. Sci. Appl. (IJACSA), vol. 7, no. 12, pp. 8093, 2016. Available: https://doi.org/10.14569/IJACSA.2016.071211.

    • Search Google Scholar
    • Export Citation
  • [14]

    I. K. Ibraheem and W. R. Abdul-Adheem , “From PID to nonlinear state error feedback controller,” Int. J. Adv. Comput. Sci. Appl. (IJACSA), vol. 8, no. 1, pp. 312322, 2017. Available: https://doi.org/10.14569/IJACSA.2017.080140.

    • Search Google Scholar
    • Export Citation
  • [15]

    B. Ashok Kumar , R. Jeyabharathi , S. Surendhar , S. Senthilrani and S. Gayathri , “Control of four tank system using model predictive controller,” in 2019 IEEE International Conference on System, Computation, Automation and Networking (ICSCAN), 2019, pp. 1-5. https://doi.org/10.1109/ICSCAN.2019.8878700.

    • Search Google Scholar
    • Export Citation
  • [16]

    A. Osman , T. Kara , and M. Arıcı , “Robust adaptive control of a quadruple tank process with sliding mode and pole placement control strategies,” IETE Journal of Research, pp. 114, 2021. https://doi.org/10.1080/03772063.2021.1892537.

    • Search Google Scholar
    • Export Citation
  • [17]

    F. D. J. Sorcia-Vázquez , C. D. Garcia-Blteran , G. Valencia-Palomo , J. A. Brizuela-Mendoza , and J. Y. Rumbo-Morales , “Decentralized robust tube-based model predictive control: application to a four-tank system,” Revista Mexicana de Ingeniería Química, vol. 19, no. 3, pp. 11351151, 2021. Available: https://doi.org/10.24275/rmiq/Sim778.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [18]

    K. Kiš , M. Klaučo and A. Mészáros , “Neural network controllers in chemical technologies,” in 2020 IEEE 15th International Conference of System of Systems Engineering (SoSE), 2020, pp. 397-402. https://doi.org/10.1109/SoSE50414.2020.9130425.

    • Search Google Scholar
    • Export Citation
  • [19]

    I. K. Ibraheem and W. R. Adul-Adheem , “A novel second-order nonlinear differentiator with application to active disturbance rejection control,” in 2018 1st International Scientific Conference of Engineering Sciences - 3rd Scientific Conference of Engineering Science (ISCES), 2018, pp. 68-73. https://doi.org/10.1109/ISCES.2018.8340530.

    • Search Google Scholar
    • Export Citation
  • [20]

    I. K. Ibraheem , “Anti-Disturbance Compensator Design for Unmanned Aerial Vehicle,” jcoeng, vol. 26, no. 1, pp. 86103, 2019. https://doi.org/10.31026/j.eng.2020.01.08.

    • Search Google Scholar
    • Export Citation
  • [21]

    I. K. Ibraheem and W. R. Abdul-Adheem , “An improved active disturbance rejection control for a differential drive mobile robot with mismatched disturbances and uncertainties”, arXiv e-print, arXiv:1805.12170, 2018.

    • Search Google Scholar
    • Export Citation
  • [22]

    A. A. Najm and I. K. Ibraheem , “Nonlinear PID controller design for a 6-DOF UAV quadrotor system,” Engineering Science and Technology, an International Journal, vol. 22, no. 4, pp. 10871097, 2019. Available: https://doi.org/10.1016/j.jestch.2019.02.005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [23]

    A. J. Humaidi and I. K. Ibraheem , “Speed control of permanent magnet DC motor with friction and measurement noise using novel nonlinear extended state observer-based anti-disturbance control,” Energies, vol. 12, no. 9, p. 1651, 2019. Available: https://doi.org/10.3390/en12091651.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [24]

    B. Z. Guo and Z. H. Wu , “Output tracking for a class of nonlinear systems with mismatched uncertainties by active disturbance rejection control,” Systems & Control Letters, vol. 100, pp. 2131, 2017. Available: https://doi.org/10.1016/j.sysconle.2016.12.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [25]

    K. H. Khalil (2015). Nonlinear control, global edition, Pearson Education, 2015.

  • [26]

    A. J. Humaidi , I. K. Ibraheem , and A. R. Ajel , “A novel adaptive LMS algorithm with genetic search capabilities for system identification of adaptive FIR and IIR filters,” Information, vol. 10, no. 5, p. 176, 2019. Available: https://doi.org/10.3390/info10050176.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [27]

    M. A. Joodi , I. K. Ibraheem , and F. M. Tuaimah , “Power transmission system midpoint voltage fixation using SVC with genetic tuned simple PID controller,” International Journal of Engineering & Technology, vol. 7, no. 4, pp. 54385443, 2018. https://doi.org/10.14419/ijet.v7i4.24799.

    • Search Google Scholar
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    A. A. Najm , I. K. Ibraheem , A. T. Azar , and A. J. Humaidi , “Genetic optimization-based consensus control of multi-agent 6-DoF UAV system,” Sensors, vol. 20, no. 12, p. 3576, 2020. Available: https://doi.org/10.3390/s20123576.

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    V. Chaudhari , B. Tamhane , and S. Kurode , “Robust liquid level control of quadruple tank system - second order sliding mode approach,” IFAC-PapersOnLine, vol. 53, no. 1, pp. 712, 2020. Available: https://doi.org/10.1016/j.ifacol.2020.06.002.

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    I. K. Ibraheem , “On the frequency domain solution of the speed governor design of non-minimum phase hydro power plant,” Mediterr J Meas Control, vol. 8, no. 3, pp. 422429, 2012.

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    I. A. Mohammed , R. A. Maher , and I. K. Ibraheem , “Robust controller design for load frequency control in power systems using state-space approach,” Journal of Engineering, vol. 17, no. 3, pp. 265278, 2011.

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    F. M. Tuaimah and I. K. Ibraheem , “Robust h∞ controller design for hydro turbines governor,” 2nd Regional Baghdad, Iraq: Conf. for Eng.Sciences/ College of Eng./ Al-Nahrain University, 2010, pp. 19.

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    R. A. Maher , I. A. Mohammed , and I. K. Ibraheem , “Polynomial based H∞ robust governor for load frequency control in steam turbine power systems,” International Journal of Electrical Power & Energy Systems, vol. 57, pp. 311317, 2014. Available: https://doi.org/10.1016/j.ijepes.2013.12.010.

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    I. K. Ibraheem , “A digital-based optimal AVR design of synchronous generator exciter using LQR technique,” Al-Khwarizmi Engineering Journal, vol. 7, no. 1, pp. 8294, 2011.

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Senior editors

Editor-in-Chief: Ákos, Lakatos

Founder, former Editor-in-Chief (2011-2020): Ferenc Kalmár

Founding Editor: György Csomós

Associate Editor: Derek Clements Croome

Associate Editor: Dezső Beke

Editorial Board

  • M. N. Ahmad, Institute of Visual Informatics, Universiti Kebangsaan Malaysia, Malaysia
  • M. Bakirov, Center for Materials and Lifetime Management Ltd., Moscow, Russia
  • N. Balc, Technical University of Cluj-Napoca, Cluj-Napoca, Romania
  • U. Berardi, Ryerson University, Toronto, Canada
  • I. Bodnár, University of Debrecen, Debrecen, Hungary
  • S. Bodzás, University of Debrecen, Debrecen, Hungary
  • F. Botsali, Selçuk University, Konya, Turkey
  • S. Brunner, Empa - Swiss Federal Laboratories for Materials Science and Technology
  • I. Budai, University of Debrecen, Debrecen, Hungary
  • C. Bungau, University of Oradea, Oradea, Romania
  • M. De Carli, University of Padua, Padua, Italy
  • R. Cerny, Czech Technical University in Prague, Czech Republic
  • Gy. Csomós, University of Debrecen, Debrecen, Hungary
  • T. Csoknyai, Budapest University of Technology and Economics, Budapest, Hungary
  • G. Eugen, University of Oradea, Oradea, Romania
  • J. Finta, University of Pécs, Pécs, Hungary
  • A. Formica, IASI, National Research Council, Rome, Italy
  • A. Gacsadi, University of Oradea, Oradea, Romania
  • E. A. Grulke, University of Kentucky, Lexington, United States
  • J. Grum, University of Ljubljana, Ljubljana, Slovenia
  • G. Husi, University of Debrecen, Debrecen, Hungary
  • G. A. Husseini, American University of Sharjah, Sharjah, United Arab Emirates
  • N. Ivanov, Peter the Great St.Petersburg Polytechnic University, St. Petersburg, Russia
  • A. Járai, Eötvös Loránd University, Budapest, Hungary
  • G. Jóhannesson, The National Energy Authority of Iceland, Reykjavik, Iceland
  • L. Kajtár, Budapest University of Technology and Economics, Budapest, Hungary
  • F. Kalmár, University of Debrecen, Debrecen, Hungary
  • T. Kalmár, University of Debrecen, Debrecen, Hungary
  • M. Kalousek, Brno University of Technology, Brno, Czech Republik
  • J. Koci, Czech Technical University in Prague, Prague, Czech Republic
  • V. Koci, Czech Technical University in Prague, Prague, Czech Republic
  • I. Kocsis, University of Debrecen, Debrecen, Hungary
  • I. Kovács, University of Debrecen, Debrecen, Hungary
  • É. Lovra, Univesity of Debrecen, Debrecen, Hungary
  • T. Mankovits, University of Debrecen, Debrecen, Hungary
  • I. Medved, Slovak Technical University in Bratislava, Bratislava, Slovakia
  • L. Moga, Technical University of Cluj-Napoca, Cluj-Napoca, Romania
  • M. Molinari, Royal Institute of Technology, Stockholm, Sweden
  • H. Moravcikova, Slovak Academy of Sciences, Bratislava, Slovakia
  • P. Mukhophadyaya, University of Victoria, Victoria, Canada
  • B. Nagy, Budapest University of Technology and Economics, Budapest, Hungary
  • H. S. Najm, Rutgers University, New Brunswick, United States
  • J. Nyers, Subotica Tech - College of Applied Sciences, Subotica, Serbia
  • B. W. Olesen, Technical University of Denmark, Lyngby, Denmark
  • S. Oniga, North University of Baia Mare, Baia Mare, Romania
  • J. N. Pires, Universidade de Coimbra, Coimbra, Portugal
  • L. Pokorádi, Óbuda University, Budapest, Hungary
  • A. Puhl, University of Debrecen, Debrecen, Hungary
  • R. Rabenseifer, Slovak University of Technology in Bratislava, Bratislava, Slovak Republik
  • M. Salah, Hashemite University, Zarqua, Jordan
  • D. Schmidt, Fraunhofer Institute for Wind Energy and Energy System Technology IWES, Kassel, Germany
  • L. Szabó, Technical University of Cluj-Napoca, Cluj-Napoca, Romania
  • Cs. Szász, Technical University of Cluj-Napoca, Cluj-Napoca, Romania
  • J. Száva, Transylvania University of Brasov, Brasov, Romania
  • P. Szemes, University of Debrecen, Debrecen, Hungary
  • E. Szűcs, University of Debrecen, Debrecen, Hungary
  • R. Tarca, University of Oradea, Oradea, Romania
  • Zs. Tiba, University of Debrecen, Debrecen, Hungary
  • L. Tóth, University of Debrecen, Debrecen, Hungary
  • A. Trnik, Constantine the Philosopher University in Nitra, Nitra, Slovakia
  • I. Uzmay, Erciyes University, Kayseri, Turkey
  • T. Vesselényi, University of Oradea, Oradea, Romania
  • N. S. Vyas, Indian Institute of Technology, Kanpur, India
  • D. White, The University of Adelaide, Adelaide, Australia
  • S. Yildirim, Erciyes University, Kayseri, Turkey

International Review of Applied Sciences and Engineering
Address of the institute: Faculty of Engineering, University of Debrecen
H-4028 Debrecen, Ótemető u. 2-4. Hungary
Email: irase@eng.unideb.hu

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2020  
Scimago
H-index
5
Scimago
Journal Rank
0,165
Scimago
Quartile Score
Engineering (miscellaneous) Q3
Environmental Engineering Q4
Information Systems Q4
Management Science and Operations Research Q4
Materials Science (miscellaneous) Q4
Scopus
Cite Score
102/116=0,9
Scopus
Cite Score Rank
General Engineering 205/297 (Q3)
Environmental Engineering 107/146 (Q3)
Information Systems 269/329 (Q4)
Management Science and Operations Research 139/166 (Q4)
Materials Science (miscellaneous) 64/98 (Q3)
Scopus
SNIP
0,26
Scopus
Cites
57
Scopus
Documents
36
Days from submission to acceptance 84
Days from acceptance to publication 348
Acceptance
Rate

23%

 

2019  
Scimago
H-index
4
Scimago
Journal Rank
0,229
Scimago
Quartile Score
Engineering (miscellaneous) Q2
Environmental Engineering Q3
Information Systems Q3
Management Science and Operations Research Q4
Materials Science (miscellaneous) Q3
Scopus
Cite Score
46/81=0,6
Scopus
Cite Score Rank
General Engineering 227/299 (Q4)
Environmental Engineering 107/132 (Q4)
Information Systems 259/300 (Q4)
Management Science and Operations Research 136/161 (Q4)
Materials Science (miscellaneous) 60/86 (Q3)
Scopus
SNIP
0,866
Scopus
Cites
35
Scopus
Documents
47
Acceptance
Rate
21%

 

International Review of Applied Sciences and Engineering
Publication Model Gold Open Access
Submission Fee none
Article Processing Charge 1100 EUR/article
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Limited number of full waiver available. Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription Information Gold Open Access

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.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2062-0810 (Print)
ISSN 2063-4269 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Dec 2021 0 86 84
Jan 2022 0 104 53
Feb 2022 0 57 68
Mar 2022 0 60 57
Apr 2022 0 27 31
May 2022 0 18 25
Jun 2022 0 0 0