esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Related Research
### Particle Swarm Optimization Algorithm (PSO)  
PSO [21; 22; 23] is a populated search method, which is used to select \(c\) and \(\sigma\) parameters in SVM. It is similar to genetic algorithms. PSO is performed by a population (called swarm) of individuals (called particles) that are updated from iteration to iteration [24; 25]. The particle of improved PSO-SVM is composed of two parts, \(c\) and \(\sigma\). To discover the optimal solution, each particle moves in the direction of its previously best position (_pbest_) and its best global position (_gbest_). For each particle, \(i\), and dimension,\(j\), search space, assume: particle vector \(x_{i}=\left(x_{i_{1}},x_{i_{2}},...x_{i_{g}}\right)^{T}\) denotes the current position of the \(ith\) particle, the velocity vector \(v_{i}=\left(v_{i_{1}},v_{i_{2}},...v_{i_{g}}\right)^{T}\) denotes the fly velocity of the \(ith\) particle, the velocity and position of particles can be updated by the following equations:  
\[v_{i_{g}}^{t+1}=wv_{i_{g}}^{t}+c_{i}r_{i}\left(p_{id}-x_{i_{g}}^{t}\right)+c_{ 2}r_{2}\left(p_{gs}-x_{i_{g}}^{t}\right) \tag{5}\]  
\[x_{i_{g}}^{t+1}=x_{i_{g}}^{t}+v_{i_{g}}^{t+1} \tag{6}\]  
In the above formula, \(t\) is the evolutionary time. \(v_{i_{g}}\) is the velocity of particle \(i\) on dimension \(j\), of which the value is limited to the range \(\left(-v_{\max},v_{\max}\right)\), \(v_{\max}\) value is very important for the algorithm. \(x_{i_{g}}\) is the position of particle \(i\) on dimension \(j\), of which the value is limited to the range \(\left(-x_{\max},x_{\max}\right)\). The inertia weight w is used to balance the global exploration and local exploitation. The \(r_{i}\) and \(r_{2}\) are random function in the range \(\left(0,\ 1\right)\), positive constants \(c_{1}\) and \(c_{2}\) are personal and social learning factors.  
The method has a great effect on the size of the search space, it is easy to cause the particles to miss the optimal solution if this value is set too large; however, if too small, it can also cause an incomplete search process.  
Figure 1 shows velocity and position adjustment of particle at time \(t_{0}\) and \(t_{0}+1\). The global optimal solution is at \(\mathfrak{G}\). \(v_{i}\) indicates flight velocity of \"self-awareness\" particle toward \(pbest\) direction at time \(t_{0}\). \(v_{2}\) indicates flight velocity of \"social-consensus\" particle toward \(gbest\) direction at time \(t_{0}+1\). \(v_{3}\) represents the particle's own current velocity. The particle reaches new particle position \(x_{{}_{t+1}}\) at a speed of \(v_{{}_{t+1}}\) by the three velocities. Velocity and position of the particle are an iteration process by the method. Finally, the particle constantly keeps close to the optimal position.
## 4 Results
### Fairness Assessment via Adversarial Debiasing  
To address potential biases in predictive modeling, adversarial debiasing was applied to the logistic regression model using gender and school type as sensitive attributes. Table 9 summarizes the fairness metrics before and after the debiasing process.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Parameters** & **F1 Score** \\ \hline XGBoost: lr=0.05,max\_depth=5,n\_est=100 & 0.9571 \\ XGBoost: lr=0.05,max\_depth=3,n\_est=100 & 0.9570 \\ Random Forest: max\_depth=None,min\_split=2,n\_est=200 & 0.9559 \\ Random Forest: max\_depth=10,min\_split=2,n\_est=200 & 0.9544 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Selected grid search configurations and corresponding F1 scores.  
Figure 2: ROC Curve—Logistic Regression.  
The results demonstrate a substantial improvement in algorithmic fairness. Demographic parity (DP) decreased from 0.048 to 0.021, indicating a marked reduction in the disparity of predicted \"pass\" outcomes across demographic groups. Equalized Odds (EO) also decreased from 0.298 to 0.180, meaning that true positive and false positive rates became more aligned between groups. Notably, these fairness improvements came with a modest 1.8 percentage point drop in classification accuracy.  
To ensure robustness, fairness metrics were evaluated across five different random seeds. The improvements remained consistent, affirming the stability of adversarial debiasing even under stochastic training conditions. Furthermore, separate experiments confirmed that debiasing with both sensitive variables (gender and school) led to more balanced outcomes than targeting them individually.
## Appendix A Operation of the Converter in Continuous Conduction Mode  
To avoid power loss in the DC/DC converter, the latter must work in continuous conduction mode (CCM) [17; 18]. This mode is characterized by permanently having the inductor current positive (\(I_{L}>0\)). To ensure operation in CCM mode, we follow the following steps to calculate the inductor value. For the boost converter circuit presented in Figure 3, two cases are possible. When the switch \(K\) is closed, we have  
\[V_{L}=V_{i} \tag{1}\]  
when the switch \(K\) is open, the voltage Kirchhoff's law yields  
\[V_{L}=V_{i}-V_{o} \tag{2}\]  
The voltage across the inductor is given by  
\[V_{L}=L\frac{dI_{L}}{dt} \tag{3}\]  
From Equations (1)-(3), the inductor current can be written as  
\[I_{L}=\int_{0}^{dT}\frac{V_{i}}{L}dt+\int_{dT}^{T}\frac{V_{i}-V_{o}}{L}dt \tag{4}\]  
where \(d\) is the duty cycle of the Pulse Width Modulation (PWM) signal applied to the switch, \(K\), shown in Figure 1.  
From Equations (1)-(4), the current curve through the inductance and its voltage are represented in Figure 2.  
The current ripple of \(I_{L}\), is defined as,  
\[\Delta I_{L}=I_{LMax-}I_{LMin} \tag{11}\]  
where if \(0<t<dT\) relation  
\[I_{L}=\frac{V_{i}}{L}t+I_{LMin} \tag{12}\]  
holds, whereas when \(dT<t<T\)  
\[I_{L}=\frac{V_{i}-v_{o}}{L}(t-dT)+I_{LMax} \tag{13}\]  
The average voltage across the inductor, \(L\), is zero, which results in  
\[VL\ =\ \frac{1}{T}\int_{0}^{T}V_{L}\cdot dt=\frac{1}{T}\left(\int_{0}^{dT}V_{i} \cdot dt+\int_{dT}^{T}(V_{i}-V_{o})\cdot dt\right)=0 \tag{14}\]  
\[V_{i}\cdot dT=(1-d)T(V_{o}-V_{i}) \tag{15}\]  
and  
\[V_{o}=\ \frac{1}{1-d}\ V_{i} \tag{16}\]  
The duty cycle value d is between 0 and 1 so the output voltage, \(V_{o}\), is necessarily greater than the input voltage, \(V_{i}\).  
The sizing of the inductor in DC/DC converters supplied by PVG is difficult because its value is calculated and optimized for a given input power.  
At the limit between continuous and discontinuous conduction mode (DCM), over a period \(T\), the ripple current through the inductor verifies relation  
\[\Delta I_{L}>\frac{I_{L\ max}}{2} \tag{17}\]  
At \(t=dT\) and from Equation (12) we find that:  
\[\Delta I_{L}>\frac{dTV_{i}}{2L} \tag{18}\]  
From Equation (18) we can calculate the inductor value for a given ripple current through the coil from  
\[L=\frac{V_{i}\ d}{\Delta I_{L}f} \tag{19}\]  
where \(V_{i}\) is input voltage, \(d\) is the duty cycle, \(I_{L}\) is the inductor current and \(f\) is the frequency of the PWM signal.
# A Blockchain and IoT-Enabled Framework for Ethical and Secure Coffee Supply Chains
## 4 Results and Discussion
### Administrative Gas Overhead in the Smart Contract  
Smart contracts often include administrative functions to support secure role transitions, especially when there are multiple parties involved in a process such as a supply chain. In the context of our smart contract for coffee supply chains, the two functions _transferOwnership()_ and _renounceOwnership()_ were observed during testing, allowing for further insights into the gas efficiency of control-layer operations such as supply chains.  
The _renounceOwnership()_ function, which removes the current owner by assigning the zero address, recorded the lowest average gas fee at approximately ETH 0.000058. This is consistent with its simple design involving a single state update and emission of an ownership change event.  
On the other hand, the _transferOwnership()_ function, which is used to delegate control to another address, has a slightly higher average gas fee of ETH 0.000227. This marginal increase also reflects the additional logic required to validate the new owner's address and update the relevant storage variable.  
While not part of the primary supply chain flow, these administrative functions are still essential for managing access control and contract governance. Their relatively low gas consumption demonstrates that critical updates to contract roles can be performed efficiently without notably introducing computational overhead or affecting the scalability of the system.  
Figure 7: This figure presents the distribution of transaction completion times for 1000 interactions on the Sepolia testnet. Most confirmations occurred between 90–100 s (29%), with variability across other intervals. The results highlight potential latency challenges for time-sensitive IoT-integrated supply chains.
# Performance Analysis of Dual-Hop Hybrid RF-UOWC NOMA Systems
## 3 Outage Probability Analysis
### Diversity Order  
To gain more insight, we study the achievable diversity order \((DO)\) of the obtained OPs. \(DO\) is the slope of \(OP_{l}\) where \(l\in\{1,2,sys\}\). According to [21], we can calculate diversity order as \(DO_{l}=-\lim\limits_{\rho\rightarrow\infty}\left(\log(OP_{l})\Big{/}\log(\rho)\right)\). It is clear from (12)-(14) that \(DO_{l}~{}=~{}\min(1,\frac{1}{r})\). As \(\frac{ac}{r}>>1\) in all scenarios, this result is consistent with the plots in Figure 2.
# The POSEIDON Ocean Observing System: Technological Development and Challenges
## 2 The POSEIDON System
### System Operations
#### 2.3.3 Platforms Upgrades  
The POSEIDON platform upgrades include new sensors, modules and replacements of aged equipment used to monitor the core parameters, but also the addition of new technologies to expand the group of the measured scientific parameters. In both cases, the multi-stage procedures described below allow for an evaluation of technologies and identify potential limitations or other relative issues in advance.  
* The initial activities include validation and calibration experiments in the laboratory as well as integration to platforms. Extra components such as battery packs, supportingbrackets, housings and transmission systems can be manufactured to support the equipment operations;
* In situ testing focuses on sensor/equipment deployment in coastal stations or other platforms with direct access. During the testing period, samples for cross-data validation can be collected and maintenance or service tasks are performed with smaller boats without the use of large costly R/Vs;
* In the final stage, the new equipment is operational for an extended period on the platforms of the POSEIDON system. The data obtained from the modules are cross-checked against the measurements and data flows of the observatory.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Source** & \begin{tabular}{l} **Manufacturer’s** \\ **Specification** \\ \end{tabular} & \
\begin{tabular}{l} **Assumed** \\ **Probability** \\ \end{tabular} &
\begin{tabular}{l} **Observed** \\ **Uncertainty** \\ \end{tabular} \\ \hline Temperature bath & - & - & 0.0009 \({}^{\circ}\)C & 0.0009 \({}^{\circ}\)C \\ Temperature bath & - & - & 0.0012 \({}^{\circ}\)C & 0.0012 \({}^{\circ}\)C \\ homogeneity & 0.001 \({}^{\circ}\)Cy\({}^{-1}\) & Rectangular & - & 0.0006 \({}^{\circ}\)C \\ Reference thermometer & 0.001 \({}^{\circ}\)C & Rectangular & - & 0.0006 \({}^{\circ}\)C \\ Accuracy & 0.001 \({}^{\circ}\)C & Rectangular & - & 0.0006 \({}^{\circ}\)C \\ Combined standard & & & 0.0017 \({}^{\circ}\)C \\ uncertainty & & & 0.0034 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 4: The uncertainty of the temperature calibrations.  
Figure 5: Panel (**A**) summarizes the temperature calibration procedure for 12 SBE 37 IM CT sensors. Panel (**B**) shows all sensors’ data that were collected during a calibration step. Panel (**C**) is the same as panel (**B**), only zoomed in for clarity. Bold lines denote the reference sensors and cycles denote the readings that belong to a calibration “window”.  
It is demonstrated that the technology refresh and the new additions improve radically the system performance and capabilities [15]. An example is presented in Figure 7.
## 3 Experimental Results
### Fourier-Transform Infrared Spectroscopy (FTIR)
#### 3.3.3 Non-Encapsulated and Encapsulated MAPb\({}_{3}\)-ETL Samples  
The degradation of the MAPb\({}_{3}\) layer was also evaluated in terms of its interaction with an ETL layer, due to being exposed to UV irradiation. In Figure 9, a reduction in the characteristic peaks can be observed at 3181 cm\({}^{-1}\) (38.71%), at 3124 cm\({}^{-1}\) (36.20%) and at 1465 cm\({}^{-1}\) (40.79%). The observed intensity reductions in the degraded MAPb\({}_{3}\) samples for these peaks were 73.73%, 72.91% and 69.79%, respectively. This difference suggests that the degradation of the MAPb\({}_{3}\) with ETL samples is lower than that of MAPb\({}_{3}\) ones. Finally, no degradation was observed in the encapsulated samples.  
Figure 8: (**A**) MAPb\({}_{3}\) before and after 50 min and 70 min under the solar spectrum and the UV irradiation lamp and (**B**) MAPb\({}_{3}\) + EVA before and after 350 h under solar spectrum. (* is used to appoint the maximum peaks).
## 3 Dual-Polarized 3D absorber  
### Description of the Structure  
In this section, a dual-polarized 3D absorber is proposed for dual-polarized wave absorption. The notch-slot resonators with coupled U-shaped microstrip lines are arranged along the \(x\)- and \(y\)-axes, and they are responsible for TM and TE polarizations, respectively, as shown in Figure 6. Considering the fabrication, the substrates along the \(x\)- and \(y\)-axes should be cross-joined together through the securing slits cut between the two adjacent unit cells. Compared with the single-polarized design in Section 2, additional notch slots with a length of \(L/2\) and a width of \(t\) are etched on the top and bottom sides of the unit cells for TM and TE polarizations, respectively, as shown in Figure 6b. These slots may introduce unexpected resonances that deteriorate the absorption. Therefore, some shorting pins are added inside the slots to eliminate these unexpected resonances. The shorting pins fabricated on the unit cells for TE polarization are inside the slot of the unit cells for TM polarization and vice versa. The difference is that there are two shorting pins inside the slot of the unit cells for TM polarization, and there is only one for TE polarization.  
Figure 5: Simulated \(\ket{S_{11}}\) and \(\ket{S_{21}}\) of the proposed 3D absorber without the reflecting plate.  
Figure 6: Structure of the proposed dual-polarized absorber: (**a**) 3D view (2\(\times\)2 unit cells); (**b**) 2D view of two unit cells for TM and TE polarizations.
# Model Predictive Control of Grid Forming Converters with Enhanced Power Quality
## 2 Converter Model and System Description  
### Converter Model  
Figure 2 shows the circuit schematic of a two-level three-phase VSC. The power switches in each leg operate in a complementary mode. The switching states can be represented by the switching signals \(S_{ka}\), \(S_{kb}\), and \(S_{kc}\), which are defined as follows:  
\[S_{ka}=\begin{cases}1\text{ if }S_{1}\text{ on and }S_{4}\text{ off}\\ 0\text{ if }S_{1}\text{ off and }S_{4}\text{ on}\end{cases} \tag{1}\]  
\[S_{kb}=\begin{cases}1\text{ if }S_{2}\text{ on and }S_{5}\text{ off}\\ 0\text{ if }S_{2}\text{ off and }S_{5}\text{ on}\end{cases} \tag{2}\]  
\[S_{kc}=\begin{cases}1\text{ if }S_{3}\text{ on and }S_{6}\text{ off}\\ 0\text{ if }S_{3}\text{ off and }S_{6}\text{ on}\end{cases} \tag{3}\]  
The filter inductance equation can be expressed in the vectorial form as:  
\[L_{f}\frac{\text{d}i_{L_{f}}}{\text{d}t}=V_{i}-V_{c_{f}} \tag{4}\]  
where \(L_{f}\) is the filter inductance (\(L_{a}\), \(L_{b}\), \(L_{c}\)). The equation that describes the dynamic behaviour of the output voltage can be expressed mathematically as:  
\[C_{f}\frac{\text{d}V_{c_{f}}}{\text{d}t}=i_{L_{f}}-i_{o} \tag{5}\]  
where \(C_{f}\) is the filter capacitance (\(C_{a}\), \(C_{b}\), \(C_{c}\)). These equations can be rewritten in the state space model as:  
\[\frac{\text{d}x}{\text{d}t}=Ax+BV_{i}+B_{2}i_{o} \tag{6}\]  
where,  
\[x=\begin{bmatrix}i_{L_{f}}\\ V_{c_{f}}\end{bmatrix} \tag{7}\]  
\[A=\begin{bmatrix}-R_{f}/L_{f}&-1/L_{f}\\ 1/C_{f}&0\end{bmatrix} \tag{8}\]  
\[B=\begin{bmatrix}1/L_{f}\\ 0\end{bmatrix} \tag{9}\]  
\[B_{2}=\begin{bmatrix}0\\ -1/C_{f}\end{bmatrix} \tag{10}\]  
where \(i_{L_{f}}\) and \(V_{c_{f}}\) are the filter current and voltage respectively. \(i_{o}\) is the load current, which can be estimated or measured. In this paper, \(i_{o}\), \(i_{L_{f}}\), and \(V_{c_{f}}\) are measured and transformed to the alfa-beta reference frame within the state space model. \(V_{i}\) is the inverter voltage of the system, and it has eight different voltage vectors, as shown in Figure 3. More details for the state-space model derivation and discretization method are presented in [31]. A discrete model is obtained from (6), and it can be expressed as follows:  
\[x\left(k+1\right)=A_{q}x\left(k\right)+B_{q}v_{i}\left(k\right)+B_{dq}i_{o} \left(k\right) \tag{11}\]  
where,  
\[A_{q}=exp^{AT_{q}} \tag{12}\]\[B_{q} =\int_{0}^{T_{s}}exp^{A\tau}Bd\tau \tag{13}\] \[B_{dq} =\int_{0}^{T_{s}}exp^{A\tau}B_{d}d\tau \tag{14}\]  
where \(T_{s}\) is the sampling time. This model is used to predict the filter voltages and currents for every possible input voltage. The selection of the optimal input voltage depends on the CF. In the next subsections, the conventional FCS-MPC algorithm and the proposed one will be discussed.
## 2 Results and Discussion
This suggests that the aroma of vegetable oils is rendered by the volatile compounds present in the plant materials, such as short-chain fatty acids, heterocyclic compounds, ketones, alcohols, esters, and aldehydes, or results from the processing or storage of the materials [28]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **RT** & **Area \%** & **Odor Description** & **References** \\ \hline
3,5-Hepttariene, (E,E)- & & 2.19 \(\pm\) 0.09 & & \\
1,6-Heptadiene-4-ol & 876 & 0.66 \(\pm\) 0.05 & & \\
3-Methyl-1 butanol & 736 & 2.51 \(\pm\) 0.22 & woody, whiskey, sweet & [29] \\
3-Methyl-1-butanol, acetate & 878 & 1.13 \(\pm\) 0.10 & banana & [35] \\
2-Methyl-1-propanol & 622 & 1.94 \(\pm\) 0.14 & wine, penetrating & [29] \\
2-Hexanal, (E)- & 854 & 1.02 \(\pm\) 0.07 & green leaf, apple-like & [29] \\
3-Methyl-3-Butenen-1-ol & 734 & 1.30 \(\pm\) 0.09 & fresh, fruity, green, slight lavelander & [36] \\
3-Hexen-1-ol, acetate, (Z)- & 1009 & 1.05 \(\pm\) 0.07 & & \\ Acetic acid & 609 & 2.17 \(\pm\) 0.16 & sour vineary & [29] \\ Acetic acid, methyl ester & 513 & 1.08 \(\pm\) 0.06 & ethereal, sweet & [29] \\ Benzene & & 1.25 \(\pm\) 0.08 & petroleum-like & [37] \\ Ethanol & & 1.60 \(\pm\) 0.07 & alcohol & [30] \\ Ethyl Acetate & & 8.78 \(\pm\) 0.52 & fruity & [38] \\ Hexanal & 801 & 2.48 \(\pm\) 0.21 & grassy, fatty & [29] \\
2,2-Dimethylpropanal & 110 & 3.14 \(\pm\) 0.29 & & \\ Propylene oxide & & 1.20 \(\pm\) 0.08 & ethereal & [39] \\ p-Xylene & & 1.22 \(\pm\) 0.09 & sweet & [40] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Percentage composition of volatile compounds from raspberry seed oil obtained by sonification. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **RT** & **Area \%** & **Odor Description** & **References** \\ \hline
3-Methyl-1,4-heptadiene & 725 & 1.09 \(\pm\) 0.07 & & \\
1H-1,2,3-Tiazrole & & 1.08 \(\pm\) 0.06 & & \\
2,4-Heptadiene, (E,E)- & 999 & 1.04 \(\pm\) 0.10 & fatty, rancid & [29] \\
2-Heptrenal, (Z)- & 960 & 1.25 \(\pm\) 0.11 & oxidized, fallowy, pungent & [30] \\
2-Octene & 817 & 1.19 \(\pm\) 0.10 & & \\
2-Pentenal, (E)- & 353 & 1.14 \(\pm\) 0.04 & fruity aroma & [31] \\ Acetic acid & 609 & 1.53 \(\pm\) 0.13 & sour vineary & [29] \\ Acetic acid, anhydride with formic acid & 645 & 1.20 \(\pm\) 0.09 & & \\ Acetic acid, methyl ester & 513 & 2.17 \(\pm\) 0.15 & ethereal, sweet & [29] \\ Benzaldehyde & & 1.69 \(\pm\) 0.14 & bitter almonds, penetrating & [29] \\
2-Nitrobutane & & 1.20 \(\pm\) 0.08 & & \\
1,1-Dimethylcyclopropane & 460 & 2.46 \(\pm\) 0.18 & & \\ Ethyl Acetate & 610 & 4.26 \(\pm\) 0.30 & sticky, sweet & [30] \\ Hexanal & 801 & 2.05 \(\pm\) 0.15 & grassy, fatty & [29] \\ Hexane & 600 & 3.81 \(\pm\) 0.15 & petroleum-like & [32] \\ Methacrolein & 568 & 3.95 \(\pm\) 0.28 & smell of ozone & [33] \\ Trimethylene oxide & & 1.71 \(\pm\) 0.15 & agreeable aromatic & [34] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Percentage composition of volatile compounds from blueberry seed oil obtained by sonification.
## 3 Controller Design for WWTP
### Mfa-Nfitsmc Design  
For the system shown in Equation (8), the discrete time tracking error is defined as follows:  
\[e(k)=y_{d}(k)-y(k) \tag{20}\]  
where \(y_{d}(k)\) is the desired output at time \(k\), \(y(k)\) is the system output at time \(k\).  
The discrete form of the FITSMS (12) is defined as follows:  
\[s(k)=e(k)+TE(k-1) \tag{21}\]  
where \(T\) is the sample time. The integral error term is  
\[\begin{split}& E(k)=\sum\limits_{i=1}^{k}\left[\alpha|e(i)|^{ \frac{p_{1}}{p_{2}}}\text{sgn}(e(i))+\beta\text{sgn}(e(i))\right]\\ &=E(k-1)+\alpha|e(k)|^{p_{1}/p_{2}}\text{sgn}(e(k))+\beta\text{ sgn}(e(k))\end{split} \tag{22}\]  
Due to the interference of the inlet flow rate and the unknown component concentration in WWTP, the tracking error of the DO concentration cannot always be on the sliding surface, which will lead to a deterioration of the global robustness of the system. In order to meet the reachability of tracking error to sliding mode surface, accelerate convergence speed, and reduce chattering, the following approach law [27] is selected:  
\[\dot{s}=-m|s|^{\lambda}\text{sgn}(s)-ns \tag{23}\]  
where \(m\) and \(n\) are constants that are positive, \(0<\lambda<1\). Its discrete form is as follows:  
\[s(k+1)-s(k)=-mT|s(k)|^{\lambda}\text{sgn}(s(k))-nTs(k) \tag{24}\]  
Considering Equations (8) and (20)-(22), we can obtain \[s(k+1)-s(k) =e(k+1)+TE(k)-e(k)-TE(k-1) \tag{25}\] \[=y_{d}(k+1)-y(k+1)-(y_{d}(k)-y(k))+T\bigg{(}\alpha|e(k)|^{\frac{p_{ 1}}{p_{2}}}\text{sgn}(e(k))+\beta\text{sgn}(e(k))\bigg{)}\] \[=\Delta y_{d}(k)-\hat{\phi}_{c}(k)\Delta u(k)+T\Big{(}\alpha|e(k) |^{p_{1}/p_{2}}\text{sgn}(e(k))+\beta\text{sgn}(e(k))\Big{)}\]  
By combining Equations (24) and (25), the following control law can be obtained  
\[\Delta u(k)=\frac{1}{\hat{\phi}_{c}(k)}(mT|s(k)|^{\lambda}\text{sgn}(s(k))+nTs (k)+\Delta y_{d}(k)+\alpha T|e(k)|^{p_{1}/p_{2}}\text{sgn}(e(k))+\beta T\text{ sgn}(e(k)) \tag{26}\]  
In Equation (26), the desired output increment \(\Delta y_{d}(k)\) is required to calculate the control variable. In fact, the trajectory to be tracked is usually predefined in the control system, so \(\Delta y_{d}(k)\) is a priori known. When the desired output is a constant value, Equation (26) can be expressed as:  
\[\Delta u(k)=\frac{1}{\hat{\phi}_{c}(k)}(mT|s(k)|^{\lambda}\text{sgn}(s(k))+nTs (k)+\alpha T|e(k)|^{\frac{p_{1}}{p_{2}}}\text{sgn}(e(k))+\beta T\text{sgn}(e( k))) \tag{27}\]  
[PERSON] and [PERSON] and [PERSON] (2018) have proved that the PPD estimation value \(\hat{\phi}_{c}(k)\) is bounded and the reset algorithm (7) guarantees that the lower bound of \(\hat{\phi}_{c}(k)\) is not zero, so the control law given by Equation (27) is nonsingular. Thus, a complete MFA-NFITSMC method for the WWTP control system is constructed by Equations (4)-(7) and (20)-(27), and the structure of control system is shown in Figure 2.