Fractional-Order Predictive PI Controller for Dead-Time Processes With Set-Point and Noise Filtering

In most of the industrial process plants, PI/PID controllers have been widely used because of its simple design, easy tuning, and operational advantages. However, the performance of these controllers degrades for the processes with long dead-time and variation in set-point. Up next, a PPI controller is designed based on the Smith predictor to handle dead-time processes by compensation technique, but it failed to achieve adequate performance in the presence of external noise, large disturbances, and higher-order systems. Furthermore, the model-based controllers structure is complex in nature and requires the exact model of the process with more tunable parameters. Therefore, in this research, a fractional-order predictive PI controller has been proposed for dead-time processes with added filtering abilities. The controller uses the dead-time compensation characteristics of the Smith predictor and the fractional-order controller’s robustness nature. For the high peak overshoot, external noise, and disturbance problems, a new set-point and noise filtering technique is proposed, and later it is compared with different conventional methods. In servo and regulatory operations, the proposed controller and filtering techniques produced optimal performance. Multiple real-time industrial process models are simulated with long dead-time to evaluate the proposed technique’s flexibility, set-point tracking, disturbance rejection, signal smoothing, and dead-time compensation capabilities.


I. INTRODUCTION
Simple control structure and easy tuning parameters made the PID controller trustworthy in process industries evien after the emergence of new process control strategies like model-based controllers, adaptive control, fault tolerance control, etc., [1]- [3]. PI controller is largely adopted in the process and automation industry among all the PID variants [4], [5]. Even though the derivative action in a PID controller leads to phase advance due to its predictive capability, it becomes problematic when long dead-time and The associate editor coordinating the review of this manuscript and approving it for publication was Norbert Herencsar .
high-frequency noise are involved because of the noise sensitivity introduced by the derivative part [6], [7]. Therefore, conventional PI controllers are inadequate to be employed in a delayed environment, high-frequency noise, and other uncertainty systems [8]- [10]. In such environments, if the PI controllers are used, the system will lead to oscillatory and unstable response because of the limited gain constant [11], [12]. For instance, if the gain is small, the response of the system becomes sluggish. On the other hand, if the gain is large, the response becomes oscillatory with high peak overshoot and may lead to system instability. Several enhancements in conventional PI controller resulted in the development of different controllers like VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ fractional-order PI (FOPI), set-point weighted PI (SWPI), predictive PI (PPI), and nonlinear PI (NPI) which are utilized by various researchers to control processes with long dead-time [13]- [16]. On the other hand, hybridizing the PI controller with the advanced control techniques like dead-time compensators (DTC), model-based predictive controller (MPC), internal model controller (IMC), and generalized predictive controller (GPC) to enhance its performance were carried out by various researchers [17]- [19]. Even though all the above approaches improved the controller performance, they failed to withstand in the industrial processes because of their complex design, more added tuning parameters, maintenance, and implementation difficulty. Many of these controllers need an exact process model to achieve an optimized control [17], [18]. To highlight the above discussed constraints and drawbacks, the various controllers and process model parameters needed to be tuned are shown in Table 1. Control of dead-time processes is comprehensively researched because most of the real-time industrial process exhibits the inherent time delay. In these situations, increased phase lag in PI controllers will lead to the destabilization of the closed-loop control system. Researchers in [6], [20]- [22] came up with a new predictive PI controller which is based on conventional PI and Smith predictor to solve these issues faced by the process plants with longer dead-time. However, the controller is unable to achieve robust performance during large disturbances and shows poor closed-loop performance due to the mismatch between the real-time plant and the designed process model. Conventional PI controller is also a type of fractional-order control that will be obtained by making the fractional-order parameter lambda (λ) value equal to unity (i.e. λ=1) in the integral part of the PI controller. Podlubny [23] first proposed these modifications in the conventional controller. This adjustable parameter gives a way for achieving the most flexible and dynamic properties of the fractional controller [24]- [26]. As a result, the fractionalorder controllers are extensively used in many engineering control applications like process industries, unmanned aerial vehicles (UAV's), military applications, trajectory tracking etc., [27]- [33]. Among these applications, some of the researchers designed the fractional-order controllers for dead-time process plants [34]- [36]. Results have shown that the fractional-order PI controller produced robust control actions but settled slower and produced higher overshoot than the conventional methods. Also, an extensive review of the recent advances in fractional-order control for the time delay process can be found in [37]. Therefore still, there is a need for designing an adequate controller to achieve robust performance even in the presence of longer dead-time.
Earlier literature is discussed about the presence of external noise, set-point variation and longer dead-time in the real-time process makes it more difficult to control. Thus, alternate approaches like set-point filtering are introduced for preventing the large variation in the control signal often results in high peak overshoot which fastens the wear and tear of components in final control elements. Vijayan and Panda [38] proposed this filtering to solve this issue. But this method involves tedious calculations and the user has to define multiple parameters to obtain the filter time constant. Also, this method did not reduce much overshoot in closed-loop processes. For example, their filter time constant calculation will be given as: where, τ -filter time constant; k-system gain (k = Mp1 0.6321 ); tp -peak time; Mp -peak overshoot.
At the same time, processes associated with noise often experience the control signal fluctuations due to the regulatory performance degradation [39]- [41]. Therefore, filtering is needed to remove the noise signal from the process signal to get the effective control signal output. In [17], [42], [43] researchers proposed various filtering techniques to deal with the external noise and set-point variation problems. These results indicated that it is not essentially higher order filters that are needed to achieve good performance in the PI controller. Thus a new first-order filter is designed without changing the conventional structure and it is compared with the existing techniques.
The issues observed in the above literature motivated and led to the intention of developing a new control technique that improves the dead-time process performance. On the other hand, the external disturbance and noise presence in most of the process control applications led to the idea of developing a filtering technique based on existing and extensively adopted techniques. The major contributions to the field of process control from this research paper will be given as follows: 1) A new fractional-order predictive PI (FOPPI) controller is designed by hybridizing the traditional fractional-order PI and the predictive PI (PPI) controller. 2) A new first-order filter is designed by including the process model parameters such as process gain (K ) and dead-time (L n ) in the filter time constant (T f ). 3) Proposed controller performances are compared against the PI, PPI, and FOPI controllers. While the proposed filter performances are compared with the widely adopted Hägglund [42] and Normey-Rico and Camacho [17] filter.
The remaining sections of the paper are organized as follows: A detailed design procedures for the proposed fractional-order predictive PI (FOPPI) controller and new filtering techniques are presented in Section II. Section III provides the simulation results and analysis of the various real-time processes plants. Filter simulation results are illustrated in Section IV and V. Conclusion and future developments of the proposed work are given in Section VI.

II. METHODOLOGY
Design of the proposed FOPPI controller using the conventional fractional-order PI controller and the smith predictor is elucidated in the first part. Later, major signals like the input signal R(s) and process feedback signal Y(s) are fed to the set-point filter and noise filter respectively to improve the process stability. A new approach for set-point and noise filtering technique is introduced and it is compared with other filter designs from Hägglund [42] and Normey-Rico and Camacho [17] to evaluate its performance and efficacy.

A. FRACTIONAL-ORDER PI (FOPI) CONTROLLER
Consider the traditional closed-loop feedback control system of Fig. 1, G c (s) is the controller, G p (s) is the process plant, N (s) and D(s) represents the external noise and disturbance, and control signal and error signal are represented as U (s) and E(s). All the system signals and process variables are represented in Laplace domain. Consider G c (s) is the PI controller in the Fig. 1, the control signal of PI controller is given as: where, K p and T i are the proportional gain and integral time constants of the controller. Fractionalize the integral action using λ of the above PI controller equation (1) yields the fractional-order PI (FOPI) controller. Hence, the fractionalorder PI controller control signal will be represented as: In Eqs. (1) and (2), the error signal E(s) is given as, Oustaloup's approximation technique is used in fractionalorder integrator 1/s λ considered in Eq. (2).

B. FRACTIONAL-ORDER PREDICTIVE PI (FOPPI) CONTROLLER
Consider the First-Order Plus Dead-Time (FOPDT) process with fractional integrator as: In the above equation, K , L p , T , and λ are the process gain, dead-time, time constant, and fractional order integrator, respectively. Using the block diagram in Fig. 1, if G c (s) is the fractional-order predictive PI controller, the control signal U (s) will be obtained by considering the First-Order Plus Dead-Time (FOPDT) transfer function of G p (s).
Closed-loop transfer function between R(s) and Y (s) is obtained from the block diagram as, Therefore, the controller G c (s) will be obtained by rearranging the above equation as follows: The desired closed-loop transfer function G o (s) is considered as follows: Thus, FOPPI controller transfer function will be obtained, by substituting Eqs (4) and (9) in (8) as follows: Expressing the controller G c (S) in terms of input-output relation, the control signal U (s) will be obtained. Thus, the control signal of fractional-order predictive PI (FOPPI) controller is given as follows: (12) where, K p = 1 K , T i = T and λ is the order of integration. Thus, the designed fractional-order PPI controller in Eq. (12) can be implemented as shown in Fig. 2. VOLUME 8, 2020 FIGURE 2. Fractional-order predictive PI controller implementable structure with set-point filter (F s ) and noise filter (F n ).

C. FILTERING
Placing the different types of filters in the closed-loop control system is illustrated in Fig. 1. Where the F s and F n are set-point filter and noise filter for the input signal R(s) and feedback signal Y (s) containing noise. These input signals to the controller are commonly filtered in distinct ways before they are fed into the controller to improve the system performance. Overshoot fluctuations and high-frequency variations in the controller output because of set-point signal R(s) led to the development of a set-point filtering technique. This set-point filter (F s ) separates the varying load disturbance response from the actual set-point response. This will result in a faster process settling because of the reduction in the overshoot and high-frequency issues. On the other hand, noise filter (F s ) is introduced in the feedback signal Y(s) to minimize or nullify the high-frequency noise in the process by compensation technique. Also, by modifying the dynamics of the transfer function this filter improves the controller performance significantly. While designing, it is essential to understand the significance of different types of filters, so they can help in improving the closed-loop feedback performance. Thus, in this research, a simple first-order filter is used for simulation and it is given by: where, T f is the filter time constant. Various researchers proposed different methods for determining and tuning this filter time constant by using information about the process parameters like peak overshoot, time constant, dead-time, process gain, and peak time. Because of some unnecessary parameters consideration in various designs resulted in extensive calculations made the filter design a complex step. So, in this article, the conventional and simple method of designing the filter approaches proposed by Hagglund and Normey is used for finding the filter time constant, and later it is compared with the proposed approach. Hagglund approach for calculating the T f utilizes the integral time of the PI controller (i.e. T f = T i ). This approach may fail to obtain effective performance if the controller is not tuned properly. Also, it did not consider any of the process dynamics which have a huge impact on process settling time overshoot reduction. In Normey approach the process dead-time only used for the filter time constant calculation leaving the process gain (i.e. T f = L n /2) led to the high overshoot problem.
The above-mentioned method performs well in the lower order process and small dead-time systems with unity process gain (K) and fail to achieve effective performance in higher order and processes with long dead-time. Thus, using the major plant dynamics in the filter time constant will help the filter to perform effectively than the existing methods. In the proposed technique both process gain and dead-time are used for calculating the filter time constant (i.e. T f = K /L n ). The time constants T fs and T fn of the set-point filter and noise filter are added in the process directly since they are considered as non-influencing parameters concerning the controller design.

III. RESULTS AND DISCUSSION
In different applications like industrial electrical drives, precision positioning, unmanned vehicle control, autonomous pathfinders, and trajectory mapping, continuous tracking of the control signal is needed to obtain the optimized path [29], [31], [44]- [46]. In process control applications the main objectives are set-point tracking, disturbance rejection, and noise reduction/regulation [47]- [49]. Thus, the controller signal is shown in all the results and analysis figures to understand more about the effective controller signal amongst all. The simulation results are analyzed and compared in performance conditions like rise time, settling time, overshoot, set-point tracking, disturbance rejection, and noise reduction for different controllers like PI, PPI, FOPI, and FOPPI in the various real-time process models considered. Additionally, set-point and noise filter designs from Hagglund, Normey, and the proposed filter is added with the controller to evaluate their performance for disturbance, overshoot, and noise reduction capabilities. In the feedback loop, a white noise signal of 0.01 magnitude shown in Fig. 3 is injected for examining the noise removal and process signal smoothing characteristics of the filters under comparison.

A. MODEL SELECTION AND CONTROLLER PARAMETERS
In this research real-time process models are used for simulation, which exhibit real industrial plant dynamics and behaviour. For instance, an industrial model of a thermal chamber used by Tan et al. in [11] is utilized as a first-order process model. The other second and third-order process models are given as: Optimised controller parameters for all the controllers obtained are given in Table 2. To get the optimised controller performance, the fractional-order integrator (λ) value is chosen based on trial and error method using the proposed FOPPI controller. The performance under different lambda values is shown in Fig. 4. Additionally, Oustaloup approximation technique parameters used here are frequency range of interest (ω b ,ω h ) = (10 −5 , 10 5 ) and order of approximation N = 5. The parameters are selected based on the works reported in [14], [50]. Thus, transfer of fractional-order integrator is   In this subsection, real-time process model of the thermal chamber which is given as G 1 (s) in Eq. 14 has been evaluated for set-point tracking, disturbance rejection and variable set-point tracking using the tuned controller parameters in Table 2 and the performance results are shown in Fig. 5. Furthermore, the areas inside the dotted rectangles A,B,C, and D in Fig.5 are enlarged and shown in Fig. 6. Then, the numerical analysis for rise time (t r ), settling time (t s ) and percentage overshoot (%OS) is given in Table 2. Observing Fig. 5, 6 and Table 2, it can be easily seen that the proposed fractional-order PPI controller performed better in-terms of set-point tracking and disturbance rejection compared to PI, FOPI and PPI controllers. Though FOPPI is having a slower rise time of 11.8699s, the controller managed  to settle faster at 359.4802s while others settled slower at 362.3357s (PI), 361.9219s (FOPI), and 362.1703s (PPI). In peak overshoot, the FOPPI performed well with less overshoot of 2.2517% compared to 7.6436, 5.1177, and 4.0463% for PI, FOPI, and PPI respectively. Furthermore, the performance of variable set-point tracking for the plant with all the compared controllers is shown in Fig. 7. The figure clearly shows that the proposed method recovered faster and without overshoot from the effect of the variation in set-point and disturbance compared to other controllers. On the other side, while observing controller action, the aggressiveness of the control signal is more or less the same for all the controllers at the set-point change with less steady stare error.

1) STABILITY ANALYSIS
The graphical representation of the gain margin and phase margins of a control system provides a comprehensive understanding of the system's behavioral dynamics [51], [52]. These control system characteristics are used in the Bode plot, a traditional and most convenient method of finding the stability of the system used by most of the researchers is utilized for this research. Consider the single-input-singleoutput (SISO) system in the continuous-time domain shown in Fig. 1. Frequency domain representation of First-Order Plus Dead-Time (FOPDT) process will be represented as: The modulus and the argument functions of the above transfer function will be given as, arg(G p (jω)) = arg( Using the controller parameters from the Table 2 and the process model (G 1 (s)), the open-loop transfer function of the system will be obtained as given below: 0.00018769s 1.96 +0.0274s 0.98 +1 2.3461e−05s 1.96 +0.0017125s 0.98 e −5s (21) The above transfer function will be used to obtain the Bode response of the fractional-order predictive PPI controller along with the first order system (G 1 (s)). Furthermore, this transfer function will be approximated using Oustaloup approximation in the desired frequency range (ω l , ω h ) to obtain the s λ . The Oustaloup approximation of s λ is given as: where The Bode plot analysis of the open loop system with various controller parameters and the corresponding approximated fractional-order transfer function results are shown in Fig. 8. From the Bode plot, based on the gain and phase margin values both the system and the controller are robust and stable in all the considered processes.

C. SECOND-ORDER SYSTEM
Performance study of the second-order plant G 2 (s) given in Eq. 15 results are given in Table 2. All the analysis and comparisons are performed in a similar fashion to the first-order system. The performance results of this process plant are given in Fig. 9 and the zoomed regions of A, B, C, and D are highlighted in Fig. 10. The figures and numerical analysis represent the analogous trends of the first-order plant is observed in the second-order plant as well. The proposed controller rise time is noticeably increased than the previous first-order process. This resulted in achieving the faster settling time of 488.7413s while others settled at 498.4690,   498.5718, and 491.3066s for PI, FOPI, and PPI respectively. If we observe the Fig. 10 and numerical results in Table 2, during the set-point change most of the controllers had their peak overshoot.
In this plant, the FOPPI controller produced the least overshoot of 2.0660% but it lags behind the PPI by 0.03%. The other controllers PI, FOPI, and PPI have a high peak overshoot of 16.9419, 14.5728, and 2.0396% respectively. In addition, during the variable set-point tracking and disturbance rejection analysis, the FOPPI performed better than all controllers with faster control actions. Since all the compared controllers are from PI family, they continuously manage to give a similar pattern of steady-state error with a close range of each other. Same to the first-order system Bode plot stability analysis, the fractional-order transfer function of the second-order process is given in Eqn. (23) and the respective approximated Bode plot results are illustrated in Fig. 12.

D. THIRD-ORDER SYSTEM
The simulation results for the third-order process plant G 3 (s) are shown in Fig. 13 and the various regions of interest A, B, C, and D are given in Fig. 14. The numerical analysis of the plant is summarised in Table 2. This plant results also adhere to the trend of the first and second-order process plant performance. The proposed FOPPI has a rise time of 11.9880s which is the slowest one while comparing with PI, FOPI, and PPI of 8.9926, 9.2550, and 11.5466s respectively. However, the FOPPI maintained the faster settling time (354.2014s) including the huge 13.1576 seconds difference in settling time with the second-fastest PPI controller. Also in peak overshoot performance, the FOPPI produced less peak overshoot of 5.4231% comparing the PPI (9.4396%), FOPI (17.7708%), and PI (23.0499%) which is a 17.6268% reduction in overshoot against the highest value. While observing the control   signals in Fig. 14, there is aggressive control actions produced by FOPPI and PPI controller to reach the set-point at a faster rate with minimal overshoot. Set-point tracking and disturbance rejection performance of the controllers is shown in Fig. 15. This figure illustrates, all the controllers maintained less steady-state error even during the variation of set-point. In a similar fashion with the first and second-order processes, the fractional-order transfer function of the process is given in Eqn. (24). The Bode plot analysis of this system is shown in Fig. 16.  (24) All the performance analysis and comparison results indicate, the FOPPI controller outperformed all the compared controllers in all the process plants. So, the proposed FOPPI controller alone will be further studied for the performance assessment in the presence of set-point and noise filtering in upcoming simulations.

IV. SET-POINT FILTER
Set-point filters are mostly used along with the PI controller family. As mentioned in the filtering section II-C, this filter is aimed at the reduction of peak overshoot to a desired or tolerable limit. Usually, the selection of this set-point filter depends on various factors and different methods. Mostly this filter is chosen as low-pass in nature with the T f values of unity or less to ensure the process output and set-point equality in the steady-state period. For the filter evaluation, processes given in the Eqs. 14, 15, and 16 are used with the proposed FOPPI controller. Numerical analysis of the filters and their filter time constant values are given in Table 3.

A. FIRST-ORDER SYSTEM
First-order process plant simulation along with the set-point filtering results are shown in Fig. 17 and the zoomed-in regions of interest A, B, C, and D are given in Fig. 18. Observing the figures and numerical results of this order, there is a huge time difference of 61.0837 seconds in settling time between the process without filter (actual process) (361.4082s) and the proposed filtering (300.3245s), which shows the significant improvements of proposed controller and filtering technique. Remaining Hagglund and Normey filters settled slightly slower than the proposed method of 304.8526 and 301.3071s respectively.
Furthermore, the proposed filtering method achieves the objective of set-point filtering by reducing the peak overshoot of the actual process (2.2517%) with further minimization of 1.8016%. Other filters also reduced little amount with the values of 1.9447%, and 1.9601% for Hagglund, and Normey methods. FOPPI performs 1.0277s faster than the actual process in the rise time performance. The Hagglund approach shown faster recovery from the set-point change and disturbance but settled slower than others [See Fig. 18].

B. SECOND-ORDER SYSTEM
The simulation results of the second-order plant are shown in Fig. 19. The zoomed-in regions of interest A, B, C, and D are given in Fig. 20. The numerical analysis of the above-mentioned figures is given in Table 3. These results indicate the proposed filter and proposed controller combination have the second-fastest rise time of 6.3484s followed by Normey (9.6486s), and Hagglund. (16.6895s) than the actual process (5.6489s).
In the settling time performance, same combination topped with the fastest settling time of 423.1467s having a 67.4946 seconds time difference from the actual process (490.6413s). Observing Fig. 20 and the numerical analysis, the controller shows aggressive control actions in all the filter combinations which resulted in less peak overshoot for Hagglund (1.1141%) and Normey (1.1143%). The proposed combination had a slightly higher overshoot of 1.7147% than the compared methods but less than the actual process (2.0660%).

C. THIRD-ORDER SYSTEM
The simulation results of the third-order system are shown in Fig. 21 and the numerical analysis is given in Table 3. The zoomed-in regions of interest A, B, C, and D are shown in Fig. 22. Unlike the first and second-order processes, the third-order performance of the proposed combinations  had a rise time of 12.0525s which is marginally slow when compared with the actual process (11.9880s). Likewise, in overshoot analysis, the proposed controller together with all filters combinations performed well. Among those, the proposed filter topped in overshoot reduction with the value of 1.6905% followed by Normey (1.7623%), Hagglund (1.8692%), and actual process (5.4231%). In process settling time, a vast difference of 59.1629 seconds is observed between the actual process (354.2014s) and the proposed approach (295.0385s). While Hagglund and Normey filters settled slightly slower than the proposed method of 315.1967 and 305.2037s respectively. Observing the different control signals in Fig. 22, the proposed approach and the actual process had less aggressive signals than others during the variation in set-point.

V. NOISE FILTER
When a noisy signal is used in control, filtering the noise component from the feedback signal is essentially needed to avoid the excessive controller output which will result in final control element damages and other loop failures. In this simulation, a first-order filter is used to solve this problem. Due to the absence of derivative actions in the controllers used for simulation, this filter will act as a derivative part to compensate for the noise signal. In the feedback loop a white noise signal of 0.01 magnitude shown in Fig. 3 is injected, for the filter evaluation, processes given in the Eqs. 14, 15, and 16 are used with the proposed FOPPI controller. Numerical analysis of the filters and their filter time constant values are given in Table 4.

A. FIRST-ORDER SYSTEM
Analysis of the noise filter with the FOPPI controller is performed similarly with the previous process plants. Simulation results of the first-order process plant along with the noise filtering are shown in Fig. 23. In contrast with set-point filtering, noise filters produced very high overshoot exceeding the actual process. In that, the Hagglund method produced a twenty-seven times higher overshoot value of 55.8215% than the least one having 2.2517%.
It is noted that, this technique had the overall fastest rise time of 8.1452s but settled very slow at 540.3089s because of the overshoot problem. The proposed and Normey techniques also had a high overshoot of 13.4355 and 20.0537% respectively. Astonishingly, the proposed filter had a faster rise and settling times of 8.7994s and 358.1023s compared to other techniques. However, the proposed filter produced high overshoot compared with the real process. The zoomed-in regions of interest A, B, C, and D are given in Fig. 24. Paying attention to this figure reveals faster control actions were taken by the proposed filter and controller combo than other filter combinations with the FOPPI controller. After the disturbance injection via set-point change, both proposed and Normey filters had a faster recovery rate because of effective control [See regions B and D of Fig. 24].

B. SECOND-ORDER SYSTEM
The simulation results of the second-order plant are shown in Fig. 25. The zoomed-in regions of interest A, B, C, and D are given in Fig. 26. Table 4 shows only a minor variation in rise time performance is experienced among the compared filtering techniques. In this, the Hagglund technique topped with 6.0243s followed by Normey (6.0402s) and proposed  technique (6.0904s). Though there is a small rise time variations, the proposed filter settled faster at 421.7944s with a huge difference of 68.8469 seconds than the actual process (490.6413s). While Hagglund and Normey methods settled at 427.3101 and 426.0506s respectively.
Additionally, in overshoot performance, the proposed combinations performed well by having a less peak overshoot of 3.0542% slightly higher than the actual process (2.0660%). In a similar fashion with the first-order process, Hagglund and Normey technique produced a high peak overshoot of 23.6499 and 15.4379% which is seven to twelve times higher than the actual process. Variation in set-point severely affects the Hagglund and Normey filter performance, but the proposed filter managed to keep in track with the actual process and settled faster due to aggressive control signal.

C. THIRD-ORDER SYSTEM
The simulation results of the third-order plant are shown in Fig. 27. The zoomed-in regions of interest A, B, C, and D are given in Fig. 28. In this process also, the Hagglund VOLUME 8, 2020   technique had a faster rise with 11.2086s followed by Normey (11.2171s), proposed technique (11.3136s), and actual process (11.9880s). An enormous difference of 86.2713 seconds is observed in the process settling between the proposed filter (267.9301s) and the actual process (354.2014s). In overshoot performance, the proposed filter and the actual process had  nearly in-line values of 5.7872% and 5.4231% respectively. In similar to the first and second-order process, Hagglund and Normey technique had a larger peak overshoot of 27.7576% and 30.1781% which are approximately six times higher than the actual process. Observing the various control signals, a more aggressive signal is produced by the proposed filter that resulted in faster recovery during the variation of set-point.

D. REMARKS
The major improvements obtained in process control because of this new controller and filtering are given as follows: 1) Dead-time compensation ability of the Smith predictor based PPI and the fractional-order PI controller's robustness character is retained by the proposed FOPPI controller. 2) Concerning the controller complexity and implementable structure, the proposed controller manages to keep the same number of tuning parameters possessed by conventional PID [See Table 1]. The newly added fractional-order integrator (λ) further enhanced the overall process performance by meeting more frequency-domain requirements. 3) Filters, noise, and disturbance shown in Fig. 2 are made as non-influential constraints while designing the new FOPPI controller, since they don't have any direct relation with the controller design.

E. SUMMARY
Comparative analysis of various controllers namely PI, FOPI, PPI, and FOPPI controllers have allowed us to study their performance in various conditions. Furthermore, filter designs by Hagglund and Normey are compared with the proposed approach to examine their efficiency. Some of the important analyses and findings from the simulation results are highlighted below: 1) In all the process plants considered, the proposed FOPPI controller outperformed the PI, FOPI, and PPI controllers in rise time, settling time, and peak overshoot performances.
2) The proposed controller deals effectively with the variation in set-point and disturbance rejection by taking more aggressive control actions even in process plants with longer dead-time.
3) The proposed set-point filter greatly reduces the overshoot problems in all the process plants. 4) The proposed noise filter results have shown that it immensely smoothens the process signal by making the control signals free from noise. 5) While comparing with the set-point filter, noise filter control signals are smoother which results in reduced offset errors in the process output signal.

VI. CONCLUSION
The design and implementation of a new fractional-order predictive PI (FOPPI) controller for real-time industrial process plants has been presented in this article. Various performance analyses have been conducted with different controllers to evaluate the proposed controller effectiveness of handling the process with long dead-times and disturbance rejection. Additionally, the set-point and noise filtering technique is introduced in the closed-loop control system. Their simulation results showed effective handling of the overshoot problems, disturbance rejection, set-point tracking, and noise reduction in the process plants considered. In the future, the proposed FOPPI controller will be implemented in the real-time pressure process plant. We will attempt to optimize parameters using any of the most widely used optimization algorithms, since the λ value is chosen based on trial and error method in this research. The real-time implementation will also be carried out in comparison with the wired and wireless process plants to validate the design and latency performance handling by the proposed controller.