PAPERmaking! Vol11 Nr1 2025

™™™Ǥƒ–—”‡Ǥ ‘Ȁ• ‹‡–‹ˆ‹ ”‡’‘”–•Ȁ

”‘’‘•‡†–‡ Š‹“—‡ˆ‘”–—‹‰  ’ƒ”ƒ‡–‡”• A flexible method for improving the presentation file and setting the FOPID controller addition limits is proposed. The new JSO algorithm utilizes the speeder calculation span of the other improvement algorithms. The JSO is one of the methods which is used to fit the progression reaction of the framework and numerical system that creates an arrangement of improving in exact answers for a class of issues. Here, JSO algorithm is utilized for deciding the fit boundaries, which is used to fit the specific headbox model reaction. Utilizing the proposed method, the partial request framework Y ( s ) is tuned by the set of best FOPID regulator gains. The JSO is used to create the ideal increase boundaries of the FOPID regulator. The JSO algorithm is used for choosing the ideal control boundaries dependent on the satisfactory increase boundaries of the FOPID regulator 43 . The cycle of the proposed strategy is introduced in another segment.   ‘–”‘ŽŽ‡”ˆ‘” ‘–”‘ŽŽ‹‰’”‡••—”‡ƒ†•–‘ Ž‡˜‡Ž‹Š‡ƒ†„‘š Applying the broadest regulator for a mechanical application in view of its simplicity in agreement and tuning is the traditional Proportional-Integral-Derivative (PID) regulator. The best grace is in the master plan to postpone the repeated mixed question from the basic request to the fragmentary request, and in this way is responsible for the broader scope of the structural elements. Fractional order regulator is further proportional value ( K p ) , Integral value ( K i ) and Derivative value ( K d ) with additional factors as integral order ( λ ) , and the derivative order ( μ ) . Using two additional administrators in this way widens the opportunities for the controller and creates the possibility of further improving the presentation of regular PID controllers 44,45 . To decide the Fractional Order Proportional-Integral-Derivative (FOPID) regulator ( P − λ i D μ ) Fractional request differential condition is used. The differential condition of fragmentary request regulator is depicted as, u ( t )= K P e ( t )+ k i D − λ t e ( t )+ K d D μ t Ee ( t ) (13) Where, e ( t ) is value of error parameter and u ( t ) is the value of control parameter. As shown in Fig. 3, the FOPID controller summarizes the required PID controller as a regular integer and expands from the highlight plan. This augmentation of necessary and subordinate request will give significantly more adaptability and precision in PID regulator plan 46,47 . The ideal estimations of FOPID regulator boundaries The JSO algorithm is a nature inspired algorithm involves the movement of jellyfish in the water. It demonstrates the transition of its various activities with respect to time. The research work explains the use of JSO algorithm to showcase the tuning parameters of FOPID controller to yields optimum performance than other optimal methods. Direction trend The nutrients in the water items which is taken by jelly fish. Its direction taken as  −−−→ trend  → trend = X best − 3 . 1 ∗ rand (0 , 1) ∗ μ (14) for limiting the wellness work are tuned utilizing a proposed JSO algorithm. ’–‹ƒŽ   ‘–”‘ŽŽ‡”’ƒ”ƒ‡–‡”•‡ƒ” Š—•‹‰ ƒŽ‰‘”‹–Š

Where, X best represents the area and an update actvity is given as,

→ trend

(15)

i ( t +1)= X

L i ( t )+ rand (0 , 1) ∗

X L

i ( t ) is the locality of i

th jellyfish with respect to time t .

Where, X L

Fig. 3 . Structure of Fractional order PID controller.

ͼ

ȁŠ––’•ǣȀȀ†‘‹Ǥ‘”‰ȀͷͶǤͷͶ͹;Ȁ•ͺͷͻͿ;ǦͶ͸ͻǦ;ͻ;ͷͶǦͿ

 ‹‡–‹Ƥ ‡’‘”–• |

(2025) 15:1631

Made with FlippingBook interactive PDF creator