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Figure 8. Plotted graph of input 2 versus input 1 FLC

Figure 8 Plotted graph of input 2 versus input 1 FLC

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Figure 3. Matlab/Simulink closed-loop block diagram Figure 2. Transient response of the ROV model
Figure 3. Matlab/Simulink closed-loop block diagram Figure 2. Transient response of the ROV model
Figure 1. System identification approach for modelling of ROV
Figure 1. System identification approach for modelling of ROV
This generated model was then simulated in Matlab/Simulink as a closed-loop system shown in the block diagram in Figure 3. From Figure 4, the closed-loop model had a faster Tr (9.07 s) and Ts (14.76 s) compared to the open-loop result but the steady-state error shoot up to 55.55% from the input given to the system. From the output result, the controller needs to be applied to get a better output response.
This generated model was then simulated in Matlab/Simulink as a closed-loop system shown in the block diagram in Figure 3. From Figure 4, the closed-loop model had a faster Tr (9.07 s) and Ts (14.76 s) compared to the open-loop result but the steady-state error shoot up to 55.55% from the input given to the system. From the output result, the controller needs to be applied to get a better output response.
Figure 6. Basic configuration of FLC component The common 7 X 7 FLC table is shown in Table |. The Z in the table stand for zero which indicate the center of the decision table. PL stand for positive large, PM stand for positive medium and PS stand for positive small. The NL, NM, and NS are the opposite of PL, PM and PS where they indicate the negative side of the table. The output result for FLC is selected based on the table.
Figure 6. Basic configuration of FLC component The common 7 X 7 FLC table is shown in Table |. The Z in the table stand for zero which indicate the center of the decision table. PL stand for positive large, PM stand for positive medium and PS stand for positive small. The NL, NM, and NS are the opposite of PL, PM and PS where they indicate the negative side of the table. The output result for FLC is selected based on the table.
Figure 5. PID controller block diagram eee PID controller is the basic controller applied to the ROV system. The P, I, and D blocks were put i parallel in front of the plant to control the system. The P-block counters the direct error, the I-block rectifie the total errors in the system while the D-block minimizes the speed of the errors. The P-controller will mak the response faster but intends to produce overshoot. The I-controller eliminates SSE while the D controlle decrease overshoot. The PID controller block diagram is shown in Figure 5. The PID was tuned usin: automatic tuning in Matlab/Simulink [38].
Figure 5. PID controller block diagram eee PID controller is the basic controller applied to the ROV system. The P, I, and D blocks were put i parallel in front of the plant to control the system. The P-block counters the direct error, the I-block rectifie the total errors in the system while the D-block minimizes the speed of the errors. The P-controller will mak the response faster but intends to produce overshoot. The I-controller eliminates SSE while the D controlle decrease overshoot. The PID controller block diagram is shown in Figure 5. The PID was tuned usin: automatic tuning in Matlab/Simulink [38].
Figure 4. Open-loop and close loop transient output comparison Indonesian J Elec Eng & Comp Sci
Figure 4. Open-loop and close loop transient output comparison Indonesian J Elec Eng & Comp Sci
Figure 7. Derivation of d, the distance between point Q and P Figure 7 shows the derivation of d, which is the distance between point, Q, and point, P. The ~onventional FLC table is now reduced to Table 2 where the diagonal line was represented by LNL, LNM, _NS, LZ, LPS, LPM, and LPL while NL, NM, NS, Z, PS, PM, and PL represent the output of corresponding liagonal lines. This input-output of SIFLC can be replaced by a lookup table. SIFLC was then tuned using the proposed lambda (4) tuning method. The value of (A) was heuristically changed to obtain the best output. The (A) was linked to the FLC by the input of the FLC. The range of error and integral error was plotted in < graph shown in Figure 8.
Figure 7. Derivation of d, the distance between point Q and P Figure 7 shows the derivation of d, which is the distance between point, Q, and point, P. The ~onventional FLC table is now reduced to Table 2 where the diagonal line was represented by LNL, LNM, _NS, LZ, LPS, LPM, and LPL while NL, NM, NS, Z, PS, PM, and PL represent the output of corresponding liagonal lines. This input-output of SIFLC can be replaced by a lookup table. SIFLC was then tuned using the proposed lambda (4) tuning method. The value of (A) was heuristically changed to obtain the best output. The (A) was linked to the FLC by the input of the FLC. The range of error and integral error was plotted in < graph shown in Figure 8.
Figure 9. Flow diagram for SIFLC heuristic tuning ‘ae 5 Manes, 6 NGS Ss ee Sees TSS ANE Re SID The gradient of the line i 1S lambda (A). The lambda (A) was varied up and down heuristically. The variation of (A)-tuned SIFLC result was then analyzed, and the best result was selected. Figure 9 shows the flow diagram of the heuristic tuning process.
Figure 9. Flow diagram for SIFLC heuristic tuning ‘ae 5 Manes, 6 NGS Ss ee Sees TSS ANE Re SID The gradient of the line i 1S lambda (A). The lambda (A) was varied up and down heuristically. The variation of (A)-tuned SIFLC result was then analyzed, and the best result was selected. Figure 9 shows the flow diagram of the heuristic tuning process.
Figure 10. Flow diagram of gradient descent algorithm 3.6. SIFLC PSO tuning method PSO was proposed by [43 in 1995. It is inspired by the behaviors of fishes schooling and birds flocking to search for foodstuff at a certain speed and position. The likeness is recognized between a particle and a swarm element [34], [44]. The particle movement is categorized by two factors: its current position x and velocity v, respectively. It has been useful effectively to a variety of optimization problems [45]-[47] The particle swarm optimization algorithm is analyzed by using standard results from the dynamic theory [48]. The PSO algorithm begins by iterations, t and t + 1 correspond to t initializing the swarm randomly in the search space. Two consecutive he position x of each particle that changes during the iterations by adding anew velocity v. The new velocity is estimated by summing an increment to the previous velocity value. The increment is a function of two components representing cognitive and social knowledge [49]. The cognitive knowledge of each particle is included by evaluating the difference between the current position x and its best position, pbest. The social knowledge of each particle is incorporated through the difference between its current position x and the best swarm global position achieved, gbest. He cognitive and social knowledge factors are multiplied by randomly uniform generated terms respectively [49]. Equation (6) shows the position vector while (7) shows the velocity vector. P in the equation is pbest while G is gbest.
Figure 10. Flow diagram of gradient descent algorithm 3.6. SIFLC PSO tuning method PSO was proposed by [43 in 1995. It is inspired by the behaviors of fishes schooling and birds flocking to search for foodstuff at a certain speed and position. The likeness is recognized between a particle and a swarm element [34], [44]. The particle movement is categorized by two factors: its current position x and velocity v, respectively. It has been useful effectively to a variety of optimization problems [45]-[47] The particle swarm optimization algorithm is analyzed by using standard results from the dynamic theory [48]. The PSO algorithm begins by iterations, t and t + 1 correspond to t initializing the swarm randomly in the search space. Two consecutive he position x of each particle that changes during the iterations by adding anew velocity v. The new velocity is estimated by summing an increment to the previous velocity value. The increment is a function of two components representing cognitive and social knowledge [49]. The cognitive knowledge of each particle is included by evaluating the difference between the current position x and its best position, pbest. The social knowledge of each particle is incorporated through the difference between its current position x and the best swarm global position achieved, gbest. He cognitive and social knowledge factors are multiplied by randomly uniform generated terms respectively [49]. Equation (6) shows the position vector while (7) shows the velocity vector. P in the equation is pbest while G is gbest.
Figure 11. Block diagram for the 6 signals investigated equation was used (SIFLC PSO) and PSO result when the lookup table was used (SIFLC PSO1). This scope output shows an identical result (Figure 12) as expected. Figure 12 shows the output result for scope 1. In Figure 13, SIFLC GDA showed the most identical result to the step input given. It was then followed by the SIFLC heuristic. The SIFLC PSO showed improvement in the Tr but with a slight steady-state error. The PID showed some overshoot but no steady-state error. The output result is tabulated in Table 3.
Figure 11. Block diagram for the 6 signals investigated equation was used (SIFLC PSO) and PSO result when the lookup table was used (SIFLC PSO1). This scope output shows an identical result (Figure 12) as expected. Figure 12 shows the output result for scope 1. In Figure 13, SIFLC GDA showed the most identical result to the step input given. It was then followed by the SIFLC heuristic. The SIFLC PSO showed improvement in the Tr but with a slight steady-state error. The PID showed some overshoot but no steady-state error. The output result is tabulated in Table 3.
Table 3. Output result of the controllers' implementation to ROV system
Table 3. Output result of the controllers' implementation to ROV system
Figure 13. The output result of scope 1
Figure 13. The output result of scope 1
Figure 14. Bar chart of the performance parameters From the bar chart in Figure 14, it is obvious that the SIFLC GDA control method showed the best result as it managed to get the lowest values for all the performance parameters. In terms of the rise time, Tr, the SIFLC GDA recorded 0.7992 s while the SIFLC heuristic was the worst at 7.2592 s, nearly ten times the SIFLC GDA record. The heuristic approach and PID approach had almost similar values at 7 s. These records showed that SIFLC GDA had the fastest response time to the change of input level. For settling time, Ts, the SIFLC GDA method recorded 0.9790 s and PID recorded the worst at 24.6687 s. Other than SIFLC GDA, other methods to stabilize the ROV took ten to twenty times longer. For the percentage of overshoot, the SIFLC GDA showed the best result which is at 0.1021%. It is then followed by the SIFLC heuristic (0.7988%), PID (7.3613%), and SIFLC PSO (16.2368%). These results showed that when the ROV was controlled using the SIFLC GDA method, the error to attain the target was very small. Figure 15 shows the comparison of SIFLC GDA with step signal. The SIFLC GDA looks nearly identical to the given step input.
Figure 14. Bar chart of the performance parameters From the bar chart in Figure 14, it is obvious that the SIFLC GDA control method showed the best result as it managed to get the lowest values for all the performance parameters. In terms of the rise time, Tr, the SIFLC GDA recorded 0.7992 s while the SIFLC heuristic was the worst at 7.2592 s, nearly ten times the SIFLC GDA record. The heuristic approach and PID approach had almost similar values at 7 s. These records showed that SIFLC GDA had the fastest response time to the change of input level. For settling time, Ts, the SIFLC GDA method recorded 0.9790 s and PID recorded the worst at 24.6687 s. Other than SIFLC GDA, other methods to stabilize the ROV took ten to twenty times longer. For the percentage of overshoot, the SIFLC GDA showed the best result which is at 0.1021%. It is then followed by the SIFLC heuristic (0.7988%), PID (7.3613%), and SIFLC PSO (16.2368%). These results showed that when the ROV was controlled using the SIFLC GDA method, the error to attain the target was very small. Figure 15 shows the comparison of SIFLC GDA with step signal. The SIFLC GDA looks nearly identical to the given step input.
Figure 15. Comparison of SIFLC GDA with step signal
Figure 15. Comparison of SIFLC GDA with step signal
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