Application of Variable Universe Fuzzy PID Controller Based on ISSA in Bridge Crane Control
Abstract
:1. Introduction
2. Bridge Crane System Modeling
3. Improved Sparrow Search Algorithm
3.1. Standard Sparrow Search Algorithm
3.2. Proposed ISSA Algorithm
3.2.1. Tent Chaotic Map Strategy
3.2.2. Northern Goshawk Location Exploration Strategy
3.2.3. Adaptive T-Distribution Variation Strategy
3.2.4. General Structure of ISSA
3.3. Performance of ISSA
4. Proposed ISSA-VUFPID Control Algorithm
4.1. Fuzzy PID Controller
4.2. Variable Universe Fuzzy PID Controller
4.3. Proposed ISSA-VUFPID Controller
5. Simulation Experiments
5.1. Experimental and Simulation Analysis of the VUFPID Controller
5.2. Experimental and Simulation Analysis of the ISSA-VUFPID Controller
5.3. Robustness Simulation Experiments
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Function Name | Search Space | Dimensionality | Optimum Value |
---|---|---|---|
F1 Sphere | [−100, 100] | 30 | 0 |
F2 Schwefel 2.22 | [−10, 10] | 30 | 0 |
F3 Schwefel 1.2 | [−100, 100] | 30 | 0 |
F4 Schwefel 2.21 | [−100, 100] | 30 | 0 |
F5 Generalized Rosenbrock | [−30, 30] | 30 | 0 |
F6 Step Function | [−100, 100] | 30 | 0 |
F7 Quartic | [−1.28, 1.28] | 30 | 0 |
F8 Schwefel 2.26 | [−500, 500] | 30 | −12,569.5 |
F9 Rastrigin | [−5.12, 5.12] | 30 | 0 |
F10 Ackley | [−32, 32] | 30 | 0 |
F11 Griewank | [−600, 600] | 30 | 0 |
F12 Generalized Penalized Function 1 | [−50, 50] | 30 | 0 |
F13 Generalized Penalized Function 2 | [−50, 50] | 30 | 0 |
F14 Shekel’s Foxholes | [−65.53, 65.53] | 2 | 1 |
F15 Kowalik | [−5, 5] | 4 | 0.0003075 |
F16 Six-Hump Camel-Back | [−5, 5] | 2 | −1.031628 |
F17 Branin | lb = [−5, 0] ub = [10, 15] | 2 | 0.398 |
F18 Goldstein-Price | [−2, 2] | 2 | 3 |
F19 Hartman’s Family n = 3 | [0, 1] | 3 | −3.98 |
F20 Hartman’s Family n = 6 | [0, 1] | 6 | −3.32 |
F21 Shekel’s Family m = 5 | [0, 1] | 4 | −10.536 |
F22 Shekel’s Family m = 7 | [0, 10] | 4 | −10.536 |
F23 Shekel’s Family m = 10 | [0, 10] | 4 | −10.536 |
Algorithm | Parameter |
---|---|
ISSA | = 30, = 0.2, = 0.8, = 0.1 |
SSA | = 30, = 0.2, = 0.8, = 0.1 |
NGO | = 30, = 0.9, |
DBO | = 30, = 0.1, = 0.1, = 0.3, = 0.5 |
GWO | = 30, = [0, 2] |
GWCA | = 30, = 1, = 8.3, = 9.8, = 3, = 0.1, = 9, = 6 |
WOA | = 30, = 1, = 1 |
SABO | = 30 |
RIME | = 30, |
Function Name | DBO | GWO | GWCA | WOA | SABO | RIME | NGO | SSA | ISSA | |
---|---|---|---|---|---|---|---|---|---|---|
F1 | mean | 9.39 10−112 | 8.59 10−28 | 9.62 10−3 | 2.05 10−63 | 5.78 10−197 | 1.9668 | 1.81 10−87 | 1.33 10−61 | 3.99 10−262 |
std | 4.84 10−111 | 1.15 10−27 | 2.21 10−3 | 9.21 10−63 | 0 | 0.79139 | 5.84 10−87 | 7.17 10−61 | 0 | |
best | 7.34 10−168 | 1.52 10−29 | 4.39 10−6 | 9.23 10−74 | 6.39 10−201 | 1.0675 | 3.99 10−90 | 6.54 10−161 | 0 | |
worst | 2.65 10−110 | 4.97 10−27 | 9.21 10−2 | 4.98 10−62 | 7.94 10−196 | 4.0912 | 3.23 10−86 | 3.93 10−60 | 8.06 10−261 | |
median | 2.99 10−135 | 4.21 10−28 | 4.47 10−4 | 3.58 10−67 | 5.20 10−198 | 1.8376 | 3.14 10−88 | 1.24 10−76 | 9.71 10−297 | |
F2 | mean | 6.60 10−57 | 9.93 10−17 | 0.76209 | 2.15 10−36 | 9.22 10−111 | 1.459 | 9.53 10−46 | 2.50 10−29 | 1.96 10−136 |
std | 3.51 10−56 | 7.75 10−17 | 1.6517 | 5.35 10−36 | 3.02 10−110 | 1.0507 | 6.08 10−46 | 1.19 10−28 | 1.07 10−135 | |
best | 3.19 10−79 | 1.70 10−17 | 0.00094916 | 6.91 10−40 | 1.64 10−112 | 0.47875 | 1.92 10−46 | 8.49 10−90 | 4.68 10−174 | |
worst | 1.92 10−55 | 3.62 10−16 | 7.0488 | 2.74 10−35 | 1.65 10−109 | 5.2636 | 2.12 10−45 | 6.53 10−28 | 5.89 10−135 | |
median | 1.62 10−68 | 8.22 10−17 | 0.099576 | 1.37 10−37 | 1.03 10−111 | 1.1931 | 7.83 10−46 | 8.12 10−40 | 3.10 10−152 | |
F3 | mean | 1.47 10−44 | 5.33 10−6 | 2244.3776 | 8448.6005 | 1.96 10−16 | 1369.3627 | 1.76 10−21 | 4.43 10−26 | 3.43 10−226 |
std | 8.07 10−44 | 8.56 10−6 | 1329.0103 | 17,620.2865 | 1.07 10−15 | 429.6009 | 8.32 10−21 | 2.16 10−25 | 0 | |
best | 1.98 10−155 | 1.81 10−9 | 446.7755 | 8.51 10−15 | 3.77 10−93 | 772.551 | 2.05 10−28 | 9.23 10−85 | 1.92 10−298 | |
worst | 4.42 10−43 | 4.41 10−5 | 1931.0912 | 80,147.4375 | 5.88 10−15 | 2546.0483 | 4.55 10−20 | 1.18 10−24 | 1.02 10−224 | |
median | 3.79 10−105 | 3.38 10−6 | 6780.7869 | 461.7524 | 1.99 10−60 | 1296.4459 | 3.16 10−24 | 7.77 10−37 | 5.41 10−261 | |
F4 | mean | 1.59 10−50 | 5.57 10−7 | 19.7814 | 0.0022505 | 4.92 10−77 | 7.0876 | 1.91 10−37 | 6.57 10−27 | 5.62 10−128 |
std | 8.72 10−50 | 3.51 10−7 | 4.3306 | 0.0042854 | 1.07 10−76 | 3.3242 | 1.87 10−37 | 3.60 10−26 | 3.02 10−127 | |
best | 1.07 10−81 | 5.85 10−8 | 27.902 | 2.11 10−7 | 8.39 10−79 | 2.0849 | 2.06 10−38 | 0 | 2.85 10−156 | |
worst | 4.77 10−49 | 1.42 10−6 | 27.3122 | 0.018345 | 5.37 10−76 | 13.5455 | 6.57 10−37 | 1.97 10−25 | 1.65 10−126 | |
median | 9.99 10−65 | 4.86 10−7 | 38.6198 | 3.29 10−4 | 1.26 10−77 | 6.0807 | 1.07 10−37 | 7.05 10−36 | 1.86 10−142 | |
F5 | mean | 25.75 | 27.1879 | 320.7621 | 0.19366 | 28.4004 | 437.163 | 25.9039 | 3.58 10−5 | 1.07 10−6 |
std | 0.21424 | 0.85872 | 341.0196 | 0.26607 | 0.37114 | 500.128 | 0.34525 | 6.52 10−5 | 3.26 10−6 | |
best | 25.3382 | 25.9722 | 84.6814 | 3.62 10−6 | 27.6297 | 77.0943 | 24.9708 | 3.23 10−9 | 2.85 10−25 | |
worst | 26.5107 | 28.769 | 1925.8737 | 1.1366 | 28.8586 | 1930.9445 | 26.4504 | 2.25 10−4 | 1.52 10−5 | |
median | 25.7159 | 27.1313 | 187.4818 | 0.062476 | 28.5784 | 208.3892 | 25.9212 | 4.70 10−6 | 2.50 10−14 | |
F6 | mean | 9.54 10−3 | 0.74849 | 1.91 10−2 | 6.31 10−3 | 2.5388 | 2.0549 | 5.90 10−4 | 9.38 10−12 | 1.06 10−14 |
std | 4.84 10−2 | 0.44364 | 9.41 10−2 | 7.66 10−3 | 0.70133 | 0.77482 | 9.96 10−4 | 2.44 10−11 | 5.59 10−14 | |
best | 1.70 10−6 | 4.57 10−5 | 2.77 10−6 | 7.38 10−5 | 0.8522 | 0.71478 | 8.58 10−7 | 1.44 10−14 | 6.41 10−24 | |
worst | 0.26518 | 1.7456 | 0.51592 | 3.29 10−2 | 4.0982 | 3.7398 | 4.11 10−3 | 1.18 10−10 | 3.06 10−13 | |
median | 9.17 10−5 | 0.73947 | 2.79 10−4 | 2.98 10−3 | 2.4158 | 2.0292 | 2.38 10−4 | 47.71 10−13 | 6.36 10−18 | |
F7 | mean | 1.21 10−3 | 1.80 10−3 | 1.4846 | 8.59 10−4 | 1.19 10−4 | 0.04276 | 5.08 10−4 | 1.78 10−3 | 7.59 10−4 |
std | 9.64 10−4 | 9.79 10−4 | 0.63634 | 1.51 10−3 | 8.33 10−5 | 0.017635 | 2.37 10−4 | 1.36 10−3 | 4.99 10−4 | |
best | 9.90 10−5 | 5.24 10−4 | 0.3052 | 1.58 10−5 | 9.85 10−6 | 0.014542 | 7.27 10−5 | 1.73 10−4 | 8.87 10−7 | |
worst | 3.40 10−3 | 4.71 10−3 | 3.1716 | 7.33 10−3 | 3.58 10−4 | 0.083719 | 1.06 10−3 | 6.65 10−3 | 1.99 10−3 | |
median | 8.58 10−4 | 1.54 10−3 | 1.3275 | 2.80 10−4 | 9.69 10−5 | 0.040291 | 4.88 10−4 | 1.58 10−3 | 6.63 10−4 |
Function Name | DBO | GWO | GWCA | WOA | SABO | RIME | NGO | SSA | ISSA | |
---|---|---|---|---|---|---|---|---|---|---|
F8 | mean | −8701.6518 | −5962.9142 | −7326.0442 | −12,520.058 | −3046.0754 | −10,031.3763 | −7370.6748 | −8710.4366 | −10,546.595 |
std | 1536.4065 | 1088.7869 | 672.2149 | 212.389 | 429.4755 | 454.5367 | 570.973 | 611.253 | 1600.8078 | |
best | −12,224.1201 | −7658.8421 | −8612.3715 | −12,569.4866 | −4184.9217 | −10,916.8954 | −9632.8237 | −9801.3347 | −12,569.4866 | |
worst | −6332.7066 | −3218.494 | −5264.5562 | −11,449.6129 | −2484.7529 | −8965.0533 | −7367.174 | −7701.3047 | −8307.1842 | |
median | −8327.171 | −6113.4139 | −7326.4124 | −12,569.4361 | −2992.0223 | −10,065.0948 | −7367.174 | −8721.4395 | −10,472.5097 | |
F9 | mean | 0.099857 | 3.5357 | 60.1949 | 1.89 10−15 | 0 | 62.4197 | 0 | 0 | 0 |
std | 0.54694 | 5.7095 | 20.2894 | 1.03 10−14 | 0 | 12.9842 | 0 | 0 | 0 | |
best | 0 | 0 | 26.8639 | 0 | 0 | 28.3564 | 0 | 0 | 0 | |
worst | 2.9957 | 27.8712 | 101.4854 | 5.68 10−14 | 0 | 84.343 | 0 | 0 | 0 | |
median | 0 | 4.63 10−12 | 61.1898 | 0 | 0 | 59.5512 | 0 | 0 | 0 | |
F10 | mean | 4.44 10−16 | 9.86 10−14 | 10.7485 | 3.76 10−15 | 3.9968 10−15 | 2.0771 | 5.41 10−15 | 4.44 10−16 | 4.44 10−16 |
std | 0 | 1.49 10−14 | 2.0209 | 2.27 10−15 | 0 | 0.5365 | 1.77 10−15 | 0 | 0 | |
best | 4.44 10−16 | 7.50 10−14 | 5.473 | 4.44 10−16 | 3.99 10−15 | 0.75586 | 3.99 10−15 | 4.44 10−16 | 4.44 10−16 | |
worst | 4.44 10−16 | 1.28 10−13 | 14.7352 | 7.54 10−16 | 3.9968 10−15 | 3.1255 | 7.54 10−15 | 4.44 10−16 | 4.44 10−16 | |
median | 4.44 10−16 | 9.99 10−14 | 10.7861 | 3.99 10−15 | 3.9968 10−15 | 2.1323 | 3.99 10−15 | 4.44 10−16 | 4.44 10−16 | |
F11 | mean | 0 | 5.09 10−3 | 1.0888 | 0 | 0 | 0.97002 | 0 | 0 | 0 |
std | 0 | 1.08 10−2 | 1.4707 | 0 | 0 | 0.053822 | 0 | 0 | 0 | |
best | 0 | 0 | 0.01026 | 0 | 0 | 0.84559 | 0 | 0 | 0 | |
worst | 0 | 4.76 10−2 | 5.5992 | 0 | 0 | 1.0393 | 0 | 0 | 0 | |
median | 0 | 0 | 0.43747 | 0 | 0 | 0.98059 | 0 | 0 | 0 | |
F12 | mean | 1.70 10−5 | 0.045456 | 6.5837 | 4.16 10−4 | 0.27779 | 3.1901 | 2.26 10−4 | 2.22 10−12 | 6.97 10−19 |
std | 2.72 10−5 | 0.022784 | 3.7344 | 5.16 10−4 | 0.16756 | 1.3387 | 1.21 10−3 | 4.94 10−12 | 3.60 10−18 | |
best | 7.05 10−8 | 0.013342 | 0.1498 | 5.28 10−6 | 0.11111 | 0.5982 | 1.38 10−7 | 2.07 10−15 | 2.44 10−32 | |
worst | 0.0001187 | 0.102 | 14.473 | 2.29 10−3 | 0.94211 | 5.9181 | 6.62 10−3 | 1.99 10−11 | 1.97 10−17 | |
median | 6.51 10−6 | 0.042712 | 6.1956 | 1.91 10−4 | 0.24347 | 3.3092 | 4.02 10−6 | 1.44 10−13 | 8.62 10−24 | |
F13 | mean | 0.75689 | 0.6581 | 14.9114 | 6.16 10−3 | 2.5375 | 0.23964 | 0.33124 | 1.54 10−11 | 4.70 10−17 |
std | 0.48984 | 0.23023 | 7.0883 | 8.05 10−3 | 0.58422 | 0.12762 | 0.22137 | 2.62 10−11 | 2.27 10−16 | |
best | 0.09966 | 0.13345 | 2.1393 | 6.44 10−5 | 1.4763 | 0.053259 | 0.014171 | 1.51 10−14 | 1.41 10−31 | |
worst | 2.1934 | 1.0985 | 30.4566 | 3.16 10−2 | 3.0286 | 0.5779 | 0.75713 | 1.11 10−10 | 1.24 10−15 | |
median | 0.61844 | 0.66773 | 14.5231 | 3.11 10−3 | 2.9364 | 0.21828 | 0.28106 | 5.84 10−12 | 4.55 10−23 |
Function Name | DBO | GWO | GWCA | WOA | SABO | RIME | NGO | SSA | ISSA | |
---|---|---|---|---|---|---|---|---|---|---|
F14 | mean | 1.2954 | 4.5218 | 1.0643 | 1.5587 | 3.9472 | 0.998 | 1.1303 | 5.2195 | 0.998 |
std | 0.78737 | 4.2943 | 0.25219 | 1.2875 | 3.0438 | 3.49 10−12 | 0.50338 | 5.4117 | 5.83 10−17 | |
best | 0.998 | 0.998 | 0.998 | 0.998 | 0.99841 | 0.998 | 0.998 | 0.998 | 0.998 | |
worst | 3.9683 | 12.6705 | 1.992 | 5.9288 | 12.6705 | 0.998 | 2.9821 | 12.6705 | 0.998 | |
median | 0.998 | 2.9821 | 0.998 | 0.998 | 2.9949 | 0.998 | 0.998 | 0.998 | 0.998 | |
F15 | mean | 7.48 10−4 | 3.08 10−3 | 1.12 10−3 | 5.64 10−4 | 7.44 10−4 | 4.13 10−3 | 3.08 10−4 | 3.46 10−4 | 3.37 10−4 |
std | 3.79 10−4 | 6.89 10−3 | 3.65 10−3 | 5.12 10−4 | 6.68 10−4 | 7.39 10−3 | 2.97 10−7 | 8.99 10−5 | 8.16 10−5 | |
best | 3.07 10−4 | 3.08 10−4 | 3.07 10−4 | 3.17 10−4 | 3.19 10−4 | 3.11 10−4 | 3.07 10−4 | 3.07 10−4 | 3.07 10−4 | |
worst | 1.54 10−3 | 2.03 10−2 | 2.04 10−2 | 2.25 10−3 | 3.34 10−3 | 2.04 10−2 | 3.08 10−4 | 5.71 10−4 | 6.41 10−4 | |
median | 7.49 10−4 | 3.82 10−4 | 3.08 10−4 | 3.78 10−4 | 4.55 10−4 | 7.72 10−4 | 3.07 10−4 | 3.07 10−4 | 3.07 10−4 | |
F16 | mean | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0258 | −1.0316 | −1.0316 | −1.0316 | −1.0316 |
std | 6.04 10−16 | 3.00 10−8 | 6.45 10−16 | 6.47 10−8 | 0.0138 | 3.55 10−7 | 6.38 10−16 | 5.60 10−16 | 5.29 10−16 | |
best | 1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | |
worst | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −0.95709 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | |
median | −1.0316 | −1.03166 | −1.0316 | −1.0316 | −1.0303 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | |
F17 | mean | 0.39789 | 0.39789 | 0.39789 | 0.39794 | 0.44857 | 0.39789 | 0.39789 | 0.39789 | 0.39789 |
std | 0 | 2.37 10−6 | 0 | 8.18 10−5 | 0.09735 | 5.22 10−7 | 0 | 0 | 0 | |
best | 0.39789 | 0.39789 | 0.39789 | 0.39789 | 0.39794 | 0.39789 | 0.39789 | 0.39789 | 0.39789 | |
worst | 0.39789 | 0.39789 | 0.39789 | 0.39816 | 0.71491 | 0.39789 | 0.39789 | 0.39789 | 0.39789 | |
median | 0.39789 | 0.39789 | 0.39789 | 0.39789 | 0.40278 | 0.39789 | 0.39789 | 0.39789 | 0.39789 | |
F18 | mean | 3 | 3 | 3 | 5.7034 | 4.8679 | 8.4 | 3 | 5.7 | 3 |
std | 1.30 10−10 | 3.85 10−5 | 1.80 10−15 | 8.2487 | 4.4462 | 20.5504 | 1.11 10−15 | 8.2385 | 1.30 10−15 | |
best | 3 | 3 | 3 | 3 | 3.0013 | 3 | 3 | 3 | 3 | |
worst | 3 | 3.0002 | 3 | 30.0474 | 25.8388 | 84 | 3 | 30 | 3 | |
median | 3 | 3 | 3 | 3 | 3.1489 | 3 | 3 | 3 | 3 | |
F19 | mean | −3.8612 | −3.8619 | −3.8628 | −3.8109 | −3.6273 | −3.8628 | −3.8628 | −3.8628 | −3.8628 |
std | 0.0032065 | 0.0020026 | 2.53 10−15 | 0.063631 | 0.12864 | 3.65 10−7 | 2.68 10−15 | 2.20 10−15 | 2.23 10−15 | |
best | −3.8628 | −3.8628 | −3.8628 | −3.8628 | −3.8459 | −3.8628 | −3.8628 | −3.8628 | −3.8628 | |
worst | −3.8549 | −3.8551 | −3.8628 | −3.6106 | −3.3468 | −3.8628 | −3.8628 | −3.8628 | −3.8628 | |
median | −3.8628 | −3.8626 | −3.8628 | −3.8371 | −3.6312 | −3.8628 | −3.8628 | −3.8628 | −3.8628 | |
F20 | mean | −3.2247 | −3.2656 | −3.2824 | −3.0891 | −3.2291 | −3.2467 | −3.2824 | −3.2744 | −3.322 |
std | 0.11556 | 0.068509 | 0.057005 | 0.17479 | 0.12286 | 0.058275 | 0.057005 | 0.059241 | 1.17 10−15 | |
best | −3.322 | −3.322 | −3.322 | −3.3143 | −3.3209 | −3.322 | −3.322 | −3.322 | −3.322 | |
worst | −2.8404 | −3.0904 | −3.2031 | −2.4059 | −2.8765 | −3.203 | −3.2031 | −3.2031 | −3.322 | |
median | −3.2031 | −3.322 | −3.322 | −3.1332 | −3.2692 | −3.2031 | −3.322 | −3.322 | −3.322 | |
F21 | mean | −6.7714 | −9.1118 | −5.5709 | −10.0417 | −5.0932 | −8.3842 | −10.1532 | −7.6042 | −10.1532 |
std | 2.4299 | 2.1192 | 3.4081 | 0.18435 | 0.28311 | 2.5794 | 4.83 10−6 | 2.5926 | 5.36 10−15 | |
best | −10.1532 | −10.1527 | −10.1532 | −10.1532 | −6.5842 | −10.1531 | −10.1532 | −10.1532 | −10.1532 | |
worst | −5.0551 | −4.3089 | −2.6305 | −9.312 | −4.9072 | −2.6304 | −10.1532 | −5.0552 | −10.1532 | |
median | −5.1008 | −10.1516 | −3.869 | −10.0969 | −5.0529 | −10.1523 | −10.1532 | −7.6042 | −10.1532 | |
F22 | mean | −8.1267 | −10.4017 | −6.7233 | −10.151 | −5.069 | −8.5179 | −10.4029 | −9.5171 | −10.4029 |
std | 2.8877 | 0.00077288 | 3.6027 | 1.0223 | 0.90107 | 2.9738 | 5.84 10−6 | 2.0147 | 8.72 10−16 | |
best | −10.4029 | −10.4027 | −10.4029 | −10.4 | −7.4215 | −10.4029 | −10.4029 | −10.4029 | −10.4029 | |
worst | −2.7646 | −10.3994 | −1.8376 | −4.745 | −2.9267 | −2.7657 | −10.4029 | −5.0877 | −10.4029 | |
median | −10.3931 | −10.4018 | −5.1288 | −10.3386 | −5.0741 | −10.402 | −10.4029 | −10.4029 | −10.4029 | |
F23 | mean | −7.8152 | −10.3562 | −6.4768 | −10.4201 | −5.0301 | −9.7419 | −10.5364 | −9.2345 | −10.5364 |
std | 3.0238 | 0.97888 | 3.6423 | 0.1815 | 1.2402 | 2.093 | 2.92 10−6 | 2.3142 | 1.77 10−15 | |
best | −10.5364 | −10.5363 | −10.5364 | −10.5363 | −10.1396 | −10.5364 | −10.5364 | −10.5364 | −10.5364 | |
worst | −2.4273 | −5.1734 | −2.4273 | −9.851 | −3.4551 | −2.8066 | −10.5364 | −5.1285 | −10.5364 | |
median | −10.5266 | −10.5349 | −4.482 | −10.5044 | −5.0483 | −10.5357 | −10.5364 | −10.5364 | −10.5364 |
NB | NM | NS | ZO | PS | PM | PB | ||
NB | PB | PB | PM | PM | PM | ZO | ZO | |
NM | PB | PB | PM | PS | PS | ZO | NS | |
NS | PM | PM | PM | PS | ZO | NS | NS | |
ZO | PM | PM | PS | ZO | NS | NM | NM | |
PS | PS | PS | ZO | NS | NS | NM | NM | |
PM | PS | ZO | NS | NM | NM | NM | NB | |
PB | ZO | ZO | NM | NM | NM | NB | NB |
NB | NM | NS | ZO | PS | PM | PB | ||
NB | NB | NB | NM | NM | NM | NS | ZO | |
NM | NB | NB | NM | NS | NS | NS | ZO | |
NS | NB | NM | NS | NS | ZO | ZO | PS | |
ZO | NM | NM | NS | ZO | PS | PS | PM | |
PS | NM | NS | ZO | PS | PS | PS | PM | |
PM | NM | ZO | PS | PS | PM | PM | PB | |
PB | ZO | ZO | PS | PM | PM | PB | PB |
NB | NM | NS | ZO | PS | PM | PB | ||
NB | NS | PS | PB | PB | PB | PM | NS | |
NM | NS | PS | PB | PM | PM | PS | ZO | |
NS | ZO | PS | PM | PM | PS | NS | ZO | |
ZO | ZO | PS | PS | PS | PS | PS | ZO | |
PS | ZO | ZO | ZO | ZO | ZO | ZO | PM | |
PM | PM | PS | PS | PS | PS | PS | PM | |
PB | NB | NM | NM | NM | NS | NS | ZO |
Parameter | Definition | Value | Unit |
---|---|---|---|
Mass of the trolley | 8 | kg | |
Mass of the payload | 8 | kg | |
Length of the payload’s cable | 4 | m | |
Damping coefficient | 0.2 | Ns/m | |
Gravitational acceleration | 9.8 | m/s2 |
Controller | Trolley Position | Payload Swing Angle | ||||
---|---|---|---|---|---|---|
Peak Time (s) | Overshoot (%) | Steady State Time (s) | Steady-State Value (m) | Max Angle (rad) | Steady State Time (s) | |
PID | 4.402 | 27.4% | 18.946 | 9.927 | 0.0439 | 21.563 |
FPID | 4.728 | 18.9% | 17.054 | 9.947 | 0.0356 | 17.554 |
VUFPID | 7.207 | 6.9% | 13.272 | 1.004 | 0.0126 | 16.390 |
Controller | Trolley Position | Payload Swing Angle | ||||
---|---|---|---|---|---|---|
Peak Time (s) | Overshoot (%) | Steady State Time (s) | Steady-State Value (m) | Max Angle (rad) | Steady State Time (s) | |
ISSA-PID | 4.093 | 14.8% | 14.172 | 0.991 | 0.0568 | 15.359 |
ISSA-FPID | 4.046 | 10.7% | 13.699 | 0.996 | 0.0532 | 13.356 |
ISSA-VUFPID | 5.181 | 0% | 5.371 | 0.997 | 0.0282 | 5.384 |
Working Condition | Trolley Mass (kg) | Payload Mass (kg) | Cable Length (m) | Damping Coefficient (Ns/m) | Gravitational Acceleration (m/s2) |
---|---|---|---|---|---|
1 | 8 | 8 | 2 | 0.2 | 9.8 |
2 | 8 | 6 | 4 | 0.2 | 9.8 |
3 | 6 | 8 | 4 | 0.2 | 9.8 |
4 | 4 | 8 | 4 | 0.2 | 9.8 |
5 | 8 | 8 | 6 | 0.2 | 9.8 |
Working Condition | Improved PID Controller | Trolley Position | Payload Swing Angle | ||||
---|---|---|---|---|---|---|---|
Peak Time (s) | Overshoot (%) | Steady-State Time (s) | Steady-State Value (m) | Max Angle (rad) | Steady State Time (s) | ||
1 | ISSA-PID | 3.703 | 10.2% | 9.905 | 0.9964 | 0.0629 | 10.763 |
ISSA-FPID | 3.892 | 6.1% | 9.082 | 0.9961 | 0.0577 | 10.310 | |
ISSA-VUFPID | 5.102 | 2.1% | 7.333 | 1.0000 | 0.0281 | 9.902 | |
2 | ISSA-PID | 3.987 | 15.1% | 12.909 | 0.9953 | 0.0753 | 13.855 |
ISSA-FPID | 12.503 | 10.8% | 12.351 | 0.9961 | 0.0688 | 13.107 | |
ISSA-VUFPID | 8.861 | 0% | 7.879 | 1.0000 | 0.0388 | 10.631 | |
3 | ISSA-PID | 3.988 | 15.2% | 13.821 | 0.9954 | 0.0598 | 15.485 |
ISSA-FPID | 4.038 | 11.1% | 13.370 | 0.9960 | 0.0562 | 13.610 | |
ISSA-VUFPID | 4.992 | 0% | 5.393 | 1.0000 | 0.0287 | 7.920 | |
4 | ISSA-PID | 3.975 | 13.6% | 14.420 | 0.9952 | 0.0594 | 2.856 |
ISSA-FPID | 3.917 | 9.7% | 13.839 | 0.9962 | 0.0598 | 2.817 | |
ISSA-VUFPID | 5.193 | 0% | 7.631 | 1.0000 | 0.0295 | 3.012 | |
5 | ISSA-PID | 3.994 | 11.6% | 16.144 | 0.9951 | 0.0882 | 19.113 |
ISSA-FPID | 4.031 | 7.9% | 15.731 | 0.9965 | 0.0814 | 18.591 | |
ISSA-VUFPID | 6.881 | 1.3% | 9.281 | 1.0000 | 0.0405 | 12.748 |
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Share and Cite
Zhang, Y.; Liu, L.; He, D. Application of Variable Universe Fuzzy PID Controller Based on ISSA in Bridge Crane Control. Electronics 2024, 13, 3534. https://doi.org/10.3390/electronics13173534
Zhang Y, Liu L, He D. Application of Variable Universe Fuzzy PID Controller Based on ISSA in Bridge Crane Control. Electronics. 2024; 13(17):3534. https://doi.org/10.3390/electronics13173534
Chicago/Turabian StyleZhang, Youyuan, Lisang Liu, and Dongwei He. 2024. "Application of Variable Universe Fuzzy PID Controller Based on ISSA in Bridge Crane Control" Electronics 13, no. 17: 3534. https://doi.org/10.3390/electronics13173534
APA StyleZhang, Y., Liu, L., & He, D. (2024). Application of Variable Universe Fuzzy PID Controller Based on ISSA in Bridge Crane Control. Electronics, 13(17), 3534. https://doi.org/10.3390/electronics13173534