Hybrid Recurrent Laguerre-Orthogonal-Polynomial NN Control System Applied in V-Belt Continuously Variable Transmission System Using Particle Swarm Optimization

<div>Numerical results of the iteration performance for two learning rates in the recurrent Laguerre-orthogonal-polynomial NN by means of modified PSO from 0 s to 0.6 s with 240 iterations (runs) at 188.4 rad/s (1800 rpm) case under the lumped nonlinear external disturbances with parameter variation <svg height="14.4363pt" id="M311" style="vertical-align:-5.47418pt" version="1.1" viewbox="-0.0498162 -8.96212 77.9185 14.4363" width="77.9185pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z" id="g113-85"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="637" vert-adv-y="637"></glyph.data></g><g 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230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,59.94,0)"><path d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z" id="g113-85"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="637" vert-adv-y="637"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,67.116,3.132)"><path d="M527 54L498 55C459 56 451 63 451 114V445C436 442 413 438 384 435C353 432 318 430 291 429V402L328 396C361 390 370 387 370 331V101C336 70 300 54 262 54C217 54 173 78 173 166V300C173 361 173 412 176 445C160 442 132 438 105 434C77 431 52 430 29 429V402L59 395C83 390 92 385 92 331V141C92 30 150 -12 218 -12C246 -12 266 -4 295 13C324 29 346 47 370 64V-6L376 -12C396 -7 421 1 448 8C476 15 504 21 527 24V54Z" id="g58-115"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="541" vert-adv-y="541"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,72.039,3.132)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="557" vert-adv-y="557"></glyph.data></g></svg>: (a) response of learning rates <svg height="9.39034pt" id="M312" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.9619 9.39034" width="11.9619pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g 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Mathematical Problems in Engineering

fig14

Figure 14

Figure 14: Hybrid Recurrent Laguerre-Orthogonal-Polynomial NN Control System Applied in V-Belt Continuously Variable Transmission System Using Particle Swarm Optimization 

Figure 14 | Hybrid Recurrent Laguerre-Orthogonal-Polynomial NN Control System Applied in V-Belt Continuously Variable Transmission System Using Particle Swarm Optimization 