# Electromagnetic Actuator System Using Witty Control System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. System Description

#### 2.2. System Model

## 3. Methods

## 4. Tests and Results

## 5. Analyses and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

${w}_{u}$, ${w}_{v}$ | $u-v$ axis stator voltages |

${q}_{u}$, ${q}_{v}$ | $u-v$ axis stator currents |

${q}_{ur}$, ${q}_{vr}$ | $u-v$ axis rotor currents |

${L}_{u}$, ${L}_{v}$, ${L}_{uv}$ | $u-v$ axis self inductances, mutual inductance |

${r}_{a}$, ${r}_{b}$ | stator and equalized rotor resistances. |

${\mu}_{v}$, ${\mu}_{u}$, ${\mu}_{t}$ | mechanical and electrical angular speeds, electrical angular speed of synchronous flux in the ISM |

${F}_{a}$ | electromagnetic torque |

${\phi}_{u}$, ${\phi}_{v}^{}$ | $u-v$ axis flux linkages |

${P}_{t}$ | number of pole |

${F}_{v}$, ${F}_{d}$, ${F}_{b1}$ | electromagnetic torque of the ISM, the output torque of idler 2 and the output torque of the main idler |

${f}_{a}$, ${f}_{c}$, ${f}_{d}$, ${f}_{b}$ | four moments of inertia in the ISM, in idler 2, in the main idler and in idler 1 |

${g}_{v}$, ${g}_{c}$, ${g}_{d}$, ${g}_{b}$ | four viscid frictional coefficients in the ISM, in idler 2, in the main idler and in idler 1 |

${\varphi}_{b}$ | transposition ratios regarding idler 2 and the main idler for the rice milling machine system |

${F}_{b}^{l}({R}_{vb},{F}_{vb},{F}_{vl},{g}_{b})$ | nonlinear coalescence disturbances function |

${R}_{vb}$, ${F}_{vb}$, ${F}_{vl}$ | rolling force, wind force, braking force |

${\mu}_{v}$, ${\mu}_{b}$ | speed in idler 2 and the speed in the main idler. |

${g}_{r}={g}_{a}+{g}_{c}$ | coalescence viscid friction coefficient including the main idler and the ISM |

${f}_{r}={f}_{a}+{f}_{c}$ | coalescence moment of inertia including the main idler and the ISM |

$\mathsf{\Delta}{F}_{a}+{F}_{b1}$ | huge comprehensive coalescence disturbances and parameter variations |

${F}_{t}({F}_{1c},{F}_{2c},{F}_{3c})$ | coalescence torque |

${F}_{3c}$, ${F}_{2c}$, ${F}_{1c}$ | coulomb friction torque, Stribeck effect torque, adding load torque |

${F}_{b1}$ | comprehensive coalescence disturbances |

$\mathsf{\Delta}{F}_{a}$ | comprehensive parameter variations |

$\mathsf{\Delta}{F}_{a}+{F}_{b1}+{F}_{e}$ | comprehensive coalescence disturbances |

${h}_{v}=-{g}_{r}{f}_{r}^{-1}$ | friendly ratio constant |

${R}_{v}({\mu}_{v})$ | bounded with functional-bounded value |

${h}_{w}=-{f}_{r}^{-1}$ | friendly constant concerning the coalescence moment of inertia |

${h}_{x}={f}_{r}^{-1}$ | friendly constant concerning the coalescence moment of inertia |

${R}_{b}$, ${R}_{c}$ | two friendly values with bound |

${l}_{v}={F}_{v}$ | electromagnetic torque of the ISM |

${s}_{a}$ | speed difference |

${c}_{v}$ | positive control gain |

${l}_{x}$, ${l}_{y}$, ${l}_{z}$, ${l}_{w}$ | RRJPNN control, dominator control, two remunerated controls |

${a}_{2}^{1}={s}_{a}(1-{z}^{-1})=\mathsf{\Delta}{s}_{a}$, ${a}_{1}^{1}=\mu *-{\mu}_{v}={s}_{a}$ | speed difference alteration, speed difference |

$m$, $\chi $ and $K$ | node number of the center layer, the recurrent gain of the center layer and the iteration number |

${\rho}_{rt}^{1}(K)$, ${\rho}_{ts}^{2}(K)$ | recurrent weight, conjoined weight |

${y}_{r}^{1}$, ${y}_{s}^{2}$, ${y}_{t}^{3}$ | three linear activation functions in the forehead, center and readward layers |

${d}_{r}^{1}(K)$, ${d}_{s}^{2}(K)$, ${d}_{t}^{3}(K)$ | information of three outputs of nodes in the forehead, center and readward layers |

${P}_{s}^{(\alpha ,\beta )}(b)$ | Jacobi polynomial function |

${P}_{0}^{(\alpha ,\beta )}(b)$, ${P}_{1}^{(\alpha ,\beta )}(b)$, ${P}_{2}^{(\alpha ,\beta )}(b)$ | 0-, 1- and 2-order Jacobi polynomial functions |

${d}_{t}^{3}(K)={l}_{x}$ | output information in the readward layer |

$\mathit{D}={\left[\begin{array}{ccc}{d}_{0}^{2}& \cdots & {d}_{m-1}^{2}\end{array}\right]}^{T}$, $\mathit{C}={\left[\begin{array}{ccc}{\rho}_{10}^{2}& \cdots & {\rho}_{1,\hspace{0.17em}m-1}^{2}\end{array}\right]}^{T}$ | input information and weight vectors in the readward layer |

$\lambda $ | minimum difference |

${l}_{x}^{*}={d}_{t}^{*}={({\mathit{C}}^{*})}^{T}\mathit{D}$ | excellent control rule of the RRJPNN control |

${\mathit{C}}^{*}$ | excellent weight vector |

$\delta $ | greater than zero real number |

${x}_{a}(t)$ | uniformly continuous function |

${V}_{x}(0)$, ${V}_{x}(t)$ | two bounded |

$\mathrm{sgn}(\cdot )$ | sign function |

${V}_{y}$ | objective function |

$\frac{d\mathit{C}}{dt}$ | attunement law |

${\upsilon}_{1}$, ${\upsilon}_{2}$ | learning rate of the conjoined weight, learning rate of the recurrent weight |

${\tau}_{1}$, ${\tau}_{2}$ | two positive evaluation rates |

$\widehat{\gamma}-\gamma $, $\widehat{\delta}-\delta $ | two evaluation differences |

$d\widehat{\gamma}/dt$, $d\widehat{\delta}/dt$ | two evaluation laws |

${z}_{i}(n-1)$, ${f}_{i}(n-1)$ | position of the bat i at n − 1 time, flight velocity of the bat i at n − 1 time |

${z}_{i}(n)$, ${f}_{i}(n)$ | position of the bat i at n time, flight velocity of the bat i at n time |

$z*$ | current global optimal position |

${N}_{\mathrm{max}}$ | maximum number of iterations |

${k}_{\mathrm{max}}$, ${k}_{\mathrm{min}}$ | maximum and minimum frequencies of the soundwaves produced by the bat |

$\sigma $ | random number at [−1, 1] |

${z}_{old}(n-1)$ | solution selected from the current optimal solution at n − 1 time |

${\overline{d}}_{i}(n)$ | average loudness from the bat generation at n time |

${d}_{i}(n+1)$, ${e}_{i}(n+1)$ | modified loudness at n + 1 time, modified pulse rate at n + 1 time |

${e}_{i}(0)$, ${d}_{i}(0)$ | initial rate, initial loudness |

$\varsigma $, $\xi $ | constant between 0 and 1, positive constant |

## References

- Zuo, L.; Cheng, T.; Zuo, J.; Liu, Y.; Yang, S. A hierarchical intelligent control system for milling machine. In Proceedings of the IEEE International Conference on Intelligent Processing Systems, Beijing, China, 28–31 October 1997; pp. 1–6. [Google Scholar]
- Huang, S.; Tan, K.K.; Hang, G.S.; Wang, Y.S. Cutting force control of milling machine. Mechatronics
**2007**, 17, 533–541. [Google Scholar] [CrossRef] - Lobinho, G.; Armando, S. Control of milling machine cutting force using artificial neural networks. In Proceedings of the 6th Iberian Conference on Information Systems and Technologies (CISTI 2011), Chaves, Portugal, 15–18 June 2011; pp. 1–6. [Google Scholar]
- Tadeusz, M. Numerical control system of conventional milling machine. Appl. Mech. Mater.
**2016**, 841, 179–183. [Google Scholar] - Tu, F.; Hu, S.; Zhuang, Y.; Lv, J.; Wang, Y.; Sun, Z. Hysteresis curve fitting optimization of magnetic controlled shape memory alloy actuator. Actuators
**2016**, 5, 25. [Google Scholar] [CrossRef] [Green Version] - Nakshatharan, S.S.; Vunder, V.; Poldsalu, I.; Johanson, U.; Punning, A.; Aabloo, A. Modelling and control of ionic electroactive polymer actuators under varying humidity conditions. Actuators
**2018**, 7, 7. [Google Scholar] [CrossRef] [Green Version] - Xia, B.; Miriyev, A.; Trujillo, C.; Chen, N.; Cartolano, M.; Vartak, S.; Lipson, H. Improving the actuation speed and multi-cyclic actuation characteristics of silicone/ethanol soft actuators. Actuators
**2020**, 9, 62. [Google Scholar] [CrossRef] - Lee, T.; Kim, I. Design of a 2DOF ankle exoskeleton with a polycentric structure and a bi-directional tendon-driven actuator controlled using a PID neural network. Actuators
**2021**, 10, 9. [Google Scholar] [CrossRef] - Wang, L.; Duan, M.; Duan, S. Memristive Chebyshev neural network and its applications in function approximation. Math. Probl. Eng.
**2013**, 2013, 1–7. [Google Scholar] [CrossRef] - Ting, J.C.; Chen, D.F. Novel mingled reformed recurrent hermite polynomial neural network control system applied in continuously variable transmission system. J. Mech. Sci. Technol.
**2018**, 32, 4399–4412. [Google Scholar] [CrossRef] - Soltani, M.; Hegde, C. Fast and provable algorithms for learning two-layer polynomial neural networks. IEEE Trans. Signal Process.
**2019**, 67, 3361–3371. [Google Scholar] [CrossRef] - Ting, J.C.; Chen, D.F. Nonlinear backstepping control of SynRM drive systems using reformed recurrent Hermite polynomial neural networks with adaptive law and error estimated law. J. Power Electron.
**2018**, 8, 1380–1397. [Google Scholar] - Richard, A.; James, W. Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials; American Mathematical Soc.: Providence, RI, USA, 1985; p. 54. [Google Scholar]
- Guo, B.Y.; Shen, J.; Wang, L.L. Generalized Jacobi polynomials/functions and their applications. Appl. Numer. Math.
**2009**, 59, 1011–1028. [Google Scholar] [CrossRef] [Green Version] - Rubio, J.J.; Yu, W. Nonlinear system identification with recurrent neural networks and dead-zone Kalman filter algorithm. Neurocomputing
**2007**, 70, 2460–2466. [Google Scholar] [CrossRef] - Chen, D.F.; Shih, Y.C.; Li, S.C.; Chen, C.T.; Ting, J.C. Mixed modified recurring Rogers-Szego polynomials neural network control with mended grey wolf optimization applied in SIM expelling system. Mathematics
**2020**, 8, 754. [Google Scholar] [CrossRef] - Abbasvandi, Z.; Nasrabadi, A.M. A self-organized recurrent neural network for estimating the effective connectivity and its application to EEG data. Comput. Biol. Med.
**2019**, 110, 93–107. [Google Scholar] [CrossRef] - Park, K.; Kim, J.; Lee, J. Visual field prediction using recurrent neural network. Sci. Rep.
**2019**, 9, 8385. [Google Scholar] [CrossRef] - Jaddi, N.S.; Abdullah, S.; Hamdan, A. Multi-population cooperative bat algorithm-based optimization of artificial neural network model. Inf. Sci.
**2015**, 294, 628–644. [Google Scholar] [CrossRef] - Wang, L.; Geng, H.; Liu, P.; Lu, K.; Kolodziej, J.; Ranjan, R.; Zomaya, A.Y. Particle swarm optimization based dictionary learning for remote sensing big data. Knowl. Based Syst.
**2015**, 79, 43–50. [Google Scholar] [CrossRef] - Liu, Z.Z.; Chu, D.H.; Song, C.; Xue, X.; Lu, B.Y. Social learning optimization (SLO) algorithm paradigm and its application in QoS-aware cloud service composition. Inf. Sci.
**2016**, 326, 315–333. [Google Scholar] [CrossRef] - Wu, D.; Xu, S.; Kong, F. Convergence analysis and improvement of the chicken swarm optimization algorithm. IEEE Access
**2016**, 4, 9400–9412. [Google Scholar] [CrossRef] - Gheraibia, Y.; Djafri, K.; Krimou, H. Ant colony algorithm for automotive safety integrity level allocation. Appl. Intell.
**2017**, 8, 555–569. [Google Scholar] [CrossRef] - Yang, X.S. A new metaheuristic bat-inspired algorithm. In Nature Inspired Cooperative Strategies for Optimization (NICSO 2010); Springer: Berlin, Heidelberg, 2010; Volume 284, pp. 65–74. [Google Scholar]
- Adarsh, B.A.; Raghunathan, T.; Jayabarathi, T.; Yang, X.S. Economic dispatch using chaotic bat algorithm. Energy
**2016**, 96, 666–675. [Google Scholar] [CrossRef] - Wang, Y.; Wang, P.; Zhang, J.; Cui, H.; Cai, X.; Zhang, W.; Chen, J. A novel bat algorithm with multiple strategies coupling for numerical optimization. Mathematics
**2019**, 7, 135. [Google Scholar] [CrossRef] [Green Version] - Chen, D.F.; Cheng, A.B.; Chiu, S.P.C.; Ting, J.C. Electromagnetic torque control for six-phase induction motor expelled continuously variable transmission clumped system using sage dynamic control system. Int. J. Appl. Electromagn. Mech.
**2021**, 65, 579–608. [Google Scholar] [CrossRef] - Singh, G.K.; Nam, K.; Lim, S.K. A simple indirect field oriented control scheme for multiphase induction machine. IEEE Trans. Ind. Electron.
**2005**, 52, 1117–1184. [Google Scholar] [CrossRef] - Guo, Z.; Zhang, J.; Sun, Z.; Zheng, C. Indirect field oriented control of three-phase induction motor based on current-source inverter. Procedia Eng.
**2017**, 174, 588–594. [Google Scholar] [CrossRef] - Han, Y.; Jia, F.; Zeng, Y.; Cao, B. Effects of rotation speed and outlet opening on particle flow in a vertical rice mill. Powder Technol.
**2016**, 297, 153–164. [Google Scholar] [CrossRef] - Zareiforoush, H.; Minaee, S.; Alizadeh, M.R.; Samani, B.H. Design, development and performance evaluation of an automatic control system for rice whitening machine based on computer vision and fuzzy logic. Comput. Electron. Agric.
**2016**, 124, 14–22. [Google Scholar] [CrossRef] - Ruekkasaem, L.; Sasananan, M. Optimal parameter design of rice milling machine using design of experiment. Mater. Sci. Forum
**2018**, 911, 107–111. [Google Scholar] [CrossRef] - Astrom, K.J.; Hagglund, T. PID Controller: Theory, Design, and Tuning; Instrument Society of America: Research Triangle Park, NC, USA, 1995. [Google Scholar]
- Hagglund, T.; Astrom, K.J. Revisiting the Ziegler-Nichols tuning rules for PI control. Asian J. Control
**2002**, 4, 364–380. [Google Scholar] [CrossRef] - Hagglund, T.; Astrom, K.J. Revisiting the Ziegler-Nichols tuning rules for PI control-part II: The frequency response method. Asian J. Control
**2004**, 6, 469–482. [Google Scholar] [CrossRef] - Astrom, K.J.; Wittenmark, B. Adaptive Control; Addison-Wesley: New York, NY, USA, 1995. [Google Scholar]
- Slotine, J.J.E.; Li, W. Applied Nonlinear Control; Prentice-Hall: Englewood Cliffs, NJ, USA, 1991. [Google Scholar]
- Chen, D.F.; Shih, Y.C.; Li, S.C.; Chen, C.T.; Ting, J.C. Permanent-magnet SLM drive system using AMRRSPNNB control system with DGWO. Energies
**2020**, 13, 2914. [Google Scholar] [CrossRef]

**Figure 7.**Speed responses via experimental results for the ISM driving the rice milling machine system at test JA by adopting the controllers: (

**a**) TA; (

**b**) TB.

**Figure 8.**Increase in speed difference responses via experimental results for the ISM driving the rice milling machine system at test JA by adopting the controllers: (

**a**) TA; (

**b**) TB.

**Figure 9.**Responses of three-phase currents via experimental results for the ISM driving the rice milling machine system in test JA by adopting the controllers: (

**a**) TA; (

**b**) TB.

**Figure 10.**Speed responses via experimental results for the ISM driving the rice milling machine system in test JB by adopting the controllers: (

**a**) TA; (

**b**) TB.

**Figure 11.**Increase in speed difference responses via experimental results for the ISM driving the rice milling machine system in test JB by adopting the controllers: (

**a**) TA; (

**b**) TB.

**Figure 12.**Responses of three-phase currents via experimental results for the ISM driving the rice milling machine system at test JA by adopting the controllers: (

**a**) TA; (

**b**) TB.

**Figure 13.**Two speed-regulated responses when adding load torque via experimental results of test JC by adopting the controllers: (

**a**) TA; (

**b**) TB.

**Figure 14.**Responses of three-phase currents with adding load torque via experimental results of test JC by adopting the controllers: (

**a**) TA; (

**b**) TB.

**Figure 15.**Responses of two learning rates via experimental results of test JB by adopting the ant colony algorithm (ACO), particle swarm optimization (PSO) and altered bat search algorithm (ABSA) methods for: (

**a**) learning rate of conjoined weight, (

**b**) learning rate of recurrent weight.

**Figure 16.**Responses of two weights via experimental results of test JB by adopting the ACO, PSO and ABSA methods for: (

**a**) conjoined weight; (

**b**) recurrent weight.

**Figure 17.**Responses of numbers of conjoined weight via experimental results of test JB by adopting the ACO, PSO and ABSA methods.

Controllers | TA Controller | TB Controller | ||||
---|---|---|---|---|---|---|

Performance | Maximum Differences of ${\mathit{s}}_{\mathit{a}}$ | Quadratic Mean Differences of ${\mathit{s}}_{\mathit{a}}$ | Maximum Differences of ${\mathit{s}}_{\mathit{a}}$ | Quadratic Mean Differences of ${\mathit{s}}_{\mathit{a}}$ | ||

Three Test Examples | ||||||

Test JA | 82 rpm | 48 rpm | 30 rpm | 17 rpm | ||

(8.58 rad/s) | (5.02 rad/s) | (3.14 rad/s) | (1.78 rad/s) | |||

Test JB | 128 rpm | 53 rpm | 35 rpm | 19 rpm | ||

(13.40 rad/s) | (5.55 rad/s) | (3.66 rad/s) | (1.99 rad/s) | |||

Test JC | 489 rpm | 188 rpm | 192 rpm | 46 rpm | ||

(51.18 rad/s) | (19.68 rad/s) | (20.10 rad/s) | (4.81 rad/s) |

Controllers | TA Controller | TB Controller | |
---|---|---|---|

Peculiarity Performances | |||

Total harmonic distortion (THD) values in the three-phase currents in test JB | 21% | 5% | |

Responses of rising times in test JB | 0.92 s | 0.75 s | |

Regulation capabilities with adding load torque in test JC | 489 rpm (51.18 rad/s) in maximum difference | 192 rpm (20.10 rad/s) in maximum difference | |

Speed tracking differences in test JB | 128 rpm (13.40 rad/s) in maximum difference | 35 rpm (3.66 rad/s) in maximum difference | |

Denial potentialities of parameter disturbance in test JB | 128 rpm (13.40 rad/s) in maximum difference | 35 rpm (3.66 rad/s) in maximum difference |

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**MDPI and ACS Style**

Chen, D.-F.; Chiu, S.-P.-C.; Cheng, A.-B.; Ting, J.-C.
Electromagnetic Actuator System Using Witty Control System. *Actuators* **2021**, *10*, 65.
https://doi.org/10.3390/act10030065

**AMA Style**

Chen D-F, Chiu S-P-C, Cheng A-B, Ting J-C.
Electromagnetic Actuator System Using Witty Control System. *Actuators*. 2021; 10(3):65.
https://doi.org/10.3390/act10030065

**Chicago/Turabian Style**

Chen, Der-Fa, Shen-Pao-Chi Chiu, An-Bang Cheng, and Jung-Chu Ting.
2021. "Electromagnetic Actuator System Using Witty Control System" *Actuators* 10, no. 3: 65.
https://doi.org/10.3390/act10030065