# A PID-Type Fuzzy Logic Controller-Based Approach for Motion Control Applications

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Fuzzy Logic Background

#### 2.1. Fuzzy Relations

#### 2.2. Membership Functions

#### 2.3. General Model of a FLC

- The fuzzifier transforms a crisp value into a fuzzy value. The information can be presented in a discrete form while using the fuzzy sets. The discretization process performs a scale mapping to transform values measured in the variables to values of the discrete universe, either uniformly or non-uniformly, or a combination of both.
- When the system states are available for measurement and control, the rule base are written in terms of the state variables instead of error and its derivatives [36]. In general terms, this stage contains all of the information of the application to be controlled, as well as the goals of the controller.
- The inference engine combines the fuzzy if-then rules for mapping the set $\tilde{A}$ from the controller input space A to a fuzzy set $\tilde{B}$ in the controller output space B using the production rules and the knowledge base of membership functions. All of the fuzzy rules are combined in a single fuzzy relation using Equation (7).
- The defuzzification module changes from one domain to another the sets. It means that the fuzzy numbers are transformed into crisp values according to the method to use. In the literature, there exists several ways to map from one domain to another. Once the crisp number is obtained, it is sent to the electronic interface to send it to the actuator.

## 3. S-Curve Profile

## 4. PID-Type FLC Design

## 5. Design Methodology

## 6. Results and Discussion

#### Motion Control Implementation

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FL | Fuzzy Logic |

FLC | Fuzzy Logic Controller |

PID | Proportional-Integral-Derivative |

PWM | Pulse Width Modulation |

GA | Genetic Algorithm |

PSO | Particle Swarm Optimization |

DC | Direct Current |

RPM | Revolutions Per Minute |

PPR | Pulse Per Revolution |

FPGA | Field Programmable Gate Array |

ISE | Integral Square Error |

ITAE | Integral of Time Multiplied by Absolute Error |

IAE | Integral Absolute Error |

NB | Big Negative |

NM | Medium Negative |

NS | Small Negative |

ZE | Zero |

PS | Small Positive |

PM | Medium Positive |

PB | Big Positive |

AZ | Almost Zero |

S | Small |

M | Medium |

B | Big |

## References

- Gurocak, H. Industrial Motion Control: Motor Selection, Drives, Controller Tuning, Applications; John Wiley & Sons: Hoboken, NJ, USA, 2015. [Google Scholar]
- García-Martínez, J.R.; Rodríguez-Reséndiz, J.; Cruz-Miguel, E.E. A New Seven-Segment Profile Algorithm for an Open Source Architecture in a Hybrid Electronic Platform. Electronics
**2019**, 8, 652. [Google Scholar] [CrossRef] [Green Version] - Sabanovic, A.; Ohnishi, K. Motion Control Systems; John Wiley & Sons: Hoboken, NJ, USA, 2011. [Google Scholar]
- Heo, H.J.; Son, Y.; Kim, J.M. A trapezoidal velocity profile generator for position control using a feedback strategy. Energies
**2019**, 12, 1222. [Google Scholar] [CrossRef] [Green Version] - Martínez, J.R.G.; Reséndiz, J.R.; Prado, M.Á.M.; Miguel, E.E.C. Assessment of jerk performance s-curve and trapezoidal velocity profiles. In Proceedings of the 2017 XIII International Engineering Congress (CONIIN), Santiago de Queretaro, Mexico, 15–19 May 2017; pp. 1–7. [Google Scholar]
- Chien, C. Fuzzy logic in control systems: Fuzzy logic controller. IEEE Trans. Syst. Man Cybern. Part II
**1990**, 20, 429–434. [Google Scholar] - Zadeh, L.A. Fuzzy sets. Inf. Control
**1965**, 8, 338–353. [Google Scholar] [CrossRef] [Green Version] - Roose, A.I.; Yahya, S.; Al-Rizzo, H. Fuzzy-logic control of an inverted pendulum on a cart. Comput. Electr. Eng.
**2017**, 61, 31–47. [Google Scholar] [CrossRef] - Verbruggen, H.B.; Bruijn, P. Fuzzy control and conventional control: What is (and can be) the real contribution of fuzzy systems? Fuzzy Sets Syst.
**1997**, 90, 151–160. [Google Scholar] [CrossRef] - Sharma, R.; Bhasin, S.; Gaur, P.; Joshi, D. A switching-based collaborative fractional order fuzzy logic controllers for robotic manipulators. Appl. Math. Model.
**2019**, 73, 228–246. [Google Scholar] [CrossRef] - Chiu, S. Using fuzzy logic in control applications: Beyond fuzzy PID control. IEEE Control Syst. Mag.
**1998**, 18, 100–104. [Google Scholar] - Boverie, S.; Demaya, B.; Le Quellec, J.; Titli, A. Contribution of fuzzy logic control to the improvement of modern car performances. Control Eng. Pract.
**1993**, 1, 291–297. [Google Scholar] [CrossRef] - Preethi, G.; Santhi, B. Study on techniques of earthquake prediction. Int. J. Comput. Appl.
**2011**, 29, 55–58. [Google Scholar] - Von Altrock, C. Fuzzy logic technologies in automotive engineering. In Proceedings of the WESCON’94, Anaheim, CA, USA, 27–29 September 1994; pp. 110–117. [Google Scholar]
- Suganthi, L.; Iniyan, S.; Samuel, A.A. Applications of fuzzy logic in renewable energy systems—A review. Renew. Sustain. Energy Rev.
**2015**, 48, 585–607. [Google Scholar] [CrossRef] - Larkin, L.I. A fuzzy logic controller for aircraft flight control. In Proceedings of the 23rd IEEE Conference on Decision and Control, Las Vegas, NV, USA, 12–14 December 1984; pp. 894–897. [Google Scholar]
- Xu, L.; Wang, Z.; Liu, Y.; Xing, L. Energy allocation strategy based on fuzzy control considering optimal decision boundaries of standalone hybrid energy systems. J. Clean. Prod.
**2020**, 279, 123810. [Google Scholar] [CrossRef] - Essoufi, M.; Hajji, B.; Rabhi, A. Energy Management Strategy Based on a Combination of Frequency Separation and Fuzzy Logic for Fuel Cell Hybrid Electric Vehicles. In Proceedings of the International Conference on Electronic Engineering and Renewable Energy, Saidia, Morocco, 13–15 April 2020; pp. 593–606. [Google Scholar]
- Oglu, A.R.B.; Kizi, I.I.T. A Method for Forecasting the Demand for Pharmaceutical Products in a Distributed Pharmacy Network Based on an Integrated Approach Using Fuzzy Logic and Neural Networks. In Proceedings of the International Conference on Intelligent and Fuzzy Systems, Istanbul, Turkey, 21–23 July 2020; pp. 998–1007. [Google Scholar]
- Frigura-Iliasa, M.; Simo, A.; Dzitac, S.; Frigura-Iliasa, F.M.; Baloi, F.I. Fuzzy-Logic Based Diagnosis for High Voltage Equipment Predictive Maintenance. In Proceedings of the International Conference on Computers Communications and Control, Oradea, Romania, 11–15 May 2020; pp. 245–253. [Google Scholar]
- Gola, A.; Kłosowski, G. Development of computer-controlled material handling model by means of fuzzy logic and genetic algorithms. Neurocomputing
**2019**, 338, 381–392. [Google Scholar] [CrossRef] - Huang, C.I.; Fu, L.C. Adaptive approach to motion controller of linear induction motor with friction compensation. IEEE/ASME Trans. Mechatron.
**2007**, 12, 480–490. [Google Scholar] [CrossRef] - Kung, Y.S.; Fung, R.F.; Tai, T.Y. Realization of a motion control IC for X{-}Y table based on novel fpga technology. IEEE Trans. Ind. Electron.
**2008**, 56, 43–53. [Google Scholar] [CrossRef] - Bouallègue, S.; Haggège, J.; Ayadi, M.; Benrejeb, M. PID-type fuzzy logic controller tuning based on particle swarm optimization. Eng. Appl. Artif. Intell.
**2012**, 25, 484–493. [Google Scholar] [CrossRef] - Bassi, S.; Mishra, M.; Omizegba, E. Automatic tuning of proportional-integral-derivative (PID) controller using particle swarm optimization (PSO) algorithm. Int. J. Artif. Intell. Appl.
**2011**, 2, 25. [Google Scholar] [CrossRef] - Khan, S.; Abdulazeez, S.F.; Adetunji, L.W.; Alam, A.Z.; Salami, M.J.E.; Hameed, S.A.; Abdalla, A.H.; Islam, M.R. Design and Implementation of an Optimal Fuzzy Logic Controller Using Genetic Algorithm; 2008. Available online: https://thescipub.com/abstract/jcssp.2008.799.806 (accessed on 16 September 2020).
- Fereidouni, A.; Masoum, M.A.; Moghbel, M. A new adaptive configuration of PID type fuzzy logic controller. ISA Trans.
**2015**, 56, 222–240. [Google Scholar] [CrossRef] - Bejarbaneh, E.Y.; Bagheri, A.; Bejarbaneh, B.Y.; Buyamin, S.; Chegini, S.N. A new adjusting technique for PID type fuzzy logic controller using PSOSCALF optimization algorithm. Appl. Soft Comput.
**2019**, 85, 105822. [Google Scholar] [CrossRef] - Baldick, R. Applied Optimization: Formulation and Algorithms for Engineering Systems; Cambridge University Press: Cambridge, UK, 2006. [Google Scholar]
- Foulds, L.R. Optimization Techniques: An introduction; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012. [Google Scholar]
- Soyguder, S.; Karakose, M.; Alli, H. Design and simulation of self-tuning PID-type fuzzy adaptive control for an expert HVAC system. Expert Syst. Appl.
**2009**, 36, 4566–4573. [Google Scholar] [CrossRef] - Silva, I.; Eugenio Naranjo, J. A Systematic Methodology to Evaluate Prediction Models for Driving Style Classification. Sensors
**2020**, 20, 1692. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mu, S.; Goto, S.; Shibata, S.; Yamamoto, T. Intelligent position control for pneumatic servo system based on predictive fuzzy control. Comput. Electr. Eng.
**2019**, 75, 112–122. [Google Scholar] [CrossRef] - Mendel, J.M. Uncertain rule-based fuzzy systems. In Introduction and New Directions; Springer: Berlin/Heidelberg, Germany, 2017; p. 684. [Google Scholar]
- Nguyen, A.T.; Taniguchi, T.; Eciolaza, L.; Campos, V.; Palhares, R.; Sugeno, M. Fuzzy control systems: Past, present and future. IEEE Comput. Intell. Mag.
**2019**, 14, 56–68. [Google Scholar] [CrossRef] - Mendel, J.M. Explaining the Performance Potential of Rule-Based Fuzzy Systems as aGreater Sculpting of the State Space. IEEE Trans. Fuzzy Syst.
**2017**, 26, 2362–2373. [Google Scholar] [CrossRef] - Song, L.; Huang, J.; Liang, X.; Yang, S.X.; Hu, W.; Tang, D. An Intelligent Multi-Sensor Variable Spray System with Chaotic Optimization and Adaptive Fuzzy Control. Sensors
**2020**, 20, 2954. [Google Scholar] [CrossRef] - Cruz-Miguel, E.E.; Rodríguez-Reséndiz, J.; García-Martínez, J.R.; Camarillo-Gómez, K.A.; Pérez-Soto, G.I. Field-programmable gate array-based laboratory oriented to control theory courses. Comput. Appl. Eng. Educ.
**2019**, 27, 1253–1266. [Google Scholar] [CrossRef] [Green Version] - Neath, M.J.; Swain, A.K.; Madawala, U.K.; Thrimawithana, D.J. An optimal PID controller for a bidirectional inductive power transfer system using multiobjective genetic algorithm. IEEE Trans. Power Electron.
**2013**, 29, 1523–1531. [Google Scholar] [CrossRef] - Peng, J.; Dubay, R. Identification and adaptive neural network control of a DC motor system with dead-zone characteristics. ISA Trans.
**2011**, 50, 588–598. [Google Scholar] [CrossRef] - Osornio-Rios, R.A.; de Jesús Romero-Troncoso, R.; Herrera-Ruiz, G.; Castañeda-Miranda, R. FPGA implementation of higher degree polynomial acceleration profiles for peak jerk reduction in servomotors. Robot. Comput. Integr. Manuf.
**2009**, 25, 379–392. [Google Scholar] [CrossRef] - Jokić, D.; Lubura, S.; Rajs, V.; Bodić, M.; Šiljak, H. Two Open Solutions for Industrial Robot Control: The Case of PUMA 560. Electronics
**2020**, 9, 972. [Google Scholar] [CrossRef] - Ponce, P.; Molina, A.; Tello, G.; Ibarra, L.; MacCleery, B.; Ramirez, M. Experimental study for FPGA PID position controller in CNC micro-machines. IFAC-PapersOnLine
**2015**, 48, 2203–2207. [Google Scholar] [CrossRef] - Concha Sánchez, A.; Figueroa-Rodríguez, J.F.; Fuentes-Covarrubias, A.G.; Fuentes-Covarrubias, R.; Gadi, S.K. Recycling and Updating an Educational Robot Manipulator with Open-Hardware-Architecture. Sensors
**2020**, 20, 1694. [Google Scholar] [CrossRef] [Green Version]

**Figure 12.**Motion controller based on PID-like FLC, and S-curve velocity profile implementation, (

**a**) position and (

**b**) error.

**Figure 15.**Motion controller based on PID-like FLC and S-curve velocity profile implementation adding a cylindrical load of 1.9 kg, (

**a**) position and (

**b**) error.

**Figure 16.**S-curve velocity profile implementation adding a cylindrical load of 1.9 kg (

**a**) velocity and (

**b**) control signal.

**Figure 17.**Real-time response of the controller gains adding the cylindrical load of 1.9 kg (

**a**) $Kp$ and (

**b**) ${K}_{d}$.

Label | Linguistic Value | Range for Error (m) | Range for d-Error (m/s) |
---|---|---|---|

NB | Big Negative | $[-1,-0.5]$ | $[-10,-3.50]$ |

NM | Medium Negative | $[-0.75,-0.25]$ | $[-10,-0.50]$ |

NS | Small Negative | $[-0.50,0]$ | $[-5,0]$ |

ZE | Zero | $[-0.50,0.50]$ | $[-2.50,2.50]$ |

PS | Small Positive | $[0,0.50]$ | $[0,5]$ |

PM | Medium Positive | $[0.25,0.75]$ | $[0.5,10]$ |

PB | Big Positive | $[0.50,1]$ | $[3.50,10]$ |

Label | Linguistic Value | ${\mathit{K}}_{\mathit{p}}$ | ${\mathit{K}}_{\mathit{d}}$ |
---|---|---|---|

AZ | Almost zero | 0.5 | 0.0 |

S | Small | 3.5 | 0.15 |

M | Medium | 7 | 0.3 |

B | Big | 10 | 0.5 |

${\mathit{K}}_{\mathit{p}}$ | ${\mathit{K}}_{\mathit{d}}$ |
---|---|

if $e\left(t\right)$ is NB, then ${K}_{p}$ is B | if $de\left(t\right)$ is dNB, then ${K}_{d}$ is dB |

if $e\left(t\right)$ is NM, then ${K}_{p}$ is S | if $de\left(t\right)$ is dNM, then ${K}_{d}$ is dM |

if $e\left(t\right)$ is NS, then ${K}_{p}$ is S | if $de\left(t\right)$ is dNS, then ${K}_{d}$ is dS |

if $e\left(t\right)$ is ZE, then ${K}_{p}$ is AZ | if $de\left(t\right)$ is dZE, then ${K}_{d}$ is dAZ |

if $e\left(t\right)$ is PS, then ${K}_{p}$ is S | if $de\left(t\right)$ is dPS, then ${K}_{d}$ is dS |

if $e\left(t\right)$ is PM, then ${K}_{p}$ is S | if $de\left(t\right)$ is dPM, then ${K}_{d}$ is dM |

if $e\left(t\right)$ is PB, then ${K}_{p}$ is B | if $de\left(t\right)$ is dNB, then ${K}_{d}$ is dB |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

García-Martínez, J.R.; Cruz-Miguel, E.E.; Carrillo-Serrano, R.V.; Mendoza-Mondragón, F.; Toledano-Ayala, M.; Rodríguez-Reséndiz, J.
A PID-Type Fuzzy Logic Controller-Based Approach for Motion Control Applications. *Sensors* **2020**, *20*, 5323.
https://doi.org/10.3390/s20185323

**AMA Style**

García-Martínez JR, Cruz-Miguel EE, Carrillo-Serrano RV, Mendoza-Mondragón F, Toledano-Ayala M, Rodríguez-Reséndiz J.
A PID-Type Fuzzy Logic Controller-Based Approach for Motion Control Applications. *Sensors*. 2020; 20(18):5323.
https://doi.org/10.3390/s20185323

**Chicago/Turabian Style**

García-Martínez, José R., Edson E. Cruz-Miguel, Roberto V. Carrillo-Serrano, Fortino Mendoza-Mondragón, Manuel Toledano-Ayala, and Juvenal Rodríguez-Reséndiz.
2020. "A PID-Type Fuzzy Logic Controller-Based Approach for Motion Control Applications" *Sensors* 20, no. 18: 5323.
https://doi.org/10.3390/s20185323