# Parameters Tuning Approach for Proportion Integration Differentiation Controller of Magnetorheological Fluids Brake Based on Improved Fruit Fly Optimization Algorithm

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## Abstract

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## 1. Introduction

## 2. Literature Review

#### 2.1. PID Control Methods

#### 2.2. Fruit Fly Optimization Algorithm

#### 2.3. Discussion

## 3. The Proposed Method

#### 3.1. The Data Acquisition System of MRF Brake

#### 3.2. The Transfer Function of MFR Brake

#### 3.3. The Improved Fruit Fly Optimization Algorithm

- Step 1
- Initialize the master parameters of FOA. The population amount (PA), the maximum iteration number (IN
_{max}), the random flying distance range (FR), the group location range (LR), and the initial location (${X}_{-\mathit{axis}},\text{}{Y}_{-\mathit{axis}})$ of fruit fly population are determined. - Step 2
- Calculate the random direction and distance to search for food of the fruit fly individual.$$\{\begin{array}{c}{X}_{i}\text{}={X}_{-\mathit{axis}}+2\mathit{FR}\text{}\times \text{}{\mathit{Rand}}_{\mathit{i}}\text{}-\mathit{FR}\\ {Y}_{i}\text{}=\text{}{Y}_{-\mathit{axis}}+2\mathit{FR}\text{}\times \text{}{\mathit{Rand}}_{\mathit{i}}\text{}-\text{}\mathit{FR}\end{array},$$
- Step 3
- Calculate the distance between the fruit fly individual and the origin, and then calculate the flavor concentration parameter which is the reciprocal of the distance.$${\mathit{Dist}}_{i}\text{}=\text{}\sqrt{{{X}_{i}}^{2}\text{}+\text{}{{Y}_{i}}^{2}},$$$${S}_{i}\text{}=1/{\mathit{Dist}}_{i},$$
- Step 4
- Substitute ${S}_{i}$ into the fitness function, calculate the value of flavor concentration function ${\mathit{Smell}}_{i}$ and find out the best flavor concentration in the fruit fly population. The minimum value is taken as the best flavor concentration in this paper.$${\mathit{Smell}}_{i}\text{}=\text{}\mathit{Function}({S}_{i}),$$$$[\mathit{bestSmellbestindex}]\text{}=\text{}\mathrm{min}(\mathit{smell}),$$
- Step 5
- Obtain the best flavor concentration value and the coordinates of ${(X}_{-\mathit{axis}},\text{}{Y}_{-\mathit{axis}})$, the fruit fly population flies to that location through vision at this point.$$\mathit{Smellbest}\text{}=\text{}\mathit{bestSmell},$$$$\{\begin{array}{c}{X}_{-\mathit{axis}}=X(\mathit{bestindex})\\ {Y}_{-\mathit{axis}}=Y(\mathit{bestindex})\end{array},$$
- Step 6
- When the smell concentration reaches the preset precision value or the iteration number reaches the maximal IN, the circulation stops. Otherwise, Steps 2 to 4 are repeated.

Begin Initialize PA, IN _{max}, FR, LR and ${(X}_{-\mathit{axis}},\text{}{Y}_{-\mathit{axis}})$ For (p: = 1; p < PA; p++) { ${X}_{i}\text{}=\text{}{X}_{-\mathit{axis}}\text{}+\text{}2\mathit{FR}\text{}\times \text{}{\mathit{Rand}}_{i}\text{}-\mathit{FR}$; ${Y}_{i}\text{}=\text{}{Y}_{-\mathit{axis}}\text{}+\text{}2\mathit{FR}\text{}\times \text{}{\mathit{Rand}}_{i}\text{}-\text{}\mathit{FR}$; ${\mathit{Dist}}_{i}\text{}=\sqrt{{{X}_{i}}^{2}\text{}+\text{}{{Y}_{i}}^{2}}$; ${S}_{i}\text{}=1/{\mathit{Dist}}_{i}$; ${\mathit{Smell}}_{i}\text{}=\text{}{\mathit{Function}(S}_{i})$; } [bestSmell bestindex] = min (Smell); ${X}_{-\mathit{axis}}=\text{}X\text{}(\mathit{bestindex})$; ${Y}_{-\mathit{axis}}=Y\text{}(\mathit{bestindex})$; $\mathit{Smellbest}\text{}=\text{}\mathit{bestSmell}$; For (i: = 1; i< PA; i++) ${\mathit{Smell}}_{\mathit{avg}}\text{}=\text{}\frac{1}{\mathit{PA}}{{\displaystyle \sum}}_{i=1}^{\mathit{PA}}{\mathit{Smell}}_{i}$; ${\mathit{Ex}\text{}=\text{}\mathit{Smell}}_{\mathit{avg}}$; For (i: = 1; i< PA; i++) $En=\frac{1}{\mathit{PA}}\sqrt{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{{\displaystyle \sum}}_{i=1}^{\mathit{PA}}\left|{\mathit{Smell}}_{i}-\mathit{Ex}\right|$; ${\mathit{He}\text{}=\text{}10}^{\alpha}\times \mathit{En}$; ${\mathit{En}}^{\text{'}}=\text{}\mathit{norm}\text{}(\mathit{En},\text{}\mathit{He})$; For (i: = 1; i < PA; i++) ${\mathit{Rand}}_{i}\text{}=\text{}\mathrm{exp}\text{}(-\frac{{{(\mathit{Smell}}_{i}-\mathit{Ex})}^{2}}{{2(\mathit{En}}^{\text{'}}{)}^{2}})$; while (IN < IN _{max}) { $\mathit{FR}\text{}=\text{}\frac{\mathit{FR}}{2}\text{}\times \text{}(1-\frac{\mathit{IN}}{{\mathit{IN}}_{\mathit{max}}})\text{}+\text{}{\mathit{FR}}_{\mathit{min}}$; Update X _{i}; Y_{i}; Dist_{i}; S_{i}; Smell_{i}; if (bestSmell < Smellbest) { ${X}_{-\mathit{axis}}=\text{}X\text{}(\mathit{bestindex},\text{}:)$; ${Y}_{-\mathit{axis}}=\text{}Y(\mathit{bestindex},\text{}:)$; bestS = S (bestindex,:); Smellbest = bestSmell; } ${X}_{-\mathit{axis}}=X\text{}(\mathit{bestindex});\text{}{Y}_{-\mathit{axis}}=Y\text{}(\mathit{bestindex})$; $\mathit{Smellbest}\text{}=\text{}\mathit{bestSmell}$; Update Ex; En; He; Rand _{i}; IN = IN+1; } End |

#### 3.4. Tuning the PID Parameters Based on IFOA

## 4. Simulation and Experimental Results

#### 4.1. Simulation Analysis

_{max}= 100, ${(X}_{-\mathit{axis}},\text{}{Y}_{-\mathit{axis}})$ ∈ (0, 5), FR = 0.5, ${\omega}_{1}$ = 0.999, ${\omega}_{2}$ = 0.001, ${\omega}_{3}$ = 2.0, ${\omega}_{4}$ = 100.

#### 4.2. Experimental Results

## 5. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Type | Radial Dimension | Axial Dimension | Average Maximum Magnetic Field Strength | Maximum Torque |
---|---|---|---|---|

MRF brake | 270 mm | 105 mm | 0.52 T | 30.6 N |

Type | Input Range | Accuracy | AD Transfer Time | Set Frequency |
---|---|---|---|---|

PCI8735 | ±5 V | 0.1% | <1.6 μs | 100 Hz |

Type | Rated Voltage | Rated Current | Transient Response Time | Resolution |
---|---|---|---|---|

DP811A | 0–40 V | 0–5 A | <50 μs | 1 mV/0.5 mA |

Controller Type | ${\mathit{K}}_{\mathit{p}}$ | ${\mathit{K}}_{\mathit{i}}$ | ${\mathit{K}}_{\mathit{d}}$ | σ/% | ${\mathit{t}}_{\mathit{r}}$/s | ${\mathit{t}}_{\mathit{s}}$/s | Ct/s |
---|---|---|---|---|---|---|---|

Conventional | 16.292 | 5.546 | 0.356 | 6.5% | 0.048 | 0.138 | 10.873 |

FOA | 22.441 | 0.0813 | 0.539 | 0 | 0.052 | 0.082 | 54.144 |

IFOA | 86.243 | 0.0820 | 1.134 | 0 | 0.026 | 0.050 | 55.481 |

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**MDPI and ACS Style**

Liu, X.; Shi, Y.; Xu, J.
Parameters Tuning Approach for Proportion Integration Differentiation Controller of Magnetorheological Fluids Brake Based on Improved Fruit Fly Optimization Algorithm. *Symmetry* **2017**, *9*, 109.
https://doi.org/10.3390/sym9070109

**AMA Style**

Liu X, Shi Y, Xu J.
Parameters Tuning Approach for Proportion Integration Differentiation Controller of Magnetorheological Fluids Brake Based on Improved Fruit Fly Optimization Algorithm. *Symmetry*. 2017; 9(7):109.
https://doi.org/10.3390/sym9070109

**Chicago/Turabian Style**

Liu, Xinhua, Yao Shi, and Jing Xu.
2017. "Parameters Tuning Approach for Proportion Integration Differentiation Controller of Magnetorheological Fluids Brake Based on Improved Fruit Fly Optimization Algorithm" *Symmetry* 9, no. 7: 109.
https://doi.org/10.3390/sym9070109