# Design and Comparative Study of Advanced Adaptive Control Schemes for Position Control of Electronic Throttle Valve

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## Abstract

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## 1. Introduction

- To robustly control the position of the throttle plate of the throttle valve using adaptive backstepping control and adaptive sliding mode backstepping control.
- To robustly control the position of the throttle plate of the throttle valve.
- To cope the unknown (upper bounded) exerted disturbance based on adaptive backstepping control, where disturbance upper bound is needed.
- To cope the unknown upper bound of exerted disturbance using adaptive sliding mode backstepping control, where disturbance upper bound is estimated.

## 2. Mathematical Model

## 3. Controller Design and Stability Analysis

#### 3.1. Backstepping Control

#### 3.2. Adaptive Backstepping Control

#### 3.3. Adaptive Sliding Mode Backstepping Control

## 4. Computer Simulation

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**The schematic diagram of ETV system controlled by adaptive sliding mode backstepping controller.

**Figure 5.**The dynamic response of throttle valve angular position based adaptive backstepping and adaptive sliding mode backstepping controllers.

**Figure 6.**Error response of plate angular position based on adaptive backstepping and adaptive sliding mode backstepping controllers.

**Figure 7.**Plate angular speed response based on adaptive backstepping and adaptive sliding mode backstepping controllers.

**Figure 8.**Control action response based on adaptive backstepping and adaptive sliding mode backstepping controllers.

**Figure 11.**Disturbance upper bound estimation response with exerted disturbance based on adaptive sliding mode backstepping controller

**Figure 12.**Sliding surface derivative $\dot{s}$ (y-axis) versus sliding surface variable $s$ (x-axis) based on adaptive sliding mode backstepping controller

Parameters | Value | Parameters | Value |
---|---|---|---|

R | 2.1 | ${K}_{sp}$ | 0.32 |

L | 0.0017 | $N$ | 4 |

${K}_{d}$ | 0.075 | ${K}_{t}$ | 0.072 |

${B}_{m}$ | 0.03 | ${B}_{t}$ | 0.007 |

${B}_{mo}$ | $6\times {10}^{-3}$ | ${B}_{to}$ | $4\times {10}^{-3}$ |

${J}_{m}$ | 0.02 | ${J}_{t}$ | 0.01 |

Tracking Error | Time | Variance | ||||

0.5 | 3 | 5 | 8 | 10 | ||

ABSC | −0.6 | −0.02 | 0.05 | 0.04 | 0.27 | 0.2562 |

ASMBSC | −0.04 | 0 | 0.001 | 0 | 0.1 | 0.1316 |

Control Action | Time | Variance | ||||

0.1 | 2 | 5 | 8 | 10 | ||

ABSC | 14.5 | 1.1 | 1.2 | 0.1 | 3.7 | 10.3 |

ASMBSC | 24 | 0 | 0 | 0.1 | 3.7 | 11.7 |

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**MDPI and ACS Style**

Humaidi, A.J.; Hameed, A.H. Design and Comparative Study of Advanced Adaptive Control Schemes for Position Control of Electronic Throttle Valve. *Information* **2019**, *10*, 65.
https://doi.org/10.3390/info10020065

**AMA Style**

Humaidi AJ, Hameed AH. Design and Comparative Study of Advanced Adaptive Control Schemes for Position Control of Electronic Throttle Valve. *Information*. 2019; 10(2):65.
https://doi.org/10.3390/info10020065

**Chicago/Turabian Style**

Humaidi, Amjad J., and Akram H. Hameed. 2019. "Design and Comparative Study of Advanced Adaptive Control Schemes for Position Control of Electronic Throttle Valve" *Information* 10, no. 2: 65.
https://doi.org/10.3390/info10020065