# A Soft Sensor Development for the Rotational Speed Measurement of an Electric Propeller

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Rotational Speed Measurement Problems of the Prototype MAV

^{2}/rad

^{2}) is the propeller torque constant, ${T}_{p}$ (Nm) is the propeller torque, and ${\omega}_{p}$ (rad/s) is the rotational speed of the propeller.

**Remarks**

## 3. Soft Sensor Modeling and the Adaptive Learning Algorithm

- (A2) ${\dot{\omega}}_{s}$ does not change sign on $\left[{t}_{k-1},{t}_{k}\right]$,
- (A3) ${\omega}_{s}$ does not change sign on $\left[{t}_{k-1},{t}_{k}\right]$.

**Remarks**

Algorithm 1: One-step-delay adaptive learning algorithm |

At time instant ${t}_{k+1}$, |

Input: |

1. ${e}_{\theta}\left({t}_{k-2}\right),{e}_{\theta}\left({t}_{k-1}\right),{e}_{\theta}\left({t}_{k}\right),{e}_{\theta}\left({t}_{k+1}\right)$ |

2. $\left\{{\dot{\omega}}_{s}\left(t\right),t\in \left[{t}_{k-1},{t}_{k}\right]\right\}$ |

3. $\left\{{\omega}_{s}\left(t\right),t\in \left[{t}_{k-1},{t}_{k}\right]\right\}$ |

Output: ${a}_{s1}\left({t}_{k}\right),{a}_{s0}\left({t}_{k}\right),{b}_{s}\left({t}_{k}\right)$ |

Steps: |

1. if ${e}_{\theta}\left({t}_{k-2}\right),{e}_{\theta}\left({t}_{k-1}\right),{e}_{\theta}\left({t}_{k}\right),{e}_{\theta}\left({t}_{k+1}\right)$ aren’t strictly monotonic, then End; else Continue |

2. if ${\dot{\omega}}_{s}$ changes sign on $\left[{t}_{k-1},{t}_{k}\right]$, then End; else Continue |

3. if ${\omega}_{s}$ changes sign on $\left[{t}_{k-1},{t}_{k}\right]$, then End; else Continue |

4. Calculate ${a}_{s1}\left({t}_{k}\right),{a}_{s0}\left({t}_{k}\right),{b}_{s}\left({t}_{k}\right)$ according to Equation (15), End |

## 4. Experimental Tests

- (1)
- Initial values of the soft sensor: ${a}_{s1}=1.0\times {10}^{-4},\text{\hspace{0.17em}}{a}_{s0}=1.0\times {10}^{-4},\text{\hspace{0.17em}}{b}_{s}=1.0\times {10}^{-4}$;
- (2)
- Adaptive learning algorithm: ${\lambda}_{{a}_{s1}}=2.0\times {10}^{-6},{\lambda}_{{a}_{s0}}=1.8\times {10}^{-8},{\lambda}_{{b}_{s}}=2.0\times {10}^{-5}$;
- (3)
- Pole pairs of the rotor: ${N}_{p}=12$.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**The experimental setup. (

**a**) The subminiature encoder; and (

**b**) the schematic diagram; DSP: Digital Signal Processor.

**Figure 5.**Experimental results for the input triangle wave. (

**a**) ${\omega}_{m}$ and ${\omega}_{s}$; (

**b**) $e$; (

**c**) ${u}_{a}$; and (

**d**) the parameters of the soft sensor.

**Figure 6.**Experimental results for the input square wave. (

**a**) ${\omega}_{m}$ and ${\omega}_{s}$; (

**b**) $e$; (

**c**) ${u}_{a}$; and (

**d**) the parameters of the soft sensor.

**Figure 7.**Flight test results. (

**a**) ${\omega}_{m}$ and ${\omega}_{s}$; (

**b**) $e$; (

**c**) ${u}_{a}$; and (

**d**) the parameters of the soft sensor.

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**MDPI and ACS Style**

Ye, F.; Sheng, S. A Soft Sensor Development for the Rotational Speed Measurement of an Electric Propeller. *Electronics* **2016**, *5*, 94.
https://doi.org/10.3390/electronics5040094

**AMA Style**

Ye F, Sheng S. A Soft Sensor Development for the Rotational Speed Measurement of an Electric Propeller. *Electronics*. 2016; 5(4):94.
https://doi.org/10.3390/electronics5040094

**Chicago/Turabian Style**

Ye, Fengchao, and Shouzhao Sheng. 2016. "A Soft Sensor Development for the Rotational Speed Measurement of an Electric Propeller" *Electronics* 5, no. 4: 94.
https://doi.org/10.3390/electronics5040094