# Data-Driven Tuning of PID Controlled Piezoelectric Ultrasonic Motor

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{®}rotary stage, on which iterative feedback tuning of PID control parameters was applied, is given in Section 2

**.**In Section 3, single source and dual source dual frequency driving methods are summarized with motion control algorithm. Iterative feedback tuning methods, which is the main contribution in this study, is described in Section 4

**.**After analyzing the iterative tuning methods for different motor driving techniques in Section 5, the manuscript is concluded in Section 6.

## 2. PILine^{®} Rotary Stage

^{−4}°) resolution is integrated to measure the rotational movements.

## 3. Driving Methods and Motion Control

^{®}motor can be driven in two ways: one source drive and dual source dual frequency drive (DSDF).

#### 3.1. One Source Drive

#### 3.2. DSDF Drive

^{®}motor, as a typical input voltage–moving speed characteristics, the low speed region is the most problematic area. Furthermore, the difference between static and dynamic friction properties also enhances the nonlinearity found in this area. To obtain movement from the piezoelectric actuator, the vibration amplitude, thus force generated by the pusher on the stator, should be larger than the static friction force. As soon as the force generated by the stator exceeds the breakaway force, a slider would be accelerated maintaining that the dynamic friction force is smaller than the static one. These kinds of start stop movements initiate friction induced forced vibrations or noises.

#### 3.3. Motion Control

## 4. Iterative Feedback Tuning Methods

**ISE**) [22], calculated as Equation (1)

## 5. Results and Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**One source driving of the stator. During single source drive, only one of the electrodes on the piezoelectric plate is exposed to one sinusoidal voltage at a frequency of ω

_{1}. Changing the excited electrodes changes the moving direction of the slider.

**Figure 4.**Dual-source-dual-frequency (DSDF) driving of the stator. Both electrodes on the piezoelectric plate are exposed to sinusoidal voltage signals at different frequencies (ω

_{1}and ω

_{2}) and different magnitudes (A and B).

**Figure 8.**Trajectory and actual motor position at velocity of 0.2 °/s with summation of absolute value deviations.

**Figure 10.**Grid search with fitness function values for the velocity of 0.1 °/s and DSDF source driving.

**Figure 11.**Grid search with fitness function values for the angular velocity of 0.1 °/s and single source driving.

**Figure 12.**Grid search with fitness function values for the angular velocity of 2.0 °/s and DSDF source driving.

**Figure 13.**Grid search with fitness function values for the angular velocity of 2.0 °/s and single source driving.

**Figure 18.**Response of constant velocity trajectory with the optimal PID parameters at 1.0 °/s with (

**a**) single source driving and (

**b**) DSDF driving.

**Table 1.**Optimal PID parameters and corresponding ISE function values for two driving methods performed with various search algorithms at 2 °/s velocity.

Driving Methods | Search Algorithms | PID Values (P, I, D) | ISE Function Values (s) |
---|---|---|---|

Single source drive | Luus–Jaakola | (310, 209, 204) | 0.004250 |

Hybrid | (303, 187, 234) | 0.004671 | |

Genetic | (326, 178, 139) | 0.004928 | |

DSDF drive | Luus–Jaakola | (419, 704, 93) | 0.000039 |

Hybrid | (372, 629, 110) | 0.000036 | |

Genetic | (321, 895, 67) | 0.000089 |

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**MDPI and ACS Style**

Makarem, S.; Delibas, B.; Koc, B.
Data-Driven Tuning of PID Controlled Piezoelectric Ultrasonic Motor. *Actuators* **2021**, *10*, 148.
https://doi.org/10.3390/act10070148

**AMA Style**

Makarem S, Delibas B, Koc B.
Data-Driven Tuning of PID Controlled Piezoelectric Ultrasonic Motor. *Actuators*. 2021; 10(7):148.
https://doi.org/10.3390/act10070148

**Chicago/Turabian Style**

Makarem, Sarah, Bülent Delibas, and Burhanettin Koc.
2021. "Data-Driven Tuning of PID Controlled Piezoelectric Ultrasonic Motor" *Actuators* 10, no. 7: 148.
https://doi.org/10.3390/act10070148