# Multi-Physical Design and Resonant Controller Based Trajectory Tracking of the Electromagnetically Driven Fast Tool Servo

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Architecture of the VCM Actuated FTS System

#### 2.1. Design of the Voice Coil Motor

#### 2.2. Design of the Flexure Mechanism

## 3. Modeling and Verification of the VCM Actuated FTS System

#### 3.1. Magnetic Equivalent Circuit Modeling

#### 3.2. Modeling of Flexure Mechanism

_{i}, and ${T}_{{O}_{\mathrm{i}}}$ means the coordinate transfer matrix from system O

_{i}to the global system [13].

_{1}is the mass of the end-effector. Using the Lagrangian equation, the equivalent moving mass M can be expressed by [16]

#### 3.3. Finite Element Analysis Validation

#### 3.3.1. Electromagnetic Verification of the VCM

#### 3.3.2. Mechanical Verification of Flexure Mechanism

## 4. Controller Design for the Fast Tool Servo System

#### 4.1. PID Controller

#### 4.2. Resonant Controller

## 5. Experimental Testing and Results

#### 5.1. Experimental Setup

#### 5.2. Experimental Results

#### 5.2.1. Static and Dynamic Performance Testing

#### 5.2.2. Control Performance Testing

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Rakuff, S.; Cuttino, J.F. Design and testing of a long-range, precision fast tool servo system for diamond turning. Precis. Eng.
**2009**, 33, 18–25. [Google Scholar] [CrossRef] - Zhu, W.-L.; Yang, X.; Duan, F.; Zhu, Z.; Ju, B.-F. Design and adaptive terminal sliding mode control of a fast tool servo system for diamond machining of freeform surfaces. IEEE Trans. Ind. Electron.
**2019**, 66, 4912–4922. [Google Scholar] [CrossRef] - Zhu, Z.; Zhou, X.; Liu, Z.; Wang, R.; Zhu, L. Development of a piezoelectrically actuated two-degree-of-freedom fast tool servo with decoupled motions for micro-/nanomachining. Precis. Eng.
**2014**, 38, 809–820. [Google Scholar] [CrossRef] - Liu, Q.; Zhou, X.; Lin, J.; Xu, P.; Zhu, Z. A Quasiphysics Intelligent Model for a Long Range Fast Tool Servo. Sci. World J.
**2013**, 2013. [Google Scholar] [CrossRef] [PubMed][Green Version] - Liu, Q.; Zhou, X.; Liu, Z.; Lin, C.; Ma, L. Long-stroke fast tool servo and a tool setting method for freeform optics fabrication. Opt. Eng.
**2014**, 53, 092005. [Google Scholar] [CrossRef] - Byl, M.F. Design and Control of a Long Stroke Fast Tool Servo. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 2005. [Google Scholar]
- Crudele, M.; Kurfess, T.R. Implementation of a fast tool servo with repetitive control for diamond turning. Mechatronics
**2003**, 13, 243–257. [Google Scholar] [CrossRef] - Byl, M.F.; Ludwick, S.J.; Trumper, D.L. A loop shaping perspective for tuning controllers with adaptive feedforward cancellation. Precis. Eng.
**2005**, 29, 27–40. [Google Scholar] [CrossRef] - Lu, X. Electromagnetically-Driven Ultra-Fast Tool Servos for Diamond Turning. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 2005. [Google Scholar]
- Brauer, J.R. Magnetic Actuators and Sensors; John Wiley & Sons: New York, NY, USA, 2006. [Google Scholar]
- Okyay, A.; Khamesee, M.B.; Erkorkmaz, K. Design and optimization of a voice coil actuator for precision motion applications. IEEE Trans. Magn.
**2014**, 51, 1–10. [Google Scholar] [CrossRef] - Parmar, G.; Hiemstra, D.B.; Chen, Y.; Awtar, S. A moving magnet actuator for large range nanopositioning. In Proceedings of the ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Arlington, VA, USA, 31 October–2 November 2011. [Google Scholar]
- Zhu, Z.; Zhou, X.; Wang, R.; Liu, Q. A simple compliance modeling method for flexure hinges. Sci. China Technol. Sci.
**2015**, 58, 56–63. [Google Scholar] [CrossRef] - Wu, Y.; Zhou, Z. Design calculations for flexure hinges. Rev. Sci. Instrum.
**2002**, 73, 3101–3106. [Google Scholar] [CrossRef] - Koseki, Y.; Tanikawa, T.; Koyachi, N.; Arai, T. Kinematic analysis of a translational 3-dof micro-parallel mechanism using the matrix method. Adv. Robot.
**2002**, 16, 251–264. [Google Scholar] [CrossRef] - Zhu, Z.; Zhou, X.; Liu, Q.; Zhao, S. Multi-objective optimum design of fast tool servo based on improved differential evolution algorithm. J. Mech. Sci. Technol.
**2011**, 25, 3141–3149. [Google Scholar] [CrossRef] - Sadeghpour, M.; De Oliveira, V.; Karimi, A. A toolbox for robust PID controller tuning using convex optimization. IFAC Proc. Vol.
**2012**, 45, 158–163. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Mechanical structure of the voice coil motor (VCM) actuated fast tool servo (FTS) system, (

**a**) the zonal-sectional view and (

**b**) the cross-section view of the assembled structure, where (1) stator, (2) permanent magnet, (3) coil, (4) mover, and (5) air-part including air-gaps (yellow part).

**Figure 2.**Cross-section view of the double parallelogram flexure mechanism, where $R$ is radius of circular notch, $t$ is thickness between two circular notches, $a$ is the width and height of the linkage, and ${l}_{1}$ is the length of LSFH.

**Figure 3.**Lumped-circuit element based magnetic circuit model of the VCM, where ${t}_{PM}$, ${t}_{ag}$, ${t}_{a}$, and ${t}_{y}$ are the thickness of the permanent magnet (PM), air-gap, armature, and yoke, respectively. ${l}_{t}$ is the length from the outer face to the axis of the VCM. ${\mathsf{\mathcal{R}}}_{\mathrm{c}1}$, ${\mathsf{\mathcal{R}}}_{\mathrm{c}2}$, and ${\mathsf{\mathcal{R}}}_{\mathrm{c}3}$ are the equivalent reluctance of the stator material.

**Figure 5.**Static structural analysis of the flexure mechanism, (

**a**) the constraint, (

**b**) the meshed model, and (

**c**) the resultant deformation with F = 100 N.

**Figure 6.**Modal analysis of the flexure mechanism, (

**a**) the first mode without coil and (

**b**) the first mode with coil.

**Figure 8.**Experimental setup, (

**a**) schematic of the testing system and (

**b**) the photography of the prototype.

**Figure 9.**Response of experimental testing of the FTS system, (

**a**) the output motion related to the applied voltage and (

**b**) the frequency response function.

**Figure 10.**The control performance, (

**a**) tracking response for 20 Hz harmonic trajectory, (

**b**) tracking error for 20 Hz and 40 Hz trajectory, (

**c**) tracking error for 60 Hz and 80 Hz trajectory, and (

**d**) tracking error for 100 Hz and 120 Hz trajectory.

Symbol | Description | Turns/Layers | Value |
---|---|---|---|

l_{c} | Length for multiple turns | 64 | 37 mm |

h_{c} | height for multiple turns | 8 | 4.5 mm |

N_{T} | Total number of turns | 64 × 8 | 512 |

Parts | Geometric Parameters | Symbols | Value |
---|---|---|---|

Stator | thickness (outer side of yoke) | t_{y} | 10 |

thickness (central iron core) | t_{cr} | 12 | |

PM | length | l_{c} + 3 | 40 |

thickness (magnetization direction) | t_{PM} | 5 | |

width | w | 50 | |

Armature | thickness | t_{a} | 4.5 |

Air-gap | thickness | t_{ag} | 0.5 |

R | t | ${\mathit{l}}_{1}$ | a | b |
---|---|---|---|---|

1 | 0.6 | 28 | 2.6 | 30 |

k_{in} (N⁄μm) | f_{o} (Hz) | B (T) | F_{a} (N) | s (μm) | ||
---|---|---|---|---|---|---|

Without Coil | With Coil | |||||

Ana. | 1.10 | 395.51 | 240.51 | 0.432 | 132.7 | 120.63 |

FEA | 1.01 | 377.95 | 229.91 | 0.383 | 117.6 | 116.49 |

Error | 8.91% | 4.65% | 4.61% | 12.79% | 12.78% | 3.55% |

Freq. (Hz) | 20 | 40 | 60 | 80 | 100 | 120 |

Error (μm) | ±0.040 | ±0.067 | ±0.100 | ±0.128 | ±0.144 | ±0.200 |

Percentage | ±0.02% | ±0.034% | ±0.05% | ±0.64% | ±0.72% | ±1.00% |

© 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**

Hussain, I.; Xia, W.; Zhao, D.; Huang, P.; Zhu, Z. Multi-Physical Design and Resonant Controller Based Trajectory Tracking of the Electromagnetically Driven Fast Tool Servo. *Actuators* **2020**, *9*, 28.
https://doi.org/10.3390/act9020028

**AMA Style**

Hussain I, Xia W, Zhao D, Huang P, Zhu Z. Multi-Physical Design and Resonant Controller Based Trajectory Tracking of the Electromagnetically Driven Fast Tool Servo. *Actuators*. 2020; 9(2):28.
https://doi.org/10.3390/act9020028

**Chicago/Turabian Style**

Hussain, Imran, Wei Xia, Dongpo Zhao, Peng Huang, and Zhiwei Zhu. 2020. "Multi-Physical Design and Resonant Controller Based Trajectory Tracking of the Electromagnetically Driven Fast Tool Servo" *Actuators* 9, no. 2: 28.
https://doi.org/10.3390/act9020028