Modeling and Design of Robust Closed Loop Position Controllers for Linear Walking Piezoelectric Motor

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Classification of piezoelectric motors and operating principles

The piezoelectric motors can be classified according to different criteria including the motion type (linear, rotational), frequency operation range, stator geometric, and operating principle [4, 8, 26-28]. In this report, the PZMs are classified in sub-categories in order to integrate the most used criteria as shown in Fig. I-9. In the first level of Fig. I-9, the PZMs are classified based on the motion type into linear or rotary motors. These two types of PZMs can be classified according to the frequency operation range into quasi-static and ultrasonic motors. Two categories of quasi-static PZMs can be distinguished based on the driving method, which are the stepping and inertia motors.
The operating principle of the inertia motors is based on the stick-slip drive method, while the commercialized stepping PZMs can be devised into inchworm and walking principle motors. The ultrasonic motors (USM) are classified as function of the wave propagation method into traveling and standing waves USM.

Standing waves ultrasonic motors

The Standing Wave Ultrasonic Motor (SWUSM) is also called vibratory-coupler motor consists basically on a vibratory element driven close to its resonance frequency and generating elliptical motion of its tip portion. This motion is transferred to the rotor as a series of microscopic pushes. The SWUSM is generally a low cost motor (one vibration source) and has high efficiency, but its control in bidirectional motion is little complex [28]. In fact, the bidirectional motion of SWUSM can be obtained by employing two separate vibrating elements excited with a phase shift, or by superimposing two oscillations in a single resonator (bimodal motor).
Among the earlier structures of SWUSM, the simple design of unidirectional motor proposed by Sashida (Fig. I-15) [43]. It consists on a piezoelectric vibrator attached to a slider with a cant angle. When the piezoelectric element is excited, the vibrating piece will generate bending. If the bending deformation is sufficiently small compared to the piece length, elliptical motion of the piece tip will be created. This motion will be transmitted to the slider through friction contact.

Traveling waves ultrasonic motors

The Traveling Waves Ultrasonic Motor (TWUSM) was invented by Sashida in 1982 [49] and commercialized one year later by Shinsei Corporation [50] in a serie of USR motors. In this type of motor, the elliptical trajectory of the contact point between the stator and rotor results from a traveling wave. This Traveling Wave (TW) is formed by the superposition of two standing waves with a phase shift of 90° both in time and space. The TWUSM can be easily driven in bidirectional motion by switching the driving voltages phase shift between +/-90°. The original invention of TWUSM was a rotary motor and it has had a great success in the lenses drive of autofocus camera and watches. The structure of rotary TWUSM and its working principle will be explained in details in Chapter III, where an example of TWUSM motor will be studied for modeling and position control purposes.
Linear TWUSM was also proposed by Sashida in 1985 in two configurations; straight beam and ring
beam types [51]. The prototype of straight beam TWUSM is shown in Fig. I-18.a, it consists of two langevin vibrators fixed on both ends of the beam. When the vibrators are exited, one will act as vibrator and the second as absorber to prevent the reflection of the TW [42]. The generated TW will transmit through friction contact in order to move the slider pressed against the beam. TWUSM with ring-type stator was proposed by Hermann et al. [52] as shown in Fig. I-18.b. In this case, the TW is generated by the piezoelectric ceramics bonded inside the ring beam. The slider will perform linear motion when it is pressed against the linear portion of the beam. Many attempts to create linear TWUSM are also reported in [53, 54].

Working principle of rotary TWUSM (USR60)

The studied motor is a commercialized rotary TWUSM (USR60) (Fig. III-1.a) from Shinsei.Co [50]. The exploded figure of the motor is shown in Fig. III-1.a.
The stator is made of an elastic body and its bottom side is bonded to a piezoelectric ceramic ring. The piezoceramic ring has the role of exciting transversal mechanical vibrations at the stator surface. Teeth are machined into the upper side of the stator (Fig. III-1.b) and have the role of increasing the horizontal deflection of the stator at the contact interface with the rotor. The rotor is made of a metallic disc and pressed against the stator by the case. Therefore, the stator is in permanent contact with the rotor [50].
The piezoelectric ring is divided into two semicircular sectors A and B, as shown in Fig. III-2.a. Each
of these semicircular sectors is further divided into small sectors with opposite polarization. Therefore, when the motor is supplied by two sinusoidal voltages at a frequency range close to one of its mechanical resonance frequencies and with 90 degree of phase shift, one sector will contract while the other will expand. Two Standing Waves (SW) with equal amplitude and 90° of phase difference in time and space will be created based on the inverse piezoelectric effect. The traveling wave is formed by the superposition of the two SW. The surface points of the stator will follow an elliptical trajectory as shown in Fig. III-2.b. The micro-vibration of the piezoelectric ring will be transformed to rotary motion of the rotor through frictional forces. The traveling wave generation, the stator-rotor contact mechanism, and the motion of the rotor will be modeled in the USR60 modeling section.

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Literature review

Since the invention of TWUSM, intensive research works have been done to establish an accurate model of such motor. Many control methods of TWUSM have been also developed based on the designed models. In this section, a literature review of the TWUSM models and position controllers will be proposed.

Modeling of rotary TWUSM

This section treats the modeling studies of TWUSM and its applications on the motor behavior analysis and parameters estimation. The TWUSM models can be classified into; Equivalent Circuit Models (ECM), Finite Element Method (FEM), and mathematical models.
A very good introduction to the construction and operating principle of TWUSM was undertaken by Sashida and Kenjo [82]. In this book, the motor is modeled by an equivalent electrical network of capacitors, resistors, inductors, and Zener diodes. This modeling approach is simple, however, the rotorstator interface which is the origin of torque generation is missing. The Equivalent Circuit Model (ECM) have been presented in [83] to estimate the TWUSM speed and load characteristics. Elghouti and Helbo [84] highlight the importance of the electromechanical coupling factor in their proposed ECM, which is responsible for the electrical to mechanical energy conversion. The model is performed based on experimental approach combined with the electrical network method and some simplifying assumptions about the motor real behavior [85]. Similar ECM modeling approaches based on experimental tests have been also reported in [86, 87], to determine the stator parameters and vibrational behavior. When compared to other methods, the ECM has the advantages of simplicity and low computational efforts.
However, the main drawback of this model is its inability to accurately model the contact mechanism between the motor stator and rotor.

Table of contents :

Résumé en français
Introduction
I.1 Objectives and scope of the research
I.2 Initiation to piezoelectric actuators and motors
I.2.1 Direct and converse piezoelectric effects
I.2.2 Principle of piezoelectric actuator and motor
I.2.3 Nonlinearities of piezoelectric actuators
I.2.3.1 Hysteresis
I.2.3.2 Creep
I.2.3.3 Vibrational dynamics
I.3 Classification of piezoelectric motors and operating principles
I.3.1 Quasi-static piezoelectric motors
I.3.1.1 Inertia motors
I.3.1.2 Stepping motors
I.3.2 Ultrasonic piezoelectric motors
I.3.2.1 Standing waves ultrasonic motors
I.3.2.2 Traveling waves ultrasonic motors
I.4 Piezoelectric motor applications
I.5 Thesis contributions
I.6 Thesis outlines
Synthesis of Robust Position Controllers of Piezoelectric Motors
II.1 Introduction
II.2 H-infinity position controller
II.3 RST position controller
II.4 Conclusions
Modeling and Design of Robust Closed Loop Position Controllers for Rotary Traveling Wave Ultrasonic Motor
III.1 Introduction
III.2 Working principle of rotary TWUSM (USR60)
III.3 Literature review
III.3.1 Modeling of rotary TWUSM
III.3.2 Position control of rotary TWUSM
III.4 Proposed Simulink model of USR60
III.4.1 Stator
III.4.2 Contact surface
III.4.2.1 Half-contact length, x0
III.4.2.2 Stick points, xs
III.4.2.3 Torque generation
III.4.3 Rotor (vertical motion)
III.4.4 Rotor (angular motion)
III.5 Simulation of USR60 model
III.6 Experimental test bench
III.6.1 Experimental platform description
III.6.2 Experimental characteristics of USR60
III.6.3 Phase shift-position transfer function identification
III.7 Synthesis of robust position controllers of USR60
III.7.1 H-infinity position controller of USR60
III.7.2 RST position controller of USR60
III.7.3 Simulation of closed loop USR60 positionning system
III.7.3.1 Transfer function model simulations
III.7.3.2 Simulation results based on electromechanical model
III.8 Real-time implementation of TWUSM closed loop positioning system
III.8.1 H-infinity test results
III.8.2 RST test results
III.8.3 . Comparative study of controller performances
III.9 Conclusions
Modeling and Design of Robust Closed Loop Position Controllers for Piezoelectric Actuator Drive (PAD)
IV.1 Introduction
IV.2 PAD working principle and features
IV.2.1 PAD working principle
IV.2.2 PAD features
IV.3 Modeling of Piezoelectric Actuator Drive (PAD7220)
IV.4 Experimental test bench
IV.4.1 Experimental platform description
IV.4.2 Frequency-position relationship identification
IV.5 Synthesis of robust position controllers of PAD
IV.5.1 H-infinity position controller of PAD
IV.5.2 RST position controller of PAD
IV.6 Simulation results
IV.7 Real-time implementation of PAD closed loop positioning system
IV.7.1 H-infinity test results
IV.7.2 RST test results
IV.7.3 Comparative study
IV.8 Conclusions
Modeling and Design of Robust Closed Loop Position Controllers for Linear Walking Piezoelectric Motor
V.1 Introduction
V.2 Literature Review of WPZM position controllers
V.3 Contributions and outlines
V.4 Working Principle of Walking Piezoelectric Motor
V.5 Experimental test bench and motor transfer function identification
V.5.1 Experimental test bench
V.5.2 Motor transfer function identification
V.6 Synthesis of robust position controllers of WPZM
V.6.1 H-infinity position controller of WPZM
V.6.2 RST position controller of WPZM
V.7 Simulation of WPZM closed loop system
V.8 Real-time implementation of WPZM closed loop positioning system
V.8.1 H-infinity test results
V.8.2 RST test results
V.8.3 Comparative study
V.9 Conclusions
Suggestions, recommendations, and general conclusions
VI.1 Summary and contributions of this thesis
VI.1.1 Summary
VI.1.2 Contributions
VI.2 General conclusions
VI.2.1 Traveling wave ultrasonic motor (USR60)
VI.2.2 Rotary quasi-static motor (PAD7220)
VI.2.3 Linear walking piezoelectric motor (N-310.13)
VI.2.4 Recommendations for future works
Appendix A: USR60-E3T
A.1. Datasheet parameters of USR60-E3T
A.2. Simulation parameters of USR60-E3T
A.3. Real time implementation of position control of USR60 (Simulink file)
Append B: PAD7220
B.1. Datasheet parameters of PAD7220
B.2. Simulation parameters of PAD7220
B.3. Real time implementation of position control of PAD7220 (Simulink file)
B.4. Real time graphical interface for PAD7220 (ControlDesk)
Appendix C: N-310.13
C.1. Datasheet parameters of N-310.13
C.2. Real time implementation of position control of N-310.13 (Simulink file)
C.3. Real time graphical interface for N-310.13 (ControlDesk)
C.4. Schematic files for control boar

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