 Open Access
 Total Downloads : 295
 Authors : Youssef Baba, Mostafa Bouzi, Ismail Lagrat, Mounir Derri
 Paper ID : IJERTV4IS110208
 Volume & Issue : Volume 04, Issue 11 (November 2015)
 Published (First Online): 25112015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Online Controller for a Piezoelectric Motor
Youssef Baba, Mostafa Bouzi, Ismail Lagrat*, Mounir Derri
Univ Hassan 1st, Laboratory of Mechanical Engineering, Industrial Management and Innovation Faculty of Science and Technology, Settat, Morocco
*National School of Applied Sciences, Khouribga, Morocco
Abstract Travelingwave ultrasonic motor has nonlinear characteristics, which varies with driving conditions associated the variations of temperature and applied load torque. In this work, a simple online speed controller is designed to improve the control performance of the motor. First, this paper suggests a MatlabSimulink model of a travelingwave ultrasonic motor, which defines the reference model. Then the controller based on an online tuning method is proposed to identify the plant parameters and detect the parameter variations of the motor immediately, so as to compensate it. Finally, the simulation results are described to confirm the effectiveness of the proposed method. The drive frequency is used as the input for the speed control scheme.
Keywords Ultrasonic Motor, Speed Control, Tuning Algorithm.

INTRODUCTION
The travelingwave ultrasonic motor has excellent
reference is obtained by Matlabsimulink model simulations, and the driving frequency is adopted as the control input.
The paper is organized as follows: in section 2, a mathematical model of the motor is presented and a reference model for USR60 is proposed, so as to control the motor. Section 3, introduces the proposed online controller. Simulation results are presented in section 4. Section 5 offers our concluding remarks.

USR60 MODEL
Travelingwave ultrasonic motors are complex electromechanical devices in which a mechanical resonant vibration is exited in the stator through proper forcing piezoelectric ceramics. This stator vibration is transformed into a rotation through friction contact between the stator and rotor.
The model of piezoelectric and stator can be described by the following equation
performance and many useful features such as high holding torque, high torque at low speed, quiet operation, simple
M D C v Fd
(1)
structure, compact size, and no electromagnetic interferences. However, the dynamical characteristics of the travelingwave ultrasonic motor are complicated and highly nonlinear, and the motor parameters are timevarying due to temperature rise and changes in motor drive operating conditions [1]. Therefore, it is difficult to predict the performance characteristics of this motor under various working conditions.
The classical PIDcontrol has more applications because the simple structure is easier for engineering design. But the fixed PID gains are hard to deal with the travelingwave ultrasonic motor because the nonlinear and timevarying characteristics. Thus the control performance is not good. Therefore control strategies such as using adaptive PID
with represents the modal amplitude of the vibrating
system (ceramics and stator), M is the total mass matrix of system(ceramics and stator), D is the structural damping matrix assumed to be diagonal, and C is the total stiffness matrix. is the electromechanical coupling matrix and v is the voltage excitation vector. The term Fd is a nonlinear modal force vector to consider the interaction between the stator/rotorcontact. In dealing with the dynamics of the rotor, two degrees of freedom must be taken into account: first the rotation of the rotor and second the motion in zdirection. The motion in zdirection is represented by the quantity w .
The dynamics of the vertical rotor motion is obtained by the following equation
control, sliding mode control, fuzzy control and neural
network control algorithms are put forward successively,
mr w dz w Fz Fn
(2)
which have obviously improved ultrasonic motor control
with mr
is the mass of the rotor, dz
is the damping of the
performances [27]. But the complexity of these methods is
vertical motion, and Fn is the applied axial force. The
great. For example, the fuzzy neural control [7] combines the advantages of fuzzy logic and neural network, which can greatly increase control accuracy. However, it requires a large
equation of rotational motion is calculated by
Jr dr Tr Tl
(3)
amount of calculation which increases the cost of hardware
where
Jr is the rotor inertia, dr
denotes the damping in
and software. This kind of control is expensive and confined only to highprecision applications.
In this paper, the speed control of a travelingwave ultrasonic motor (USR60) based on an online algorithm is designed. This control algorithm compensates the speed characteristic variations of the motor with online parameters identification. The proposed control scheme, therefore, has robustness in terms of parameter variations. The model
spinning direction, and Tl is the applied torque.
In Fig. 1 the Matlabsimulink model of USR60 is described. The curves in Fig. 2 are derived from calculations using the Matlabsimulink model.
The speed versus drive frequency for different applied load torques is represented in Fig. 2. The speed of the motor has its maximum at the mechanical resonant frequency (40 kHz). It is
due to the fact that the revolving speed of the motor is proportional to the vibration force of piezoelectric elements. So, any deviation from this frequency degrades the motor performance. However, this effect seems more serious for frequency decrements. To avoid the consequence of these phenomena, the drive frequency variation is restricted to the extent of 40 f 42 kHz.
The effect of temperature is shown in Fig. 3 for a phosphor bronze combtooth stator [1]. From this figure, it is concluded that the frequencytemperature characteristic is almost linear from 20Â°C to 80Â°C, and it can be approximated by the following equation
f fr 50 2.5T (C)
where fr is the resonant frequency (40 kHz).

DESIGN OF ONLINE CONTROLLER
In order to design the control law, let us write (3) as
(t) a w(t 1) bu(t 1)
It is convenient to introduce the vectors
col[a1…ap b1…br ]
(4)
(5)
Fig. 2. Speedfrequency characteristics
and
(t) col[(t 1)… (t p) u(t 1)…u(t r)]
Then (5) can be written
(t) T(t)
(6)
The prediction model of (6) is
(t) T (t)
(7)
with
col[a1…a
b …b ]
is the estimation vector of . The criterion
p 1 r
t t
t
V  (s) (s) 2  (s) T (s) 2
1 1
(8)
Fig. 3. Temperaturedependance of resonant frequency, using a standard
is minimized with respect to to give the estimate .
It is wellknown how the sequence of estimates can be written recursively [8]
motor (type USR60) manufactured by Shinsei Industries Co. Ltd.
(t) (t 1) 0 S(t) (t,(t 1))
R(t)1(t)
0
S(t) 1 ((t)T R(t)1(t) 1)
R(t) R(t 1) 1((t)(t)T R(t 1))
t
(t,(t 1)) (t) (t 1)T (t)
The factor 0
corresponds to exponential forgetting of past
data, with the base 1 0 , and is added to algorithm above because tracking slowly timevarying motor parameters.
Fig.4 shows the block diagram of motor speed control
scheme, where c
actual speed.
denotes the given speed, denotes th
The presented approach is a simple identification method to avoid the unknown motor parameters.
Fig. 1. Matlabsimulink model of USR60

SIMULATION RESULTS
In order to evaluate the performance of our control scheme, the simulation results, of the proposed controller are achieved. The simulation study of the system was implemented using Matlab. The specification of the USR60 is shown in Table I. The simulation was done for 6 seconds.
The control parameters: 0 0.98 , p r 10 . The initial values: (1) 0 , and R(1) 1000I .
Fig. 6 shows the speed tracking response by applying the control law represented in Fig. 5. The motor speed tracks the given speed very much. The parameter variations of USR60 are estimated online, so as to compensate it.
It is clear that the proposed control scheme introduces excellent performance where the controller variables track their reference values exactly in a very short time.
Fig. 6. Speed tracking response
USR60
u

CONCLUSIONS
c In this paper, an online controller has been proposed for speed control of a travelingwave ultrasonic motor USR60.
CONTROLLER
The presented algorithm of control determinates the prediction
PARAMETER CALCULATION
model parameters online and compensates the motor parameter variations. A reference model is deduced from a Matlabsimulink model. Simulation results confirm the
abovementioned claims for the control scheme in traveling wave ultrasonic motors control drive.
PARAMETER ESTIMATOR
REFERENCES
Fig. 4. Speed control block diagram TABLE I SPECIFICATIONS OF USR60
Drive frequency 40kHz
Drive voltage 100Vr.m.s
Rated torque 0.32Nm
Rated speed 130r.p.m
Weight 240g
Fig. 5. Total control law u

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