Ultrasonic motor servo-drive with online trained n eu r a I - n et wo r k m o d el -f o I I ow i n g con t r o I I er

F.-J.Lin W.-J.Hwang R.-J. Wai

Indexing terms: Ultrasonic motor drive, Neural-network control

Abstract: An ultrasonic motor (USM) servo-drive with an online trained neural-network model- following controller is proposed. First, the driving circuit for the USM, which is a two-phase chopper-inverter combination, is introduced. Since the dynamic characteristics of the USM are difficult to obtain and the motor parameters are time varying, an online trained neural-network model-following controller is proposed to control the rotor position of the USM. An accurate tracking response can be obtained by random initialisation of the weights and biases of the network owing to the powerful online learning capability. Moreover, the influences of parameter variations and external disturbances of the USM servo-drive can be effectively reduced by the neural-network controller.

1 Introduction

The newly developed travelling-wave type ultrasonic motor (USM) has many excellent performance features such as high-retention torque, high torque at low speed, silence, compactness in size, no electromagnetic interferences, etc. [l]. Owing to the advantages mentioned above, the USM has been used in many practical applications, such as an autofocusing mechanism, an X-Y table and a workpiece stopper [I]. The driving principles of the USM are based on high- frequency mechanical vibrations and frictional force; therefore its mathematical model is difficult to derive and a lumped motor model of the USM is presently unavailable. Moreover, the control characteristic of the USM is complicated and highly nonlinear; and the control characteristic and motor parameters are time- varying, owing to increases in temperature and changes in motor-drive operating conditions, such as drive frequency, source voltage and load [2-61. Since the two phases of the USM construction are coupled mechanically, and the reaction from the electrical to the mechanical part is unbalanced for two phases, the eauivalent two-Dhase loads of the rotor are

0 IEE, 1997 IEE Proceedings online no. 19981727 Paper first received 25th June and in revised form 13th October 1997 The authors are with the Department of Electrical Engineering, Chung Yuan Christian University, Chung Li 32023, Taiwan, Republic of China

unbalanced, and the equivalent resistor values are varied for different rotating directions, rotor speeds, load torque, applied voltages and static pressure force between the stator and the rotor [6]. In accordance with the above limitations, a driving circuit to effectively drive the USM has been proposed by Lin and Kuo [6]. The proposed USM driving circuit is a two-phase chopper-inverter combination, and each phase contains a high-frequency boost-chopper DC-DC converter and a half-bridge series-resonant inverter with capacitor-parallel load.

In recent years, much research has been carried out to apply the neural-network to the control field in order to deal with nonllinearities and uncertainties of the control system [7, 81. According to the structure of the control system, the neural-network applications for control can be classified as supervised control, inverse control, neural adaptive control, etc. [SI. Moreover, according to the learning methods, the neural-networks can be mainly classified as general learning (off-line) and special learning (online) [S, 91. In general learning the connective weights of a back-propagation neural controller are trained off-line; therefore a tremendous amount of training dat,a must be used to include all possible operating conditions, and the training time undertaken is long. On the other hand, since the weights cannot be changed online during real-time con- trol, the neural-network based on off-line learning does not have the property of true adaptive control and is, therefore, difficult to apply to a wide range of real-time control problems [lo]. The special learning method can overcome the problem in general learning. The connec- tive weights of the neural-network are trained during online control, but some prior knowledge such as the sensitivity derivatives or the Jacobian of the system must be available in order to apply the traditional backpropagation algorithm [8]. Since the dynamic characteristics of the UlSM are difficult to obtain and the motor parameters are time varying, an online trained neural-network model-following controller is proposed to control the rotor position of the USM. In the neural-network controller, the error between the states of the plant and the reference model is used to train the connective weights and biases of the neural- network controller online. Therefore, when parameter variations and external disturbances of the USM servo- drive occur, using the model-following error-driven approach, a robust icontrol performance can be obtained. Moreover, prior off-line learning of the neu- ral-network is not necessary, and the Jacobian of the

105 IEE Puoc.-Electr. Power Appl., Vol. 145, No. 2, Murch 1998

system is replaced by a sign function to increase the learning speed of the connective weights.

, _ _ _ _ _ _ _ _ _ _ _ _ c

2 Driving circuit for the USM

, isolating and

The driving principle of the USM is based on high-fre- quency mechanical vibration, and the vibration force is generated by the piezoelectric ceramic located in the stator [l]. Moreover, the motor parameters of the USM are all dependent on the operating temperature and the time of usage [2-61. In addition, since the two phases of the USM construction are coupled mechanically, and the reaction from the electrical to the mechanical part is unbalanced for two phases, the equivalent two-phase loads of the rotor are also unbalanced, and the equiva- lent resistor values are varied for different rotating directions, rotor speeds, load torque, applied voltages and static pressure force between the stator and the rotor.

To drive the USM effectively, a two-phase chopper- inverter driving circuit was proposed by Lin and Kuo [6], as shown in Fig. 1. The proposed driving circuit can provide a balanced two-phase sinusoidal output voltage under variable frequency control. The two chopper-inverter driving circuits are identical, and each is composed of one boost chopper cascading with one half-bridge series resonant capacitor-parallel load inverter. The boost choppers are adopted here to provide variable DC voltages, VdA and VdB, for the half-bridge series-loaded resonant inverters, in order to maintain the two-phase sinusoidal output voltages V, and VB at a constant peak value, v*, under the variable output frequency control. The rotor position is measured using an optical encoder with 1000 pulses per revolution, and the position message is sent to the

phase A trigger

cw ccw

boost chopper

driving circuit phase B trigger L J

control computer. The control input to the drive circuit, up, is calculated by the control algorithm in the control computer. According to the control input, the inverter frequency is regulated by means of a voltage controlled oscillator (VCO). The split-phase circuit is designed for the two-phase inverter to provide two- phase output voltages, VA and V,, with a phase difference of 90 degrees, and the rotating direction (CW or CCW) can be controlled by letting V, lead or VB lead. The LA and L, inductances are inserted in series with the load for each inverter, respectively, in order to become resonant with the inherent parasitic capacitances, C,, and Cd2, of the USM. The resonant frequency of the L-C tank, fo, is 35kHz, and the mechanical resonant frequency of the USM (USR-60), f,, is from 39kHz to 40kHz in the ultrasonic frequency range. The switching frequency, f , , of the inverter, which is designed to vary between 41 kHz and 43 kHz, should be designed higher than the resonant frequency of the mechanical vibration [2]; and the resonant frequency of the L-C tank is designed to be lower than the resonant frequency of the mechanical vibration. Since the revolution speed of the rotor is closely related to the switching frequency of the inverter [2], i.e. the driving frequency of the USM, the switching frequency should be controlled only according to the control input resulting from the closed-loop control algorithm. The function of the choppers, which are implemented with MOSFETs, are to regulate output voltages of the inverters with PWM direct-duty cycle control. The resonant inverters, using the parasitic capacitance of the USM to provide sinusoidal voltage sources, are also implemented with MOSFETs. The driving frequency of the inverters are the major control variable; and balanced two-phase sinusoidal output

UP *

boost chopper

split-phase isolating and circuit -----* driving circuit vco 4

\ J \ J \ /

rotor f position

control er - - algorithm

voltages with both voltage-amplitude regulation and variable frequency control can result in the desired control performance of the USM servo-drive. The specifications of the tested USM are shown in Table 1. Moreover, the length of the rotating shaft and diameter of the rotor of the USM are 20" and 7.5mm, respectively.

Table 1: Specifications of the USM

Driving frequency 40 kHz Driving voltage 12OVrms

Rated torque 0.32 Nm

Rated output power 3w Rated speed 90rpm

Holding torque 0.32 Nm

Weight 240 g

Temperature -10 - +50°C

3 Neural network controller

The online trained neural-network model-following controller for the USM servo-drive is shown in Fig. 2, where x, is the state of the reference model and xp is the rotor position of the USM. In the neural-network controller, the error between the state of the plant and the reference model is used to train the connective weights and biases of the neural-network controller online to permit a favourable model-following control performance. A 2nd-order transfer function with a rise time of 1.5s [12] is chosen as the reference model. The chosen reference model has the properties of no steady- state error, no overshoot and the ability to prescribe the rising time.

reference model

x m k disturbance

y- €Ir t

Fig. 2 drive

Configuration of the neural-network controller for USA4 servo-

3. I Description of the neural-network A three-layer neural-network is adopted to implement the proposed online trained neural-network controller. The signal propagation and the activation function in each layer is introduced in the following:

Input layer: net, = z, 0, = f,(net,) = netz (1)

where x, represents the ith input to the node of the input layer.

Hidden layer:

net, = x ( W 3 z O z ) + 8, 2

(2)

where Wji are the connective weights between the input and the hidden layers, 19 are the threshold values for the units in the hidden layer, and f is the activation function, which is a sigmoidal function.

Output layer:

3

where Wkj are the connective weights between the hid- den and the output layers, 0, are the threshold values for the units in the output layer and f is the activation function, which is a sigmoidal function.

3.2 Online learning algorithm To describe the online learning algorithm of the online trained neural-network controller, first the energy func- tion E is defined as

where e, is the state error, and N indicates the number of training iterations. Within each interval from N to N + 1, the backpropagation algorithm [7-101 is used to update the weights of the output and hidden layers in the neural-network con1 roller according to the follow- ing equation:

where q is the learning rate, a is the momentum factor and A Wji,N-l (A Wkj,N-l) is the difference between Wj,,,

The exact calculation of the Jacobian of the system, axplaup in the derivation of aEla Wii and aEla Wkj, can- not be determined because of the unknown of the plant dynamic of the USM drive system. To increase the learning speed of the connective weights, according to [lo], the derivative axp/&, can be approximated by its sign function. The bias of each neuron in hidden and output layers is also trained online using the same learning algorithm.

( W ~ , N > and W,,N-I (W,,j,,v-J.

USM drive system c - - - - _ - _ _ _ _ _ - - _ _ _ _

rotor position

Fig. 3 Computer-controlled IJSM drive system

4 experimental results

Fig. 3 is the block diagram of the Pentium-based computer control system for the USM drive. A servo-

PC-based ultrasonic molar drive and some

107 IEE Proc.-Electr. Power Appl., Vol. 145, No. 2, March 199N

control card is installed in the control computer, which includes multi-channels of AID, DIA, P I 0 and two encoder interface circuits. Digital filters and frequency, multiplied by 4 circuits, are built into the encoder interface circuits to increase the precision of the position feedback. The resulting precision is 4000 pulse to 27c radian. The software flowcharts of the neural- network control system are shown in Fig. 4. In the main program, parameters and inputioutput (IiO) initialisation are proceeded first. Next, the interrupt interval for the interrupt service routine (ISR1) is set. After enabling the interrupt, the main program is used to monitor control data. The interrupt service routine ISRl with a 2 ms sampling rate is used for the encoder interface and the execution of the neural-network position controller. Moreover, the online learning algorithm is implemented to update the weights and biases of the network. The USM is loaded with a single-axis moving table with a 5mm screw pitch and 550 mm travel.

parameters initialisation

I 1

1

1

1

[io initialisation

interrupt interval setting

enable interrupt

monitor data

disable interrupt

1

encoder interface

1 er

i

4

calculate e and e

neural-network position controller

output up by DAG

I update weights and biases of

neural network

2 m s

Fig. 4 Flowcharts for the neural-network control algorithm

PI position controller disturbance 1 _ _ _ _ _ _ - - - - - - ~ _ _ _ _ _

I .- _ _ _ - - - - _ ~ _ _ _ _ _ _ _ I

Fig. 5 Configuration of the Plposition controller Jar USM servo-drive

The experimental results of the neural-network con- troller are demonstrated here. For comparison, a PI position controller is implemented to control the rotor position of the USM as shown in Fig. 5 . The gains of the PI controller must be obtained by trial and error to make the step-command tracking response of the rotor position of the USM close to the desired tracking per- formance. The gains of the PI controller are set at

K1 = 1, K p = 1, K I = 100 (7 ) 108

The measured responses of the output of the reference model and rotor position with the PI controller due to a periodic step-command change of 2n are shown in Fig. 6, and one cycle of the step responses is enlarged for detailed observation. From the experimental result, the desired step-command tracking response, which has been defined by the reference model, is difficult to satisfy using the PI controller.

Fig.6 PI controller

Measured responses o j reference model and rotor position using

(i) Refei-ence model; (ii) rotor position Top: CHI = 2V; CH2 = 2V; time scale 5 sidiv Bottom: CHI = 2V; CH2 = 2V; time scale 1 sidiv

I I I I I I ,

L t I I I I J

Fi - 7 h . 3 i den laver nodes with a = n = 0.01

Measured responses of rejerence model and rotor position for 10

(i) Refereke model; (ii) rotor position Top: CHI = 2V; CH2 = 2V; time scale 5 sidiv Bottom. CH1 = 2V; CH2 = 2V; time scale 1 sidiv

The neural-network model-following controller is now implemented, and the biases and connective weights of the neural-network are initialised with random numbers. Since the selection of the values for the hidden layer nodes and learning rate parameters, and a, has a significant effect on the network performance, the influences of different hidden layer nodes and learning rate parameters are tested. First, with the learning rate parameters, q and a, both set at 0.01, the measured responses of the output of the reference model and rotor position due to a periodic step-command change of 2n for 10, 20 and 30 hidden layer nodes are shown in Figs. 7-9; one cycle of the step responses is enlarged for the observation of the online learning effect of the neural-network. From the experimental results, compared with the use of 10 and 20 hidden layer nodes, the use of thirty hidden layer nodes gives the best control performance. Moreover,

IEE Proc.-Elertr. Power Appl., Vol. 145, No. 2, March 1998

an accurate tracking response is obtained immediately, and the accuracy in the steady-state condition is within +_ one pulse for a precision of 4000 pulse/211-. For the cases of 40 and 50 hidden layer nodes, the improvement of the control performance is limited, and the computation burden for the CPU is significantly increased.

1 I I I I f I I I 1 . 1 Fi .% h .2 1 den layer nodes with a = 11 = 0.01 (i) Reference model; (ii) rotor position Top: CHI = 2V; CH2 = 2V; time scale 5 sidiv Bottom: CH1 = 2V; CH2 = 2V; time scale I sidiv

Measured responses of reference model and rotor position for 20

Fi .9 hi3en layer nodes with a = 17 = 0.01 (i) Reference model; (ii) rotor position Top: CH1 = 2%’; CH2 = 2V; time scale 5 sidiv Bottom: CHI = 2V; CH2 = 2V; time scale 1 sidiv

Measured responses of reference model and rotor position for 30

The influences of different learning rate parameters are then tested with 30 hidden layer nodes; usually, learning rate parameters must be small numbers to ensure that the network will settle to a solution. The measured responses of the output of the reference model and rotor position due to a periodic step-com- mand change of 211- for 77 and a both set at 0.02 and 0.03 are shown in Figs. 10 and 11, respectively. Since divergence responses result for the value of 0.03, the learning rate parameters, 77 and a, both set at 0.02 with 30 hidden layer nodes are adopted for the proposed neural-network controller.

Finally, the single-axis moving table is loaded with a 120kg weight, which is approximately 80% of the rated holding-torque (0.32”) of the USM (USR-60). The measured responses of the output of the reference model and rotor position controller due to a periodic step-command change of 211- are shown in Fig. 12. The effectiveness of the proposed neural-network controller

IEE Proc -Electr Power Appl , Vol 145, N o 2, M u c h 1998

also can be observed from the experimental result. Moreover, the experimental result with a load of 120kg weight is almost identical to the experimental results without load, as shown in Fig. 10 due to the inherent high-torque driving capability of the USM. All the plots shown in Figs. 5-12 start at time = Os.

Fi .IO hic8en layer nodes with a = 17 = 0.02 (i) Reference model; (ii) rotor position Top: CHI = 2V; CH2 = 2V; time scale 5 sidiv Bottom: CHI = 2V; CH2 = 2V; time scale I sidiv

Measured responses of reference model and rotor position for 30

Fi . I 1 hic8en layer nodes with cc = 17 = 0.03 (i) Reference model; (ii) rotor position Top: CHI = 2V; CH2 = 2V; time scale 5 sidiv Bottom: CHI = 2V; CH2 = 2V; time scale 1 sidiv

Measured responses ofrejerence model and rotor position for 30

Fig. 12 loaded with 1 2 0 k ~ weight

Measured responses of reference model and rotor position

(i) Reference mod& (ii)”rotor position Top: CHI = 2V; CH2 = 2V; time scale 5 sidiv Bottom: CHI = 2V; CH2 = 2V; time scale 1 s/div

109

From the experimental results discussed above, an accurate tracking response can be obtained by random initialisation of the neural-network weights due to the powerful online learning capability. Moreover, the designed USM drive proposed in [6], with both the amplitude regulation and the variable frequency con- trol to provide balanced two-phase output voltages to the USM, can be operated in the low-speedlhigh-torque region with a satisfactory rotor response.

5 Conclusions

Since the plant dynamic of the USM is complicated and contains high nonlinearity, the derivation of a lumped dynamic model is very difficult. Moreover, the motor parameters are dependent on operating tempera- ture, load torque, rotor speed, rotating direction, applied voltage and static pressure force between the stator and the rotor. To drive the USM effectively, a USM driving circuit, which can provide a balanced two-phase voltage source for the USM, was described. Moreover, to enhance the transient response and to increase the robustness of the USM drive system, a neural-network model-following controller was pro- posed in the rotor position control loop of the USM drive. In the neural-network controller, the connective weights and biases are trained online using the error between the state of the reference model and the state of the plant. It follows that the rotor position tracking response can be controlled to closely follow the output of the reference model under a wide range of operating conditions. The effectiveness of the neural-network controller has been demonstrated by some experimental results.

6 Acknowledgment

The authors would like to acltnowledge the financial support of the National Science Council of Taiwan, R.O.C. through grant number NSC 86-2213-E033-044.

7 References

1 SASHIDA, T., and KENJO, T.: ‘An introduction to ultrasonic motors’ (Clarendon Press, Oxford, 1993)

2 FURUYA, S., MARUHASHI, T., IZUNO, Y., and NAKA- OKA, M.: ‘Load-adaptive frequency tracking control implemen- tation of two-phase resonant inverter for ultrasonic motor’, IEEE P o ~ w Electron. Spec. Conj Rec., 1990, pp. 17-24 SENJYU, T., and UEZATO, K.: ‘Adjustable speed control of ultrasonic motor by adaptive control’, IEEE Power Electron. Spec. Conf Rec., 1994, pp. 1269-1274 IZUNO, Y., and NAKAOKA, M.: ‘High performance and high precision ultrasonic motor-actuated positioning servo drive sys- tem using improved fuzzy reasoning controller’, IEEE Powev Electron. Saec. Conf Rec.. 1994. DD. 1231-1242

3

4

5

6

LIN, F.J.: “Fuzzy adaptiie modh:foIlowing position control for ultrasonic motor’, IEEE Trans., 1997, Pc12, (2), pp. 261-268 LIN, F.J., and KUO, L.C.: ‘Driving circuit for ultrasonic motor servo drive with variable-structure adaptive model-following con- trol’, IEE Proc. Electr. Power Appl., 1997, 144, (3), pp. 199-206

7 NARENDA, K.S., and PARTHASARATHY. K.: ‘Identifica- tion and control of dynamical systems using neural-networks’, IEEE Trans. Neural Netw., 1990, 1, (l), pp. 4-21 FUKUDA, T., and SHIBATA, T.: ‘Theory and applications of neural networks for industrial control systems’, IEEE Trans.,

PSALTIS, D., SIDERIS, A., and YAMAMURA, A A . : ‘A mul- tilayered neural network controller’, IEEE Control Syst. Mug., 1988, 8, (2), pp. 17-21

10 ZHANG, Y., SEN, P., and HEARN, G.E.: ‘An on-line trained adaptive neural controller’, IEEE Control Syst. Mug., 1995, 15,

11 MAHAN, N., UNDELAND, T.M., and ROBBINS, W.P.: ‘Power electronics: converters, applications, and design’ (John Wiley, New York, 1989)

12 LIAW, C.M., and LIN, F.J.: ‘A robust speed controller for induction motor drives’, ZEEE Trans., 1994, EG-241, (3) , pp. 308- 315

8

1992, G B , (6 ) , pp. 472-491 9

( 5 ) , pp. 67-75

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