Energy Conversion and Management 45 (2004) 3139–3153 www.elsevier.com/locate/enconman
Fuzzy logic based DSP controlled servo position control for ultrasonic motor G€ ung€ or Bal a
_ , Erdal Bekiro glu b, S C ß evki Demirbasß a, Ilhami ß olak
a,*
a
Faculty of Technical Education, Electrical Department, Gazi University, 06500 Besevler, Ankara, Turkey b Faculty of Engineering and Architecture, Department of Electrical and Electronics Engineering, _ Abant Izzet Baysal University, Bolu, Turkey Received 2 December 2003; received in revised form 2 December 2003; accepted 3 February 2004 Available online 11 March 2004
Abstract In this paper, position control of an ultrasonic motor was implemented on the basis of fuzzy reasoning. A digitally controllable two phase serial resonant inverter was developed to drive the ultrasonic motor by using a TMS320F243 digital signal processor. The driving frequency was used as a control input in the position control loop. The position characteristics obtained from the proposed drive and control system were demonstrated and evaluated by experiments. The experimental results verify that the developed position control scheme is highly effective, reliable and applicable for the ultrasonic motor. 2004 Elsevier Ltd. All rights reserved. Keywords: Ultrasonic motor; Position control; Fuzzy logic; Digital signal processor
1. Introduction The ultrasonic motor (USM) is a new type of motor that has different construction, characteristics and operating principles than the commonly used conventional electromagnetic motors. In recent years, a variety of novel types of USMs featuring high holding torque, high torque at low speed, no electromagnetic noise, silent operation, compactness and flexible design possibilities in their configuration have attracted special interest as servo actuators in direct drive motion control applications [1,2]. The USM is particularly superior in high holding torque and high response characteristics. As a result, it was expected to be used as a precise and accurate positioning actuator [3]. *
Corresponding author. Tel.: +90-312-212-3962; fax: +90-312-212-7575. E-mail address:
[email protected] (G. Bal).
0196-8904/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2004.02.001
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The driving principle of the USM is based on high frequency mechanical vibrations and frictional forces. Owing to this drive mechanism, it is difficult to derive a mathematical model of an USM. Moreover, the control characteristics of USMs are complicated and highly nonlinear. The exact values of the motor parameters cannot be obtained easily, and the motor parameters are time-varying due to increases in temperature and changes in motor drive operating conditions, such as driving frequency, source voltage and load torque [4,5]. Fuzzy logic control is especially preferred when the mathematical model of a control plant is difficult to obtain. The fuzzy logic controller (FLC) is designed for control purposes on the operating experience of the plant without using a mathematical model [6–8]. The fuzzy logic control technique has been applied successfully to control ultrasonic motor drives in recent years [3,9,10]. However, the position tracking characteristics under various load conditions have not yet been examined sufficiently from a practical point of view, especially for small and rapid position references. The purpose of this study is to achieve highly effective position control for a ShinseiÕs traveling wave type USR60 USM. A drive system based on the high frequency two phase serial resonant inverter was developed. Because of the complexity of the mathematical model and control of the USM, a fuzzy logic approach was used in this study. A FLC was designed and integrated into the position control loop. This drive system was controlled digitally by 16 bit fixed point TMS320F243 digital signal processor (DSP). The speed, ramp and periodical step position response characteristics of the traveling wave ultrasonic motor (TWUSM) were obtained for different references and loads. The proposed fuzzy logic based DSP controlled position control technique was tested and verified by experiments. The experimental results show that the developed drive and control system is a very suitable method for position control of the TWUSM.
2. USM and energy conversion An ultrasonic motor is a special type of motor that is driven by the mechanical vibration force of a piezoelectric ceramic in the stator. Although several USM types have been designed, the rotary TWUSM is a commonly used USM type. The operating principle and theoretical background of a TWUSM are given in this section. The energy conversion of a piezoelectric system is based on the piezoelectric element and a mechanical vibration system. When the piezoelectric elements are excited by an electrical supply with ultrasonic frequency, an ultrasonic vibration is produced in the mechanical vibration system, composed of the rotor and stator. The stator amplifies the mechanical vibrations and transmits them as a driving force to the rotor [11]. The speed of the USM is controlled by the, • frequency of the two phase voltages, • amplitude of the two phase voltages and • phase angle between the two phase voltages. An elliptic motion of points on the surface of the stator is generated by the traveling wave in the stator. The vibrations are excited by a piezoelectric ceramic layer bonded to the lower surface of
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the stator. The rotor is pressed against the stator by means of a disc spring and is driven by the frictional forces in the contact layer. The rotation direction of the rotor is opposite to the direction of the traveling wave [12]. To generate a traveling wave within the stator, it is necessary to have control of two mechanical orthogonal modes. Electrode pattern A provides the cos kh and the pattern B provides the sin kh By driving these two modes at 90 out of phase, a traveling wave is produced. Each pattern provides a standing wave individually. The superposition of these standing waves produce the traveling wave used in TWUSMs [13]: - ¼ cos xt cos kh þ sin xt sin kh;
ð1Þ
- ¼ cosðxt khÞ;
ð2Þ
k¼
2p ; k
ð3Þ
where k is the wavenumber of the piezoelectric ceramic. k is the wavelength of the (+) and ()) polarized one section. By changing the sign of one of the drive signals, the direction of the traveling wave and, thus, the direction of the rotor reverses. The speed of the USM can be controlled by the amplitude, frequency and phase difference of the two phase voltages. Since changing the driving frequency method gives a more flexible control range than the other methods [14], in the present study, the speed of the USM is controlled by the driving frequency. Fig. 1 shows the speed–frequency characteristic of the USM, which has a nonlinear behavior. In this study, the motor speed is controlled within the 41.3–43.3 kHz frequency range, which can be accepted as a linear frequency range. The speed–torque relation is also an important characteristic. In Fig. 2, the speed–frequency characteristics of the USM are 140 120
Speed (rpm)
100 80 60 40 20 0 40.5
41
41.3 41.5
42.5 42 Frequency( kHz)
43
Fig. 1. Speed–frequency characteristic of USM.
43.5
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G. Bal et al. / Energy Conversion and Management 45 (2004) 3139–3153 140 T=0.0Nm T=0.1Nm T=0.2Nm T=0.3Nm
120
speed(rpm)
100 80 60 40 20 0
41
41.5
42
42.5
43
43.5
frequency(kHz) Fig. 2. Speed–frequency characteristics of USM under the different load torques.
given under different load torques. When the load torque increases, the speed of the motor decreases.
3. DSP controlled USM drive system To drive the USM, high quality semiconductor devices that can follow the optimum operating point of the motor are required. It is difficult to drive the piezoelectric ceramic owing to its high damping capacitance. For easy drive of the piezoelectric ceramic of the USM, a resonant frequency approach is used. Fig. 3 shows a newly developed drive system of a two phase, high frequency, voltage fed, serial resonant inverter for the USM. This inverter has features of both pulse width modulation (PWM) and pulse frequency modulation (PFM) control techniques. The LA and LB inductances have been connected in series with each phase to obtain resonance with the damping capacitance (Cd ) of the USM. The inverter outputs are two phase high frequency AC voltages with 90 phase difference. The rotating direction has been controlled by letting VA or VB lead. The CW and CCW inputs provide direction control signals [15]. In practice, the driving frequency is set higher than the resonant frequency of the mechanical vibration system because of the basic operating characteristics of the USM [16,17]. Speed control of the USM was achieved by a variable driving frequency. The value of the driving frequency was determined by comparing the AC voltage (Vs) of the feedback electrode of the USM and a reference DC voltage (Vdc). The frequency signal was then applied to the optoisolator, split phase and voltage control oscillator (VCO) circuits. The control input of the drive system was the switching frequency, fs . This input was obtained from a comparison of the feedback electrode voltage (Vs) and the reference DC voltage. According to the demanded speed, the value of switching frequency was adjusted. This was
G. Bal et al. / Energy Conversion and Management 45 (2004) 3139–3153 CW CCW
fs
Vd c comparator
filter
control signal
Vs
C1
S1
FLC reference position
phase split,VCO, opto-coupler circuit phase-A inverter
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phase-B inverter
S2
LA GND
AC
rotor position
LB C2
S3
S4
USM
encoder
Fig. 3. Drive system of USM.
achieved by changing the level of the reference DC voltage. To change the level of the DC voltage, the duty cycle of the PWM signal was changed. So, according to the duty ratio of the PWM signal, the DC output of the low pass (LP) filter was controlled. Detailed explanations about the design of the low pass filter and the produced PWM signals were given in Ref. [18]. The duty cycle of the PWM was controlled with respect to the output of the FLC. The USM drive system was controlled by the 16 bit fixed point TMS320F243 EVM digital signal processor (DSP). The block diagram of the TMS320F243 controlled USM drive system is given in Fig. 4. The event manager and general purpose input/output (GPIO) units of the DSP were used for control of the USM. The PWM signal was generated by the general purpose timer-1 (GPT1). The GPT1 was set in the continuous up count mode to provide an asymmetric PWM signal. Two pins of the GPIO were set as digital output to provide the CW and CCW direction signals. The quadrature encoder pulse (QEP) circuit of the event manager was used for encoder signals. The encoder is 500-ppr and has two quadrature encoder signals and one index signal. These encoder signals were encoded digitally by the QEP circuit and converted to the speed and position information for control purposes.
4. Fuzzy logic controller (FLC) Basically, the FLC is based on the error signal of the control plant and change in this error. The aim of this controller is to obtain robust control characteristics in tracking the reference command under the parameter variations and variable operating conditions. The block diagram of the constructed FLC is given in Fig. 5. The inputs of the FLC are position error (Dh) and speed (x), and the output is the manipulated value of the driving frequency
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G. Bal et al. / Energy Conversion and Management 45 (2004) 3139–3153 USM drive system USM VA + Vd
VB
two-phase half-bridge serial-resonant inverter
GND
encoder S1 S2 S3
TMS320F243 EVM
S4
CW
Flash EEPROM
GPIO
Program memory
Event manager
Data memory
QEP circuit
VCO, phase split, opto-coupler circuit
CCW
fs LP Vd c comparator filter
PWM
Vs
QEP-A QEP-B Index
Fig. 4. TMS320F243 controlled USM drive system. θ ref
∆θ
FLC
θ d/dt
∆f
f
USM
ω f(t-1)
Fig. 5. The block diagram of FLC.
(Df ). The manipulated value of the driving frequency (Df ) is added to the previous driving frequency (f ðt 1Þ) to obtain the new control input (current driving frequency (f )) and applied to the USM. Where href is the reference position; h is the actual position; Dh is the position error; x is the speed; f ðt 1Þ is the driving frequency; f is the current driving frequency; Df is the manipulated value of the driving frequency. The relation between the driving frequency and rotary speed (x) of the USM cannot be expressed as a simple equation. The speed decreases as the frequency increases in a stable frequency range [10]. Also the f –x characteristics depend on the load variations (Fig. 2). The manipulated value of the driving frequency (Df ) is obtained using the FLC based on the position error (Dh) and the speed (x). The position error and speed of the motor are determined as follows: ð4Þ Dh ¼ href h; x¼
dh : dt
ð5Þ
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In position control of the USM, to allow design flexibility and tuning of the controller, the input and output variables are represented in terms of per unit (pu) values. KDh, Kx and KDf are related gain factors of the fuzzy logic controller. In this study, the values of these gain factors were set to 0.5, 5 and 1000, respectively, and defined as follows: DhðpuÞ ¼ Dh=KDh;
ð6Þ
xðpuÞ ¼ x=Kx;
ð7Þ
Df ðpuÞ ¼ Df =KDf :
ð8Þ
Fig. 6 shows the membership functions of the FLC. Fig. 6(a) shows the membership functions of position error; Fig. 6(b) shows the membership functions of speed; and Fig. 6(c) shows the membership functions of the manipulated value of driving frequency. While the inputs of the FLC NB
NM
NS
-1
-0.6
-0.2
Z
PS
PM
PB
0
0.2
0.6
1
∆θ (rad)
(a) NB
NM
NS
Z
PS
PM
PB
-1
-0.6
-0.2
0
0.2
0.6
1
ω (rad/s)
(b) NB
NM
NS
Z
PS
PM
PB
-1
-0.5
-0.1
0
0.1
0.5
1
∆ f(Hz)
(c) Fig. 6. Membership functions of FLC: (a) position error (Dh), (b) speed (x) and (c) manipulated value of driving frequency (Df ).
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Table 1 Control rules of FLC x NB NM NS Z PS PM PB
Dh NB
NM
NS
Z
PS
PM
PB
Z NS NM NB NM NS Z
PS Z NS NM NS Z PS
PM PS Z NS Z PS PM
PB PM PS PB PS PM PB
PM PS Z NS Z PS PM
PS Z NS NM NS Z PS
Z NS NM NB NM NS Z
PB is positive big, PM is positive medium, PS is positive small, Z is zero, NB is negative big, NM is negative medium and NS is negative small.
are determined as triangular membership functions, for easy and rapid calculation, the output is selected as singleton membership functions. The control rules of the FLC are obtained according to the expert experience and control engineering as follows. If the position error is very big and the rotary speed is very slow, the USM has to be accelerated. To accelerate the USM, the driving frequency should be decreased as shown in Fig. 1. In this case, the manipulated value of the driving frequency should be a negative value to decrease the driving frequency. Conversely, if the position error is very small and the speed is very fast, the speed of the USM should be reduced. To reduce the speed, the driving frequency must be increased. So, the manipulated value of the driving frequency should be a positive value to increase the driving frequency. In this approach, the fuzzy control rules of all cases are given in Table 1. The implementation of the FLC for position control of the USM is summarized as follows: 1. 2. 3. 4. 5. 6.
The position of the USM is sampled. The position error and the speed are calculated. Fuzzy sets and membership functions of the position error and the speed are determined. Change of control action (Df ) is determined with respect to the individual fuzzy rules. The value of Df is calculated by using the center of gravity (COG) defuzzification method. The new control signal is calculated as f ðtÞ ¼ f ðt 1Þ þ KDf Df ðpuÞ and applied to the control plant.
5. Experimental results In this section, the experimental results obtained from the fuzzy logic controlled position control of the USM are presented. The technical specifications of the driver and the USM are given in Appendix A. Firstly, to see how the two phase outputs of the inverter are obtained, an example is given. While the motor speed is 95 rpm, the measured AC voltage of the feedback electrode is shown in
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Fig. 7. Voltage of feedback electrode.
Fig. 7. The value of this voltage is 34.6 V (rms) with 42.05 kHz frequency. To obtain the demanded speed, this voltage was compared with the fixed 2 V DC voltage. By comparing these voltages, a switching signal with t ¼ 2:394 105 s (fs ¼ 41:74 kHz) was produced. This switching signal was applied to four switches via the voltage control oscillator and phase split circuits to provide the two phase AC voltages. Fig. 8 shows the waveforms of these output voltages with the frequency of 41.74 kHz, which is equal to the switching signal frequency. The output voltages are equal and 120 V (rms). By changing the level of the DC voltage, the switching frequency (fs ) is changed, so the speed of the motor is controlled. The required DC voltage for the comparing process is produced by the low pass filter circuit. This circuit converts the PWM signal to the reference DC voltage according to the duty cycle of the PWM. When the duty cycle is changed, the value of the produced DC voltage also changes, so the switching frequency is changed. As a result, the speed of the motor is varied to the demanded value.
Fig. 8. Output voltages of inverter.
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125
speed (rpm)
100 75 50 25 0
0
100
200
300
400
500
time (ms)
Fig. 9. Speed responses of USM at 75, 100 and 130 rpm.
Fig. 9 shows the speed responses of the USM at three different reference speeds, which are 75, 100 and 130 rpm. As is clearly seen from the figure, the USM tracks the reference speeds smoothly without any overshoot or undershoot. In order to examine the behavior of the motor, an experiment was performed for three different ramp position commands, and the results, as illustrated in Fig. 10, show that the USM tracks the command positions for all of the ramp responses robustly. The developed FLC position control for the USM is highly load adaptive as illustrated in Fig. 11. Fig. 11(a) shows the reference position command applied as a periodical function with p radians; Fig. 11(b) shows the actual position without load; and Fig. 11(c) shows actual position with 0.2 Nm external load. As seen from Fig. 11, good tracking control performance of the USM 16 reference position actual position
14
position(rad)
12 10 8 6 4 2 0
0
1
2
3
4
time (s)
Fig. 10. 1, 2 and 3 rad/s ramp responses of USM.
5
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Fig. 11. Periodical p radian step response of USM: (a) reference position, (b) actual position without load and (c) actual position with 0.2 Nm load.
drive and control system was obtained for the periodical step position command when the motor was unloaded and loaded.
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Fig. 12. Periodical p/2 radian periodical step response of USM.
In this study, the position responses of the USM are also obtained for faster position commands. While Fig. 12 shows the periodical p/2 step response of the USM, Fig. 13 shows the p/4 periodical step response of the USM. It is clearly seen from these figures that the USM tracks the demanded position in a short time accurately, although the position command is very fast for rotary motors. From Figs. 12 and 13, it can be said that the USM can operate like a stepping motor having 45 or 90 step angle. A 2p radian single step position response of the USM without load is given in Fig. 14(a) and with 0.2 Nm external load torque in Fig. 14(b). These figures demonstrate that the developed FLC position control system gives precise and robust position response for a single step position command.
Fig. 13. Periodical p/4 radian step response of USM.
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Fig. 14. 2p radian single step position response of USM: (a) without load and (b) with 0.2 Nm load.
6. Conclusions In this paper, a highly effective position controller for a TWUSM was implemented. A fuzzy logic controller was designed to provide effective position tracking performance of the USM. This control was achieved and optimized by a TMS320F243 DSP. A high frequency, voltage fed, serial resonant inverter was designed to drive the USM. The speed and position of the USM were controlled by the driving frequency with detecting the resonant state by the generated voltage of the feedback electrode mounted on the USM. This control system compensates the speed and position characteristics variations of the motor. Firstly, a digitally controllable drive system was designed, and then, it was integrated successfully with a DSP. The positioning servo system incorporating the USM was realized by controlling the drive frequency on the basis of the designed FLC. The performance of the proposed driving and control system was examined for step speed and ramp responses and periodical step position responses. The control technique is simple and effective since only the driving frequency of the two phase voltages is controlled. The robustness of the proposed drive and control system was demonstrated
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and evaluated by experimental investigations. The experimental results verify that the developed drive and control system give superior speed and position characteristics for the USM.
Acknowledgements This work was supported by The Scientific and Technical Research Council of Turkey TUBITAK, through grant number 100E-012.
Appendix A Technical specifications of driver and ultrasonic motor: Driver Power source voltage Drive frequency Drive voltage Inverter power
12 V DC 40–44 kHz 100–130 Vrms 12 VA
USM Rated torque Rated power Rated speed Torque per volume Power per volume Torque density Power density
0.4 Nm 4W 10 rad/s 10,000 Nm/m3 66,700 W/m3 3.5 Nm/kg 23 W/kg
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