University of Houston • University of Houston-Clear Lake • ISSO Annual Report Y2002—pp. 76-79

Model-Based Control of Piezoelectric Ultrasonic Motors for Space Robotic Applications

James B. Dabney (UHCL) and Thomas L. Harman (UHCL)

Abstract
Piezoelectric ultrasonic motors have significant potential for space-based robot applications. The motors are light in weight and mechanically simple. The motors possess high friction when static and can also function as mechanical brakes. Current control techniques for these motors are limited to non-model-based techniques unsuitable for critical applications. This research produced a motor control circuit employing a commercial driver/amplifier, a custom interface circuit, and dSpace control software. Research characterized achievable kinematic positioning accuracy in the no-load condition and no-load dynamic response characteristics. The positioning accuracy was limited by the inability of the driver to operate at speeds less than 30 RPM. The unloaded motor angular acceleration was found to be in excess of 17000 rad/sec².

SPACE-BASED ROBOTS TYPICALLY REQUIRE ACTUATORS EXHIBITING high precision, light weight, and simplicity. Piezoelectric ultrasonic motors (PUM) are well-suited to these requirements. PUM can achieve high precision as a result of low speed, lack of gears and transmissions, and freedom from backlash. They are quite simple mechanically, consisting of a single moving part that provides the same functionality as motor, transmission, and brake in a conventional motor-driven system.¹

Atypical piezoelectric ultrasonic motor (Piezo Systems/Shinsei USR 30, (Fig. 1)² consists of a toothed piezoelectric disk (stator) in contact with a metal disk (rotor). Time-varying electric fields applied to the piezoelectric stator induce a traveling wave which is mechanically rectified, causing the rotor to rotate (Fig. 2).³ This mechanism produces relatively high torque at low rotor angular velocities, obviating the need for gearing. The friction between rotor and stator provides a passive holding torque typically larger than the rotating torque, eliminating the need for mechanical brakes or active holding torque. These motors can be built such that they neither produce nor are affected by magnetic fields, making them useful in highly magnetic environments and applications in which magnetic fields are harmful.

The state of the art in control of PUM is not fully developed. Commercial motors typically employ open-loop speed controllers which are operated in cascade with non-model-based control schemes such as proportional-integral-derivative control. These techniques are effective and appropriate for many applications such as locomotion. These techniques are not suitable for precise positioning, nor for mission-critical applications requiring guaranteed stability and performance characteristics.

The goal of PUM research being conducted in the UHCL Systems Engineering Laboratory is to develop model-based real-time control algorithms for PUM. Research supported by ISSO entailed characterizing the kinematic performance of a commercial variable-frequency motor driver and designing a custom driver that provides greater variations in drive signal frequency as well as variable drive signal amplitude.

Technical Plan and Equipment
The production of drive signals for the PUM requires special circuitry that produces a pair of phased sinusoidal signals of variable frequency in the 40-60 KHz range and approximately 110 volts RMS. The motor was supplied with a standard commercial driver (Piezo Systems/Shinsei D6030) that permits open-loop speed control in the 30-300 RPM range via an analog input signal and direction control via a pair of discrete input signals.

The technical plan consisted of starting with the commercial controller and developing interface circuitry to allow its operation via dSpace/Simulink.⁴ Switching control logic was implemented to drive the commercial controller. Experiments were carried out to characterize positioning accuracy and transient response.

As a parallel effort, candidate designs were developed for a more capable custom motor driver. The all-custom controller will permit a wider range of drive signal frequencies and variable drive signal amplitude. These controllers were evaluated with circuit simulation software, and the best of them will be implemented in hardware.

Experimental Activity
The laboratory apparatus is depicted in Figs. 3-5. It consists of the PUM connected directly to a laser optical encoder (a device that produces a sequence of pulses that can be sensed to measure angular displacement). The motor is driven by the commercial motor driver which receives control signals from the dSpace controller in the PC via the custom interface circuit. The interface circuit also powers the encoder and transmits encoder signals to the PC.

The first set of experiments characterized the positioning accuracy available using the commercial driver with no load on the motor. These experiments were performed using the Simulink control diagram illustrated in Fig. 6 and dSpace graphical user interface shown in Fig. 7. The software initializes the motor and encoder by causing the motor to rotate until the encoder index mark is located and then stop. Next, on command, the motor drives to a preset position. The commercial driver can be set to operate at motor speeds between approximately 30 and 300 RPM via the SetSpeed control. Discrete inputs control direction of rotation. The inability to command speeds between zero and 30 RPM necessitates a form of switching control via direction inputs. A finite sampling period and lags in measurement, computation, and signal propagation, limit positioning accuracy.

Control software includes an element labeled DeadZone which introduces a deadband 0.09 deg (0.0016 rad) on either side of the setpoint. The deadband element reduces high-frequency chatter attributed to finite sampling time and system delays.

Figure 8 shows the positioning accuracy for sets of five trials at motor speeds ranging from approximately 5 to 30 rad/sec. From Fig. 8, it is evident that positioning accuracy of 0.5 milliradians is feasible in the no-load configuration. Therefore, for applications involving extremely low torque and acceptable position errors greater than 0.5 milliradians, the commercial driver should be satisfactory. Note, however, that occasional chatter was observed at the higher motor speeds, and, therefore, a control system using the commercial driver for positioning should decrease motor speed when approaching the setpoint.

Using a slightly modified control system configuration, researchers measured the unloaded motor time response. Here, time response is defined as the time required to accelerate to a prescribed speed. Because time response exceeded the capability of the dSpace system (the dSpace system sampled too slowly), the digital oscilloscope was used to measure time response. A plot of motor speed as a function of time is shown in Fig. 9. Note that the speed overshoots considerably. Since the commanded speed is constant, the speed overshoot can be attributed to the commercial driver. Also note that the unloaded motor initial angular acceleration is over 17000 rad/sec².

Conclusions
Preliminary experiments carried out to date demonstrate that the PUM has great promise for space-based robot applications. However, the commercial motor driver is not suitable for applications requiring positioning accuracy greater than 0.5 milliradians. Additionally, the commercial motor driver results in large overshoots in speed regulation. Therefore, continued research is warranted to develop a more capable motor driver and model-based control techniques.

Future Work
A significant amount of work remains. The first near-term task is to implement the custom motor driver and to determine its kinematic performance. Next, the apparatus will be modified to add an inertial load and measure output torque as a function of speed, input signal frequency, and input signal amplitude. In the long term, development of robust control will require characterization of variations among similar motors and temperature and time dependent variations of motor performance. More detailed friction modeling is also needed. Finally, model-based control techniques that account for all of these factors must be developed, implemented, and tested in realistic operational scenarios.

Acknowledgments
This work was partially supported by an ISSO mini-grant for the summer of 2002.

References
¹T. Sashida and T. Kenjo. An Introduction to Ultrasonic Motors. Oxford, UK: Clarendon Press, 1993.
²Operating Manual: Ultrasonic Rotary Motor and Driver. Cambridge, MA: Piezo Systems, Inc., 2001.
³N. W. Hagood and A. J. McFarland. "Modeling of a Piezoelectric Ultrasonic Motor," IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control 42.2 (1995): 210-31.
⁴J. B. Dabney and T. L. Harman. Mastering Simulink 4. Upper Saddle River, NJ: Prentice Hall, 2001.

Publications
Dabney, J. B., T. L. Harman, and J. J. Chakungal. "Kinematic Control of a Piezoelectric Ultrasonic Motor," UHCL Systems Engineering Laboratory Report, SEL-005, UHCL, 2003.

Presentations
Dabney, J. B., T. L. Harman, and F. H. Ghorbel. "Piezoelectric Ultrasonic Motor Modeling: State of the Art and Future Directions," International Conference on Signals, Systems, and Information Technology, Souse, Tunisia, March, 2003.

Funding and proposals
"Advanced Piezoelectric Ultrasonic Motor Driver Development and Testing." UHCL Faculty Research Support Fund, Grant #790, $10,180, Jan.-June, 2003.
"Real-Time Control Software for Piezoelectric Ultrasonic Motors." NASA JSC Robotic Systems Technology Branch, $28,661 (pending).

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Institute for Space Systems Operations - Y2002 Annual Report
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