Dr. Christian Benz and Dr. Bülent Delibas, development engineers for piezo motor products, Physik Instrumente (PI) GmbH & Co. KG
Positioning systems which incorporate ultrasonic piezo motors can achieve both accurate positioning in the nanometer range and fast motion, a combination that is not attained by many other drive technologies. This paper will examine functionality of these unique positioning systems, with a focus on PILine® from Physik Instrumente, which exemplifies the latest performance capabilities of ultrasonic piezo motors.
Over the past years there has been an increasingly high interest in piezoelectric motors, especially in the areas of semiconductors, optics, photonics, microscopy, medical, and life sciences where precise motion and positioning is a prerequisite for results like product performance or yield.
Some of the most demanding applications in which piezo motion and positioning systems can apply their strengths include:
- Positioning with nanometer resolution
- Fast step-and-settle within milliseconds
- Fast scanning of patterns
- Motion at constant velocities
- Slow and smooth motion
- Low position drift in standby mode
- Motion along predefined paths (sine, circles, arcs)
- Low latency triggering of motion and feedback
- Low wear and minimized power consumption
- Silent motion in all use case
One piezo positioning technology that exemplifies these capabilities is PILine® from Physik Instrumente. This paper will use PILine as an example to examine the latest functionality of ultrasonic piezo positioning systems.
Operating Principle of PILine Motion Systems
PILine positioning systems are based on ultrasonic piezo motors that are capable of direct-driven linear motion. A piezoelectric actuator, which vibrates at an ultrasonic frequency range, is preloaded against a runner using a coupling element (Figure 1).
Electrical excitement of the piezoelectric actuator at its resonance frequency causes oscillation. Due to the preload, the actuator oscillation is converted into continuous feed motion by the coupling element, which moves the runner. The preload also causes the drive to self-lock when the stage is not energized. The velocity of the motion can be adjusted by modifying the amplitude of the excitation and therefore the amount of power transferred to the runner.
Changes in position of the stage are detected accurately by an incremental, or in some cases, an absolute-measuring linear encoder. The number of counts recorded by the encoder is proportional to the distance travelled. Sub-nm resolution is possible using state-of-the-art sensors and gratings.
PILine stages are usually operated in closed-loop mode, where a proportional-integral-derivative (PID) algorithm is used to minimize trajectory deviations. Comparing the actual position (obtained from the internal sensor) with a commanded position returns the following error, which serves as a process variable for the PID algorithm
Figure 1: Schematic diagram of a PILine motor. (Image courtesy PI)
Driving Methods of PILine Motion Systems
The stator (piezoelectric actuator) of the PIline piezo motor is operated in resonance mode. It has a rectangular geometry of L (Length) × W (Width) × H (Height) and is made up of bulk PZT material that is produced by the PI subsidiary PI Ceramic (PIC). Three excitation electrodes are sputtered on the two main surfaces, one of which is covered completely. The opposite surface is divided into two equal sectors. The piezo motor is operated at one of its resonance frequencies to generate elliptical oscillations at the coupling element.
In impedance measurements one of the two separate electrodes is loaded with a low sweep signal and the second electrode is kept free to find the resonance frequencies. The measurement (Figure 2) illustrates two resonance frequencies in ultrasonic frequency range. The coupling element performs an oblique or narrow elliptical movement at , which is the main operating mode. It performs a tangential back and forth movement at frequency .
Figure 2: Impedance spectrum of the piezoelectric stator. (Image courtesy PI)
One-Source Drive
In one-source drive mode, one of the separate electrodes of the piezo stator is loaded with its resonance frequency in sine waveform and the second separate electrode is kept free. The common electrode on the opposite side is grounded. By using one-source drive, the stator held with a spring damping mechanism generates a planar mode at . The stator tip makes elliptical oscillations that are transferred to the runner (Figure 3). The direction of the movement can be altered by switching the driven electrodes.
Figure 3: One-source drive with PILine stator. (Image courtesy PI)
Dual-Source, Dual-Frequency Drive (DSDF)
Piezoelectric motors have difficulties in realizing smooth and slow movement. Additionally, slow motion noise (SMN) can be initiated by friction induced vibrations during the operation of piezo motor when the moving speed is less than 2.0 mm/s. SMN is not only undesirable for a user, it also reduces the moving accuracy of the stage. Nonlinear characteristics of friction at the contact surfaces are the main root cause for the SMN, which also affects the working atmosphere of the user substantially.
To eliminate both the SMN and the tracking error in piezo motor stages, a novel driving method was proposed. By using the dual-source dual-frequency (DSDF) driving method, which reduces the nonlinear phenomenon of transition between static and dynamic friction at the stator-runner contact points, the controllability of the smallest incremental movement is enhanced significantly.
By using DSDF drive, the stator vibrates with two eigenmodes, which superimpose to supply mixed oscillations. Movements of the coupling element have two sinusoidal trigonometric components with the loading of two different voltage amplitudes , and two operating frequencies ,. Therefore, the movements directions are not constant and modulated with respect to time . The variation between the two eigenfrequencies, which are dependent on the geometry and the mass of the piezo elements, are mostly not in the audible region. The difference between the two applied frequencies is ideally set to the servo-frequency of the digital controller to correlate to the closed-loop motion control system. The modulated oscillations of the friction tip are shown in Figure 4.
Figure 4: DSDF drive with PILine stator. (Image courtesy PI)
The second driving signal causes the friction coupling element to generate motion only in the tangential direction, and the displacement in the -axis direction remains constant. The result is the modulated vibration trajectory of the friction coupling element. Driving the stator with two sources at two frequencies excites three resonance modes on the piezoelectric body. The first two modes are excited at the main operating frequency of the stator. As the frequency difference between and is synchronized to the closed-loop servo-frequency, the resulting runner force in the -axis direction corresponds to the modulation of the two sinusoidal waveforms.
State Window Motion Control
When targeting a position, the inbuilt profile generator of the PILine controller creates a velocity profile for the motor that consists of three regions (Figure 5): a) acceleration; b) constant velocity; and c) deceleration and settling. Each of these regions can be tuned individually by adjusting the corresponding control (PID) parameters. The controller features up to five independent groups of control parameters. As depicted in Figure 5, these control parameter groups are arranged concentrically around the commanded position or around the target position (default), depending on the servo-window mode.
Figure 5: Example of a position and velocity profile created by a PILine controller for motion from 0mm (start) to 1.5mm (target position).It can be divided into three regions: A) acceleration; B) constant velocity; and C) deceleration and settling. (Image courtesy PI)
The values of the proportional, integral, and derivative parameters should decrease with an increasing control parameter group number. The number of groups to be used can be configured with parameter 0x400. It is recommended to operate with three control parameter groups. Each group of control parameters contains two windows: Window enter and window exit, specifying the activation area. As soon as the actual position of the stage reaches one of the entry windows, the corresponding control parameter group is activated automatically. The window exit parameter of the outermost parameter group is ignored by the PILine controller, leaving this PID set active even when the stage exits the window.
The control parameter group 0 (0x401 to 0x407) specifically regulates the settling behaviour. It is activated only after the commanded trajectory has finished (Figure 6). The other parameter groups (1 to 4, 0x411 to 0x447) determine the behaviour during stage motion.
Figure 6: The enter and exit windows of a configuration with three control parameter groups are represented by different colors.The window can be centered around the command position (A), or around the target position (B, default setting).The innermost control parameter group (O, green) is activated only after settling begins, for example, when the commanded position is equal to the target position.Note that in (B), the outermost control parameter group (2, red) is already active before the actual position of the stage reaches the corresponding enter window. (Image courtesy PI)
Adaptive Control with DSDF Drive
Generally, actuators may need different controller parameters for various applications or use cases to get higher performance. Users can change the parameter sets accordingly, which increases the complexity of the system. For instance, PID parameters at higher velocity scanning may have higher values than the ones at lower velocity scanning. In order to avoid it, one universal parameter set that is optimal for all applications is desired. Therefore, the adaptive control with DSDF drive for motion control of PIline piezoelectric stages is introduced in order to obtain simplicity in parameters. One parameter set can be optimized for all use cases of the piezoelectric stages.
The adaptive motion control for a PIline piezoelectric stage is presented in Figure 7 as a block diagram. The control unit is based on adaptive PID state windows that not only depend on the position error, but also on the commanded velocity. The offset logic block is implemented in the control loop in order to reduce the time requirement to overcome the friction dependent breakaway force at the start or the motion and velocity reversal.
Figure 7: Block diagram of the position control system for a piezoelectric stage. (Image courtesy PI)
Switching between motion states and corresponding parameter sets in state windows takes place depending on the current velocity and variation between the current and target position of the motor. PID parameter values for motion state can be automatically adapted to the specified target velocity (VT). Details of the individual states (0x451 to 0x485) are described below.
Control state 2, "Motion" (0x471 to 0x475) is active until the current velocity (VC) has a value less than the minimum target velocity (VT,min 0x479) and the trajectory is finished. The PID parameter adjustment takes place whenever the target velocity is in a range defined by the maximum target velocity (VT,max 0x478) and (VT,min). Since the state window algorithm is used to optimize the slow-motion performance, the values of PID terms (Kj) at the lower limit of the target velocity are specified. The relation of the adaptive PID parameters to the current velocity is given by the equation (I)
(Kj,max – Kj,min)
Kj = Kj,min + ______________________ log(VC/VT,max) (I)
Log(VT,min/VT,max)
Where, j is a variable for P, I, and D parameters. Maximum and minimum values of them are (Kj,max) and (Kj,min), which are set in the motion state.
Control state 1, "End Position" (0x461 to 0x464) is the state for the slower movement of the motor to reach the target position. This state is active until the movement has reached the on-target state, which is defined with the position tolerance band around the target position. Positioning is accomplished when the specified delay time for setting the on-target state has expired.
Control state 0, "Target" (0x451 to 0x454) is the state in which the motor holds the axis at the target position. It is active as long as the position error is within the position tolerance band specified by the parameters (0x455) and (0x456). As soon as the current position leaves this zone, the "End Position" state is activated again to move the axis back to the target.
Control state 3, "Global stable" (0x481 to 0x484) is activated to reduce the vibrations during "End Position" and "Target" states when the current velocity exceeds the threshold value defined by a parameter. If the velocity falls below half of the threshold value, the state is switched back to "End Position".
For specific applications and use cases, driving and control parameters can be further optimized to obtain better characteristics. Shorter positioning time, high-dynamics scanning, and a reduced velocity ripple during scanning are typical examples.
Fast Motion and Settling
Increasing Acceleration (Region A)
In region A (Figure 6), the stage accelerates until it reaches the maximum velocity predetermined by the profile generator. The acceleration region can be minimized by:
- Increasing the acceleration parameter
- Adjusting the drive offset parameters
Increasing the Velocity (Region B)
In region B (Figure 6), the stage has reached its constant velocity. The required time span can be shortened by increasing the stage’s closed-loop velocity (0x49). Especially when covering short distances, the stage can go directly from acceleration (region A) to deceleration (region C), without reaching the maximum velocity.
Improving Settling (Region C)
In region C (Figure 6), the motor decelerates as it approaches the target position. The deceleration region can be minimized by:
- Increasing the deceleration parameter
- Adjusting the integral term of control parameter group 1
- Increasing window enter of control parameter group 0
If accuracy is not of the utmost importance, the window enter parameter of control parameter group 0 (referred to as "settling window", 0x406) can be widened to achieve earlier settling, as shown in Figure 8.
Figure 8: Zoom-in to the settling region of Figure 6. Default settling window (a) versus increased settling window (b) leading to earlier settling. (Image courtesy PI)
Fine Positioning
When accurate positioning in the nanometer range is required, reservations on positioning speed may have to be taken into account. Minimum incremental motion and high position resolution can be obtained by using a smaller settling window; for example, by reducing the window enter 0 (0x406) and window exit 0 (0x407) parameters and optimizing the servo loop parameters.
Keep in mind that the true achievable positioning accuracy (in terms of deviation from a theoretical true position) is limited by other factors, such as the grating pitch of the scale, accuracy of the sensor, and signal conditioning of the sensor electronics. For higher accuracy consider acquiring the following:
- Stages with a fine and accurate grating pitch of the scales
- Controllers with improved interpolation systems
- Stages with calibrated or mapped accuracy
PILine systems usually provide a resolution of 0.01 to 0.4 µm, which corresponds to a bidirectional repeatability in the range of 0.05 to 2.0 µm, depending on the tolerated deviation from the target position (settling window). For applications that require higher accuracy, customized stages are available.
Figure 9: Constancy of velocity versus position, recorded several times at different sampling rates.Small local changes in velocity have significantly more impact at high sampling rates. (Image courtesy PI)
PILine motors feature a broad velocity range of 100 nm/s to over 100 mm/s. This range can be subdivided into two characteristic ranges:
- Standard motion (2.0 mm/s to 100 mm/s)
- Slow motion (100 nm/s to 2.0 mm/s)
Slow Motion
Positioning at slow speeds is essential when scanning small objects, such as when using a microscope with a PILine stage in manual mode. Slow motion going down to 100nm/s is needed, for example in high-resolution microscopy scans of biomedical samples such as cells and cell substructures, or of micro- and nanostructured samples in materials microscopy. It can also be used in optical tracking applications with slow moving molecular machines inside cells.
To achieve the optimum performance of the stage, it is imperative to customize the PID and controller parameters according to the intended use. Uniform motion is a key requirement for this velocity. Following errors, which occur particularly in this velocity range, have to be compensated by boosting the P-term of the current PID set to a very high value.
Standard Motion
This velocity range is mostly used for fast step-and-settle applications. Typical use cases are positioning lenses in a beam path or shutter applications. Here, the main requirement is fast and accurate positioning, the shape of the trajectory plays a subordinate role. In most instances, the default settings of the controller can be adopted without the need for time-consuming customization. Furthermore, the use of two-phase actuation (motor offset) is not required and might in fact lead to slower final velocities and less forward force.
Minimizing Dynamic Following Error
When a minimum position error is required, the P-term of the active control parameter group has to be adjusted according to the current velocity of the stage. To obtain the smallest possible following errors regardless of the velocity, a function adjusting the P-term to the current velocity can be implemented in all supported software environments, for example, by using an empirical formula or a lookup table.
Position Drift at Standby
Precision positioning stages, especially in microscopy, medical and metrology applications, are required to have not only accurate target positioning but must also remain at this target position over a long period of time, which is a very critical parameter for selecting positioning systems.
Drift, which is the change of the stage position over time when it is in standby, can be defined as position stability over a period of time ranging from one minute to several days. It is a nonlinear phenomenon and therefore, it has random characteristics. Causes of position drift are mainly viscoelastic features of components such as polymers, epoxies, and damping elements used in the stages. Figure 10 shows a typical position drift of a piezo motor over a minute of relaxation.
PI designs its PILine positioning system to avoid using inappropriate materials to get the lowest position drift. Because PILine stages feature an excellent self-locking mechanism, they do not require extra electrical energy for holding their position. Figure 11 illustrates the PILine positioning system with anti-drift modification. The position drift is low and stable. Therefore, there is no need to activate the closed-loop control again to move the stage back to its original position. Position drift at rest is a result of the temperature deviation of the environment.
Figure 10: Position drift example of a typical piezo motor. (Image courtesy PI)
Figure 11: Position drift of a PILine positioning system with anti-drift modification. (Image courtesy PI)
System Modelling
For the most demanding applications, it is helpful to derive a transfer model of the actual system by methods of system identification. These models can be used to analyze control loop strategies more efficiently on a virtual system.