Actuator Precision Characterization

Introduction

In order to get the best precision from your positioning devices, it's important to have an understanding of the positioning mechanisms and their limitations. The purpose of this article is to describe the motion control technology used by Zaber's positioning devices, describe and quantify the inaccuracies that arise as a result, and offer some strategies to help minimize these effects.

Zaber's computer-controlled positioning devices use stepper motors to achieve open loop position control. These devices turn by a constant angle, called a step, for every electrical impulse sent to them. This allows a system to be built without requiring feedback for accurate positioning, reducing total system cost. It is also possible to rotate the motor by an angle less than a step by using a technique called microstepping. This consists of using an analog current in the motor coil in place of full current switching. Stepper motor and microstepping technology is described in another article, Microstepping Tutorial.

There are some limitations to using open-loop position control with stepper motors. Being incremental (as opposed to absolute) in nature, they must initially be referenced by going to a home sensor. In addition, if the torque required becomes higher than the maximum torque (also called the stall load) of the motor, a stall condition will occur, and the motor will stop turning. Without encoder feedback, the actual position of the motor will vary from the controller's position after a stall. At this point, you will need to home your device again to re-synchronize the position. Many Zaber devices have encoder feedback versions, which can detect and correct when stalling occurs though. To avoid stalling again, try lowering the speed, the acceleration, or the load. Finally, keep in mind that a stalling stepper motor may cause loud noises, but stalling does not damage the motor.

Some critical characteristics of the stepper motors and mechanics used in Zaber's devices are given in Figure 1. These devices use a setting of 64 microsteps in every step by default (i.e., 1 microstep = 1/64 of a full step). They are capable of even higher resolution, but for simplicity's sake, the data below has been generated assuming the device is set to 64 microsteps/step.

Figure 1: Motor and lead screw properties of Zaber devices

Resolution

The resolution (also called addressability or microstep size) is the distance equivalent to the smallest incremental move the device can be instructed to make. In other words, it is the linear or rotational displacement corresponding to a single microstep of movement. As seen in Figure 1, the resolution for T-LA actuators is 0.09921875 µm (or approximately 0.1 µm). For T-NA devices, the resolution is 0.047625 µm. Some models have options for different lead screw pitches. The X-LSMXXXA models have a resolution of 0.047625 µm, while the X-LSMXXXB model has a resolution of 0.1905 µm. For the same model, finer pitch versions can generate more thrust, while those with coarser pitch screws can reach a higher maximum speed.

Sticktion

Because of friction, the device may not move at all when requested to move by one microstep. Requesting it to move another microstep may still yield no results. After a certain number of requests to move one microstep, the motor's torque will exceed the static friction, resulting in the motor jumping by the accumulated number of microsteps, and then it will stick again. This phenomenon is called sticktion, which is very dependent on the load and amount of wear on the lead screw.

Most positioning devices face this problem to some degree. After taking up the backlash, some devices in good condition with a small load will move on each microstep. At higher loads, which increase the lead screw friction, they may jump every micron or so. Figure 2 shows a test of the same device with different loading, where the position being requested is incremented by one microstep at a time.

Note that since the resolution of the gauge is 0.1 µm, the same as the motion being measured, some of the apparent jumps are simply due to rounding error.

Test procedure: After taking up the backlash, a T-LA28A actuator is requested to move in one-microstep (0.1 µm) increments. The position is measured with an accuracy of +/-0.1 µm. The test is done first with a small load of 5 N and then repeated with a load of 20 N.

Repeatability

The repeatability is the maximum deviation in the position of the device when attempting to return to a position after moving to a different position. Figure 3 is an example showing how this specification is determined. The histogram shows the number of times the actuator stops at a given position. The two peaks correspond to each direction of approach. Within each peak there is a Gaussian distribution with a full width at 1/e2 of about 0.3 µm. This is a typical repeatability for Zaber's T-LA actuators. The distance between the two peaks is 2.2 µm. This is a typical backlash.

Test procedure: A T-LA28A actuator is moved 1 mm from a given position and then back to that same position. This is repeated 100 times and the true position is measured each time (the accuracy of measurement is +/-0.1 µm). The test is repeated with the actuator moving 1 mm in the other direction before attempting to return to the same position. All tests are made with the actuator mounted to a TSB28 translation stage.

Backlash

As discussed in the repeatability section, backlash is the deviation of the final position that results from reversing the direction of approach. However, for small movements, the backlash is more complicated than that. In general, the actual position of the device is not uniquely determined by the requested position but depends on the exact trajectory used to get there. For small motions involving a change of direction the repeatability may be said to go to the backlash level.

Test procedure: Approaching from a large negative position, a T-LA28A actuator is requested to stop at 5 µm. It is then requested to move back to 0 µm and finally forward to 1.5 µm. The actual position is measured and plotted as a function of the requested position.

Anti-sticktion and Anti-backlash Features

If you want to move your device by small amounts, for example, to align an optical fibre on a diode laser, then sticktion and backlash can become very annoying. Zaber T-Series devices have built-in anti-backlash and anti-sticktion routines that can be enabled to help solve this problem. Note that they are disabled by default. The anti-backlash mode does not affect motion in the positive direction (increasing absolute position).

When dealing with negative motion, the device will overshoot the desired position by roughly 600 microsteps; then it will return, approaching the requested position from below. The anti-sticktion mode does not affect movements larger than 600 microsteps.

For requested movements smaller than 600 microsteps, the device will first position itself 600 microsteps below the requested position and then approach the requested position as usual. Care must be taken in certain situations. For example, when aligning an optical fibre to a laser at a distance less than 600 microsteps, the fibre may collide with the laser if the direction of travel of the positioning system is not chosen wisely.

Accuracy

The accuracy is the maximum deviation of the actual position of the device from the requested position over the full range of motion. Figures 5 and 6 are examples showing how this specification is determined. The cyclic error of +/-3 µm peak deviation with a period of one motor rotation (48 steps or 304.8 µm) is typical of lead screw systems. The big jumps are due to the poor resolution of the gauge (1 µm). A non-linearity of about +/-2.5 µm maximum deviation can be seen. To obtain the actual accuracy, you must add the cyclic error on top of this slowly-changing error. This pushes the maximum deviation to 2.5 µm (non-linearity) + 3 µm (cyclic) = 5.5 µm maximum deviation from 0 error. Therefore the accuracy of the tested actuator is +/-5.5 µm. Devices with greater travel will generally have poorer accuracy over their full range.

Figure 5: Position error vs. Position Test procedure: A T-LA28A actuator is moved in one direction in one-step (6.35 µm) increments. The position error (the measured position minus the requested position) is plotted as a function of the requested position.

Figure 6: Position error vs. Position Test procedure: The T-LA28A actuator is moved from 0 mm to 25 mm in increments of two revolutions of the stepper motor (96 steps or 0.61 mm) to avoid measuring the cyclic error shown above. The position is measured with a digital dial gauge with a resolution of 1 µm.

Stability

A specification of any positioning device is its ability to stay at the same place for an extended period of time. The worst problems for stability are internal and external temperature changes. These temperature changes produce thermal expansion and generate motion of the payload. Although powering off the motor between moves greatly reduces the thermal load on the actuator, prolonged motion at high duty cycles can generate enough heat to cause trouble. All motorized actuators, even those using DC servo motors, face this problem.

Figure 7 shows a time constant of about 20 to 30 minutes and a maximum amplitude of 37 µm. The position does not return to zero after cooling. This is likely due to creep of the lead screw in the rotor thread and/or creep of the bearing holding the rotor. The temperature rise of the motor at full current is 75°C. Note that this is a worst-case scenario with full current applied continuously. During normal operation, temperature changes are much lower.

If the long-term stability of the unit is a concern (it may not be for many applications, especially closed loop systems), the unit should be turned on at least 20 minutes before using it, and small motions with low duty cycles (< 5%) should be used.

Temperature effects should be kept in mind if larger movements or high duty cycles are required. If you repeat the same readings several times during an experiment and notice an increasing or decreasing trend in readings which you expect to be constant, consider the possibility of thermal effects.

Figure 7: Position vs. Time

Test procedure: The T-LA28A electronics are switched on but the motor is turned off. The set-up is left alone until the actuator, translation stage, and Mitutoyo Mini-Checker attain thermal equilibrium. Then (at t = 0 in the chart above) the maximum rated current is applied to the motor winding. This does not turn the motor but dissipates 3.4 watts of power inside the motor, causing its temperature to rise. The Mitutoyo is then read every 30 s until the position stabilizes. Then (at t = 30 in the chart above) the current to the motor is switched off and the gauge is read every 30 s until the position stabilizes again.

Conclusion

While not all applications require getting the most precision out of the device, knowing about the effects and techniques described above will allow you to stretch the use of lower cost and simpler devices to cover a wider range of uses. Knowing and understanding a device's limits also gives higher confidence in its performance.