Minimum Step Size is a motion system parameter listed on single and multi-axis motion system datasheets. As with many performance specifications, however, Minimum Step Size is a metric based on assumptions and is often mis-represented, as the actual load point location is not considered. Discussed will be terminology definitions needed to frame up of the discussion, influencing factors, such as design architecture and control approaches, and how accuracy and repeatability play a role.
How is load point Minimum Step Size different than actuation point Minimum Step Size?
To properly discuss Minimum Step Size, a common language needs to be established. This section will define terms that will be mentioned throughout this discussion.
Minimum Step Size is the defined as the minimum motion able to be realized by the control system. Results will differ depending on location measured, so a location should be associated with any claim of “Minium Step Size”.
Noise Floor for this discussion is the inherent electronic noise of the sensor itself. In the case of an optical, magnetic, inductive, or capacitance encoder, there is error inherent in the optics, interpolation, and any EMI that could be present. In the case of a capacitance sensor, this would be the dominated by the signal conditioning electronics, primarily the op-amps within the conditioning circuit. This value would represent the sensor output if measuring a perfectly still target.
“Static Jitter” is the amount of motion that is occurring while the system is not undergoing a move profile. Static Jitter in every application is greater than the Noise Floor. It is very common, however, that “Noise Floor” is referenced to mean “Static Jitter” and combines electronic noise with Static Jitter.
Resolution is simply the distance a single encoder count represents. For an analog sensor such as a capacitance probe, this value would be the least significant bit of the analog to digital converter. Generally, this would be 18-20 bits over the full scale range of the sensor.
Actuation location is defined as the location of the sensor nearest the force input location.
Load Point Location is the motion at, or where, the critical process activity is taking place. This could be several centimeters away from the Actuation Location.
Repeatability is the measurement of final position, relative to repeated moves into the same location, and not to the commanded position.
Accuracy is the measurement of final position relative to the commanded position.
Controllability is the ability of a servo system to impact the sensor output or a degree of freedom of actuation. Observability is the sensor’s ability to measure motion of one or more degrees of freedom. Having the ability of one, does not guarantee the ability of the other.
At the core of Minimum Step is the system design. There are many design decisions that directly impact Minimum Step Size, those being the sensor location, force delivery (direct drive versus ball screw (or other), bearing type (cross roller, truck and rail, air), and load point offset. Each of these will be discussed in terms of how they impact step size.
Sensor location has the single biggest influence on Minimum Step Size. Designs with only a sensor at the point of force delivery, and not at the load point, have no observability for load point motion. This means load point minimum step size is uncontrolled. Designs with sensors at the load point, however, have the needed observability, and depending on other factors such as force delivery and control scheme, have a good likelihood of controlling the minimum step size.
Figure 1. Sensor location
Force delivery plays a huge role in minimum step size as well. Any system with backlash, or compliance, independent of sensor location, will adversely impact step size. Designs having backlash and sensors only at the actuation point, inherently have larger minimum step sizes at the load point, as any change of direction is simply not measured.
Figure 2. Ball screw versus direct drive.
Bearing choices will play a key role in determining how the load point moves. An air bearing system, as an example, will have the best performance, as there are little residual stresses in the air film that would impede the load point from following directly the motion of the mechanics supporting it. In contrast, however, are mechanical bearings such as cross roller and truck and rail. Cross Roller bearings have better performance in terms of overall straightness and accuracy, versus truck and rail, but both are subject to internal stresses held by stiction of the mechanical contact between the ball and rolling surface. These stresses can be very unrepeatable, making movement uncontrolled.
Figure 3. Bearing Types.
For both air and mechanical bearing architectures, load point offset will impact Minimum Step Size. Load point offset is the moment arm between the Load Point Location and the supporting bearing. The moment created by the load acceleration, or force of gravity, will create a static and dynamic deflection, as mechanics are not infinitely stiff, and nanometer of deflection happen easily with seemingly inconsequential acceleration of loads. Mechanical stresses between the ball and rail and air film tilt stiffness variability can make the Abbey error caused by the offset, vary over location, temperature, and load.
Figure 4. Load Point offset.
Feedback control schemes impact the Minimum Step Size through the influence of the Integrator gain. The feedback, combined with the Plant (mechanics), must have at least one pole in the denominator (an Integrator) for a final error of zero to be possible.
Figure 5. Steady State Error versus control design
Systems meeting these criteria, but also having backlash, or other compliance in the drive train, or friction, may not reach zero steady-state error due to “stiction”, a stick, then slip, phenomenon occurring in system. In these cases, a “deadband” control scheme might be implemented, which will adversely impact the Minimum Step Size directly. The dead band algorithm shuts off the output when the system is within a position window. Once outside that window, the control effort is resumed. This approach will eliminate the stick slip behavior, but at the cost of never landing at the commanded location.
Figure 6. Stick-Slip Phenomenon and dead band
Resolution is sometimes the stated Minimum Step Size, and although at a high level, this might appear to make sense, the reality is that this metric is rarely met at the load point location. In every motion system, Accuracy and Repeatability specification are larger than Resolution, by at least an order of magnitude, if not two. As an example, a system with 5 nm of encoder resolution might have an Accuracy of 0.5um and Repeatability of 50 nm. These numbers are vastly larger than the Resolution, bringing the question of “what matters to the system?” If the system is not repeatable, does it matter what the Minimum Step Size is? In this context, Accuracy is not as linked to Minimum Step Size as Repeatability is, as a good argument can be made that a step or movement does not necessarily have to be accurate. But, for the step to have real meaning, it should be Repeatable, meaning you step forward, then back, and arrive at the same place. With Repeatability often as high as 10 times resolution, one can see Resolution is a poor value for Minimum Step Size.
Figure 7. Repeatability versus Accuracy versus Resolution and Minium Step Size
Measuring the Minimum Step Size can be very simple to modestly complex. Collecting encoder data is generally very simple, as the servo drive will have a data recording feature and final position can be recorded over time. Load point measurement, however, can become far more complicated as capacitance probes or laser interferometer tooling will be needed. Fixturing of the reflective component for the interferometer and capacitance probes will add to the measurement, so care must be taken to keep mass low, while maximizing stiffening to reduce deflection. When using an interferometer, air wiggle can be a huge component of the measurement, so accommodation in the setup or processing should be made to reduce or eliminate the air influence. For both load point and actuation point measurements, thermal drift will impact the outcome, so a temperature-controlled environment is needed.
Figure 8. Laser Interferometer setup.
Post processing data from both load point and actuation point locations will always be needed as jitter will always be larger than the Minimum Step Size. The most common processing technique is a rolling average, which as a low pass filter, removing the high frequenjcy jitter component of the signal. The averaging technique reduces both electrical noise and jitter vibration, though it is not always appropriate to disregard these factors when assessing minimum step capability.
Figure 9. Moving average filter.
The decision to average data, or not, can be difficult to make, so here are some basic guidelines and facts. First, all data has jitter. How we treat it is dependent on the question being asked. If we concerned about image quality, and the imaging hardware is sensitive to velocity, meaning a pixel will “smear” across the field of view or TDI (Time Delay Integration) , then the real jitter itself is critical, and no filtering or averaging should be done. If, however, motion is commanded to center an object in a field of view, or make an angular correction for orthogonality purposes, then the jitter is inconsequential, and averaging should be used to characterize the performance of the system. Looking at the raw data only complicates the outcome, making what is important difficult to quantity. Below are three examples of what a minimum step could look like, that being raw data, lightly averaged, and heavily averaged. The heavily averaged data clearly shows the step increment, while the raw average does not. While all of thee datasets could be used as evidence of a mimimum step, the application will ultimatley determine which level of filtering is appropariate when characterizing the minimum step size. It should be noted that if the position data is used in any closed loop, minimum to no averaging should be done, as averaging causes time delays, and the system will be limited in its performance.
Figure 10. Averaging versus no averaging.
Any Minimum Step Size specification should be associated with a location. Two choices can be made, those being the Load Point (most representative) and Actuation Point (less representative, but worth knowing). In both cases, there are many influencing factors, including the sensor location, force delivery, bearing type, control strategy, and load point offset. Each of these will play a role, varying in degrees of importance, depending on if the system is supported by air or a mechanical bearing. With each of these factors being a variable, the one constant is the interpretation of Repeatability versus Minimum Step Size. If a system has a repeatability larger than the stated Minimum Step Size, one could rightly question if that even makes sense? Care should be taken to understand the assumptions made, and most importantly, the location associated with the stated Minimum Step Size stated. In most applications, Minimum Step Size at the load point location will be smaller than that at the load point, with a value of two to three times the resolution.
Get in touch with ALIO: Expert solutions for your precision motion control needs
翻译由我们中国区合作伙伴Aunion Tech Co., Ltd（上海昊量光电设备有限公司）家提供！
