Why Sensor Resolution Matters More Than You Think in Vibration Control

In high-precision motion control systems like those used in semiconductor lithography, optical inspection, or precision manufacturing, the terms “sensor resolution” and “servo bandwidth” are often tossed around interchangeably, sometimes even confused as being functionally synonymous. But they’re not. And understanding the difference between the two isn’t just academic, it can fundamentally change how we design, implement, and optimize motion systems.

Let’s break this down.

The Misconception

At first glance, it seems intuitive. If your sensor is more sensitive (i.e., it has higher resolution), then your system should be able to respond faster and more effectively to disturbances, implying a higher servo bandwidth. But this is not how things actually work.

To unpack this, let’s define the terms properly.

What is Bandwidth

In control systems, bandwidth refers to the range of frequencies over which a system can effectively respond, either by tracking a command or rejecting a disturbance. It’s usually visualized using a Bode plot, where we see how the system’s gain behaves across frequencies.

A common (but often misleading) definition uses the -3 dB point in the Closed Loop Transfer Function. However, this definition can be overly optimistic. A more practical and rigorous definition looks at the 0 dB point in the Open Loop Transfer Function, this gives us a better idea of where the system can truly maintain control authority.

Bottom line? Bandwidth tells us where the system is capable of reacting, but not how well it reacts within those bounds.

Controllability

Now let’s talk about something that sensor resolution directly influences, controllability.

A system can’t control what it can’t sense. If a vibration or motion disturbance is smaller than the smallest increment a sensor can detect, then it effectively doesn’t exist to the control loop. This is crucial. The finer the sensor resolution, the deeper into the disturbance spectrum the system can see, and thus, the more precisely it can act, without needing to change the bandwidth.

This is where many engineers get tripped up. They observe improved performance with higher resolution sensors and mistakenly attribute it to increased bandwidth. What’s really happening is that the improved sensor is allowing the control system to attenuate smaller disturbances within the existing bandwidth.

Figure 1: When Resolution Defines the Limits of Control

This concept is well illustrated in Figure 1, where a 1 nm vibration is compared against sensors of differing resolutions. A coarse-resolution sensor (e.g., 4 nm) cannot “see” the disturbance and therefore cannot control it—resulting in no attenuation. A fine-resolution sensor (e.g., 0.1 nm), however, can resolve the disturbance and attenuate it either down to the control loop’s gain at that frequency or to the sensor’s own noise floor. This is controllability in action.

Figure 2: The Frequency Domain Tells the Story

Figure 2 moves the discussion into the frequency domain, showing auto-spectrum plots and their integrated equivalents for different sensor resolutions. When the control loop is active but sensor resolution is poor, disturbance attenuation stalls at the sensor floor (e.g., 4 nm). When resolution improves to 0.1 nm, the system continues to drive the disturbance lower, despite no change in the servo bandwidth. Notably, the plots show no further attenuation beyond the bandwidth limit, reinforcing that bandwidth was unchanged. The improvement lies entirely in the system’s ability to detect and act on smaller disturbances within the bandwidth window.

Figure 3: Real-World Results Back It Up

These principles aren’t just theoretical. Figure 3 shows actual data from a focus servo loop subjected to vibration near 12 Hz. With higher resolution sensing, the system was able to attenuate this vibration 10 times more effectively, without any adjustment to loop bandwidth. This data validates the central claim: better resolution enhances controllability, not bandwidth.

Why This Matters

So, why should you care?

If you’re working in any application where vibration can compromise precision (think wafer metrology, optical stabilization, or nanomanufacturing) you cannot afford to equate resolution with bandwidth. Doing so could lead you to waste resources on high-bandwidth control designs when the real solution is simply better sensor resolution.

Choosing the right sensor lets you extract far more performance from your existing control architecture. It allows for better disturbance rejection, lower following error, and higher-quality outcomes, without the added complexity or instability risks of pushing bandwidth limits.

The Takeaway

Improved sensor resolution doesn’t make your system faster, it makes it smarter. It allows your control loop to “see” finer details and act accordingly, all while staying within the bounds of its original bandwidth. This nuanced understanding can unlock performance improvements that might otherwise seem out of reach.

If you’re wrestling with persistent low-frequency vibrations, or if your system’s performance plateaus despite your best efforts to tune gains or increase loop speed, take a step back. The solution might not be faster control—it might be better sensing.