# Difference between Hysteresis, low pass filter and deadband in control theory?

I am trying to understand the fundamental difference between the following terms in the context of control systems:

1. Hysteresis
2. Low pass filter
3. Deadband

Are these just fancy names that can be tweaked to provide same result? By tweaking I mean some intelligent way of formulating the variables, such as using the absolute value of the output variable, instead of delta between current and previous value.

I can conceptually think of examples where the same behavior can be achieved by how we tweak any of the above three techniques. However, I am concerned that such tweaking is essentially changing the fundamental meaning of the term itself.

## 1 Answer

No, or at least not as they are generally used and understood.

1. Hysteresis is a nonlinear phenomenon where a variable trending in one direction tends to "pull" another variable along with it, and that other variable "sticks" until it's pulled the other way. Think of backlash in gears, or the B-H curve of a hard magnetic material.
2. A low-pass filter is usually linear, usually constructed. It passes low-frequency signals, and blocks high frequency signals.
3. Deadband is a memoryless nonlinear action where inputs within some band (the dead band) are not passed to the output.
• Thanks Tim! believe all these behaviors can be constructed. 1) Even hysteresis, which is a phenomenon can be replicated to some degree. For example, consider input x and output y. We can say that if x increases y increases at the same rate (some slope dx/dy), but when x reduces then y reduces by a different rate. This would give somewhat a graph similar to B-H curve, but less non-linear. Essentially, the path forward and backward is different and this is the hysteresis. – Ujjwal Gupta Jun 13 '19 at 4:58
• 2) I think of low pass filter as taking average of a signal. Consider a fixed window moving average filter. So the output is linear combination of some previous values of the signal. Both forward and backward direction computations are equivalent. So, this can be thought of as hysteresis with equal forward and backward path. Now, in strict sense, this is not hysteresis if we define hysteresis as having different forward and backward path. phenomenon. – Ujjwal Gupta Jun 13 '19 at 4:58
• 3) Can we say deadband is basically a band pass filter? Or is the word filter associated with frequency filtering only (not amplitude change)? – Ujjwal Gupta Jun 13 '19 at 4:59
• @UjjwalGupta No. A memoryless function cannot filter in the frequency domain, at all. – TimWescott Jun 13 '19 at 15:01