Bandwidth/Time Constant Relationship

[oneb91]

I'm specifying a servo-valve controlled hydraulic actuator based on an existing design. The stroke of the new design will be a bit longer than the old, the load of the new design will be a bit less. The actuator slew rate will increase substantially, requiring an increased flow rate, higher pressure, and smaller actuator cylinder. The old servo valve has 30 rad/sec bandwidth - I think that will drop to 25 with the new servo valve in order to accomodate the increased flow.

When asked to review these assumptions, the controller designer indicates that the servo valve first order time constant can be .03 to .04 sec.

How does first order time constant relate to bandwidth? I assume the time constant is inverse of bandwidth.

 

[killabyte]

w=25 rad/sec , f is 3.978Hz you can say 5 tau first time constant is aprox 0.251; 1 tau = 0.05

for a first order it is the inverse of the freq divided by the number of tau, usually 5 tau.

regards

killa

 

[Skogsgurra]

oneb91

There is no rule-of-thumb when converting from time constant to bandwidth. Not that I know about, anyhow.

But there is the good old t-rise = 0,35/bandwidth(Hz) rule. It has been used for fifty years or more in oscilloscope specifications. If you realise that t-rise is measured between the 10 and 90 percent points of the curve, then you can calculate that t-rise is equal to 2.3 times the time constant (assuming a first order system where the initial 10 percents add very little to the total time).

Using this fact you can calculate your time constant like this:

BW (Hz) = 30/6.28 = 5 Hz (almost)

Rise time = 0.35/5 = 0.07 seconds

Time constant = 0,07/2.3 = 0.03 seconds

The result seems to agree quite well with the controller designer's 0.03 to 0.04 seconds. Especially if you use the 25 rad/s bandwidth, which will give you 0.037 seconds.

 

[jbartos]

Suggestion to the previous posting: It appears that the 25 rad/sec might be used as suggested in the original posting. This will lead to:

BW (Hz) = (25 rad/sec)/6.28 = 4 Hz (almost)

Rise time = 0.35/4 = 0.0875 seconds

Time constant = 0.0875/2.3 = 0.038 seconds