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# Control the high frequency behavior of a mass-spring-damper system

## Control the high frequency behavior of a mass-spring-damper system

(OP)
Hi,

I am reading a material about feedback control of a mass-spring-damper system. As we all know, the input for this system is force, output is displacement or position. The displacement value is obtained using a sensor. The problem is The author wants to operate the system under high frequency input(1000Hz), in order to obtain accurate displacement value the sensor's sampling rate need to at least 20kHz, but unfortunately, this is beyond the capability of the sensor the author uses. Then author said "An alternative way to control the plant that acts as a stiffness is by only using an integral action. The crossover frequency,the frequency at which the open-loop transfer function crosses 0 dB, of the integral controller is chosen several factors below the first eigenfrequency of the system, which means the required sample rate is not extremely high in this case." Could anyone explain to me why does this method work?

Thanks,
CJ

### RE: Control the high frequency behavior of a mass-spring-damper system

Chengjun,

What is it you are reading at the moment? Are you trying to understand theory or solve a practical problem?

--
JHG

### RE: Control the high frequency behavior of a mass-spring-damper system

(OP)
It is just something from a book I found from the internet.
Basically I am facing the same problem with it. I have a displacement sensor whose bandwidth is not high enough. It seems the author solved this problem by simply adding an integrator. I want to first understand the theory and if it makes sense, I will use it in practice. But the problem now is I have no idea how could a sensor with low bandwidth can present accurately the high frequency displacement.

### RE: Control the high frequency behavior of a mass-spring-damper system

There's probably more to it than this, but an integrator is a low pass device so it would not need as high a sampling rate to contribute to the control loop.

### RE: Control the high frequency behavior of a mass-spring-damper system

(OP)

As far as I understand, low pass device meaning the amplitude of a high frequency signal passing through it will be significantly reduced. I really don't see there is any relationship between low sampling rate and low pass device.

By the way, may I say the process flow is like what's shown in attachment?

### RE: Control the high frequency behavior of a mass-spring-damper system

I can't see your attachment. Since it is on the internet perhaps you could point to the original article, rather than your interpretation of it. If his sensor can't detect 1000 Hz then no amount of signal processing jiggery pokery will help, but i'm guessing that's not he means.

Cheers

Greg Locock

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### RE: Control the high frequency behavior of a mass-spring-damper system

Pardon the interruption, but I just heard something in a meeting last week that puzzles me on this subject.
It was said: "mass-spring-damper model breaks down at high frequencies". They were talking about above 800-100Hz. and was related to a cab isolation system trying to damp out high freq noise.

As a vibration-neophyte fly on the wall in this mtg., I just wrote this down because it sounded like a bold proclamation.....something I wanted to verify.

Any thoughts on these comments w/ respect to this post, from the esteemed experts here?

### RE: Control the high frequency behavior of a mass-spring-damper system

"Breaks down" in what sense? That could mean a couple of different things:
> It physically breaks down, i.e. it broke
> It can't do its job because it can respond to the frequency and essentially passes the high frequency through.

TTFN
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### RE: Control the high frequency behavior of a mass-spring-damper system

Typically the attenuation across a rubber isolated cab bottoms out at around -40 to -50 dB, due to damping in the rubber, airborne transmission, and other transmission paths. To put that into context, that was about the S/N ratio of an analogue instrumentation quality tape recorder.

Cheers

Greg Locock

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