Developing MIMO Filter?

[phono]

Hello,

I've got a system with 3-dimensional-vibration input (3 Shaker) and I want to measure the vibration at 3 different output-points. I want to filter my system with an inverse FIR-Filter to suppress system attenuation ant to get the desired vibration for the desired direction.
Well, this works fine for the case of single input-single output (SISO)...
When stimulating one dimension I receive my desired signal - but also a cross-excitation in the other two directions. I'm trying to reduce this effect by changing the design but I cannot suppress it completely for some frequency ranges.
I'm measuring all in all 9 transfer functions and could build 9 inverse filters but I do not know how to combine them correctly to solve this Multiple Input/Output (MIMO)-problem.
Can anybody help me solving this problem?

 

[MikeyP]

Are you saying that you are applying force to a system in 3 dimensions but you want the system to respond in only 1 direction?

M

--
Dr Michael F Platten

 

[phono]

Yes and No

I'm applying force in 3 dimensions simultaneously.
I'm measuring the 3 dimesions on the system output.

My ideal case :
I receive in x-Dimension only the x-force
in y-Dim. only the y-force and so one.

I measure the transfer function - build a inverse FIR-filter and convolute it with my desired input signal x to get x_filtered. When applying x_filtered to the system I will receive x at the output.


unfortunately : When stimulating x I receive a "cross" force in y and z due to the system-design. The same when stimulating y or z - an acceleration could be measured at x and z or x and y.

I reduced this cross forces to be damped to -20db difference by changing the design of my system. But there are still some frequency ranges with strong cross excitation.

Starting now all 3 inputs simultaneously I receive 3 output-signals whereas each consists of a sum of the main signal in this direction and two other signals coming from the other two inputs. I got quasi 3 inputs and 3 outputs but 3x3 transfer paths.
The problem is now that every time changing an input with a filter - all 3 outputs are affected. I can optimize my system for one dimesion but then, when trying to optimize the second dimension I will become changes in my first dimension due to the channel interaction.

What I search is a method to get a approximately good solution for this problem.

 

[MikeyP]

I think you need to tell us a bit about the system you are testing.

Are you simulating this or are you doing it on a real structure?

I'm still not quite sure what you are trying to do.

You say:
"I'm applying force in 3 dimensions simultaneously.
I'm measuring the 3 dimesions on the system output.

My ideal case :
I receive in x-Dimension only the x-force
in y-Dim. only the y-force and so one."

To me this says that you want a system whose response in the x-direction depends only on the force applied in the x-direction. Similarly for the y- and z-directions. Generally this is not possible (except for a rigid body).

Or are you saying that when you apply a force using just one shaker, you measure a force in the other 2 (nominally passive) shakers which you are not expecting?

M

--
Dr Michael F Platten

 

[phono]

OK

it's a real structure. My system is a steel-bar with a mounted steering-wheel. Aim is to simulate vibration-signals on a steering wheel.

I've got one shaker connected to the system over a fork-joint to generate rotational movement.
I've got two shakers mounted vertically and horizontally for lateral vibrations (x/y) over a slide-bearing-coupling.

The steel-bar is mounted on a base frame. A slide-bearing on one side and a rubber-metall-bushing on the other side - to allow little lateral movements in x and y and the rotation (range: about +/-2deg.).

I added cross-beams to tense the base frame and to increase weight for more system-stability. The result was very good but there are still some problems.

The signals I want to simulate consist out of these 3 dimensions (x,y,rot.). My aim is to reduce the "cross-excitation" to a value less than -20db of the signal-input.

This means for example :
I apply a sinewave at input 1 (x-dimension) with frequency f(x) and amplitude of 1g and want to receive the same sinewave f(x) with amplitude of 1g at the corresponding output. The other both outputs may not vibrate with f(x) more then 0.1g (-20db) but with their "own" frequency f or f(rot) given by input 2 and 3(rot). Unfortunately every input generates signals in the other two dimensions.

In theory I do not receive this cross excitation, but in practice it is impossible to avoid it. I just want to keep it under a certain level to receive tolerably signals at the steering wheel.

I measured every channel seperately and received 9 transfer functions - but I do not know how to treat my signals to filter them.


phono

 

[GregLocock]

"In theory I do not receive this cross excitation, but in practice it is impossible to avoid it."

I think you don't understand what you are doing, quite.

If you apply a force in X and measure the response elsewhere, generally there will be a response in all 3 directions. For a few frequencies there may be no response at a particular frequency in a particular direction, but generally that is not so.

I think aiming for -20 dB crosstalk is admirable but not easily achievable for typical steering systems. I strongly suggest that you do a modal analysis of the system rather than trying to solve this by a brute force approach.




Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[phono]

I solved the problem.
It was rather quite easy. Instead ov inverting the transfer function for creating an inverse filter impuls response I had to inverse the complete complex matrix containing the 9 transfer functions.
It works - when filtering first my input with this matrix I receive my desired output.

 

[MikeyP]

I assumed you were doing that anyway (is there another way?). HOwever, I don't think it will solve your "cross-talk" problem.

M

--
Dr Michael F Platten