On Dec 26, 2:22 am, "Eilersen" <s021...@student.dtu.dk> wrote:
> Hi Peter
>
> I am not sure of what you mean by "Gain of the mass and spring"?
I was assuming a more general case for the transfer function for the
mass and spring.

T(s)=(gain*omega^2)/(s^2+2*zeta*omega*s+omega^2)

If you can assume the gain is one then you are in good shape.  Then you
know the amplitude of the response is only due to the amplitude of the
forcing function.   That makes your job much easier.

Download Scilab and try out the lsqrsolve function.

Peter Nachtwey

Hi Peter

Thanks againfor your reply. 
I do not carer about variable 1, 2 and 3 in the control signal, but I can
calculate them. 
I do care about variable 4 in the control signal as this is the number I
am trying to estimate very accurate.

I am not sure of what you mean by "Gain of the mass and spring"?

The damping factor I can estimate. 

The Natural frequency can be estimated aswell, but only when the control
signal is zero. When the control signal is non zero the natural frequency
will change and the transfer function will therefor change. That is why
the system is non linear. That is also what I mean when I write it in the
frequency domain as Y=H(x)*X, because the natural modes of the system 
(H(x)) changes with the input/control  signal.

Thanks

Tom

Can you measure the control signal directly?  The control signal only
has four variables.
1. The time to ramp up
2. The time the signal is at a constant level
3. The time to ramp down
4.  The amplitude of the constant level.

The mass and a spring has only 3 variables
1  Gain of the mass and spring.
2. damping factor
3. Natural frequency

The only problem I see is separating the gain of the mass and spring
system from the amplitude of the control signal.   I don't see how any
method can do that.   You really need to know the model for the mass
and spring or at least the gain.    Otherwise you will need to measure
the control signal directly and find the trapezoidal ramp parameters
that best match the measured data.  One of the two 'gains' must be
known.

Peter Nachtwey

>"Eilersen" <s021985@student.dtu.dk> wrote in message 
>news:WrSdnfcXPbfxHBPYnZ2dnUVZ_rCsnZ2d@giganews.com...
>> Hi
>>
>> I have an application where I would like to estimate the forcing
function
>> in a second order mechanical system (Can be modeled as a mass on a
spring
>> with a forcing function applied).
>>
>> I have noisy measurements of the position of the system.
>>
>> I have seen a lot of litterature about how to estimate the exact
position
>> of the system, but I have not been able to find anything about how to
>> estimate the forcing function?
>>
>> Anybody who have seen a paper about this or tried it?
>>
>> Thanks in advance and merry christmas and happy new year when we get
to
>> that.
>>
>> Tom
>>
>Are there any constraints on the forcing function or can it be anything?

>If the forcing function has constraints so it can be characterized by
just a 
>few parameter then there is a chance.   You don't need a Kalman filter if

>you can do this as a batch process and use a least squared minimizing 
>algorithm such as Levenberg-Marquardt.  Scilab has a lsqrsolve that does

>this.   The LM algorithm will find the parameters of the forcing function
by 
>minimizing the sum of squared errors.  If you have enough data the
algorithm 
>will find what the forcing parameters are statistically.
>
>Normally one changes the output and you measure the response to determine

>the system model.  However, if you have the model you can work it the
other 
>way around and determine the forcing function as a function of the
response 
>and the model.
>
>Peter Nachtwey
>
>
>

Hi Peter

Thanks for your reply. There is a constraint on the forcing function. It
will either be a trapez (a step with a ramp in each end) or a trapez with
a sinusoid added. 

As I have understood your answer correct then you want me to solve an
inverse problem with LMS or a deconvolution. The only problem is that the
model of the system depends on the input. The system can be modeled as a
mass on a spring, but the forcing function will add an extra mass to the
system which changes the system model so in the frequency domain you can
write the convolution as: Y=X*H(x). I believe this can be solved by
blinded deconvolution, but I am not sure if I can handel this with the
computation power I have available (the application should run in real
time). 

My idea was to try the extended Kalman filter as the system is non linear
or try an approximation and assume the system is linear and use the kalman
filter.

I will take a look at the Levenberg-Marquardt algorithm. Thanks


Tom

"Eilersen" <s021985@student.dtu.dk> wrote in message 
news:WrSdnfcXPbfxHBPYnZ2dnUVZ_rCsnZ2d@giganews.com...
> Hi
>
> I have an application where I would like to estimate the forcing function
> in a second order mechanical system (Can be modeled as a mass on a spring
> with a forcing function applied).
>
> I have noisy measurements of the position of the system.
>
> I have seen a lot of litterature about how to estimate the exact position
> of the system, but I have not been able to find anything about how to
> estimate the forcing function?
>
> Anybody who have seen a paper about this or tried it?
>
> Thanks in advance and merry christmas and happy new year when we get to
> that.
>
> Tom
>
Are there any constraints on the forcing function or can it be anything? 
If the forcing function has constraints so it can be characterized by just a 
few parameter then there is a chance.   You don't need a Kalman filter if 
you can do this as a batch process and use a least squared minimizing 
algorithm such as Levenberg-Marquardt.  Scilab has a lsqrsolve that does 
this.   The LM algorithm will find the parameters of the forcing function by 
minimizing the sum of squared errors.  If you have enough data the algorithm 
will find what the forcing parameters are statistically.

Normally one changes the output and you measure the response to determine 
the system model.  However, if you have the model you can work it the other 
way around and determine the forcing function as a function of the response 
and the model.

Peter Nachtwey

Hi 

I have an application where I would like to estimate the forcing function
in a second order mechanical system (Can be modeled as a mass on a spring
with a forcing function applied). 

I have noisy measurements of the position of the system. 

I have seen a lot of litterature about how to estimate the exact position
of the system, but I have not been able to find anything about how to
estimate the forcing function?

Anybody who have seen a paper about this or tried it?

Thanks in advance and merry christmas and happy new year when we get to
that.

Tom