## Physical system modelling

DashPi
Posts: 13
Joined: Tue Jun 10, 2014 8:16 pm

### Physical system modelling

I recently developed a new app. (LTI) for physical system modeling from a set of coefficients. I'm already working on some variants with embedded system design tools and have in mind porting it to FPGA. Any suggestions regarding the FPGA implementation?

DashPi
Posts: 13
Joined: Tue Jun 10, 2014 8:16 pm

### Re: Physical system modelling

Here is how the app. looks like:

DashPi
Posts: 13
Joined: Tue Jun 10, 2014 8:16 pm

### Re: Physical system modelling

Here's the example of the harmonic oscillator modelling and step response:

Crt Valentincic
Posts: 67
Joined: Wed May 28, 2014 12:15 pm

### Re: Physical system modelling

Nice work!

fisafisa
Posts: 29
Joined: Fri Jun 06, 2014 6:02 pm

### Re: Physical system modelling

What about a state space model?
X(t+1) = A X(t) + B U(t)
Y(t+1) = C X(t) + D U(t)

U and Y are 2 value vectors
X is n values (let's say 20)
A is square matrix describing system dynamics
B and D are 2 * 20 matrices
C is 20 * 2 matrices

With this model you can describe any (limited to X size dynamic order) 2x2 linear system

Nice work!

DashPi
Posts: 13
Joined: Tue Jun 10, 2014 8:16 pm

### Re: Physical system modelling

Thanks Črt and fisafisa.

The state space is certainly an option. Any DSP code can be simply added to the file
https://github.com/dashpi/RedPitaya/blo ... fpga_lti.c
from line 367 on and compiled.
Arrays cha_state, chb_state or other arrays can be used to register the state X, while the arrays
cha_dsp_par, chb_dsp_par can be used to pass the system parameters ABCD.

In SS you can even extend the app. to a 2x2 MIMO by using both inputs and outputs.

I think with SS is more convenient to pass the matrixes through files.

bingoiceono
Posts: 5
Joined: Thu Jun 19, 2014 9:21 am

### Re: Physical system modelling

This is a great app.
I have one question. When I set a0 and b0 to 1 and others be 0. Is there must be some gain on the signal? The output I got is about 2 times than the input

Rudolf
Posts: 1
Joined: Wed Jul 23, 2014 8:14 pm

### Re: Physical system modelling

Great app!
@bingoiceono: On my Redpitaya it works fine even with your filter settings. The signals have equal amplitudes. I'm using one of the Redpitaya outputs to generate the input signal + "generate" command. How are you feeding your Redpitaya input?

bingoiceono
Posts: 5
Joined: Thu Jun 19, 2014 9:21 am

### Re: Physical system modelling

I use an external signal generator and oscilloscope to test it. Signal generator outputs signal to the RP's input port and the oscilloscope. The programmed RP signal is also connected to the same oscilloscope.

DashPi
Posts: 13
Joined: Tue Jun 10, 2014 8:16 pm

### Re: Physical system modelling

bingoiceono, have you checked impedance settings of oscilloscope inputs and signal generator (50 ohm / HIZ)? Sometimes wrong impedance selection may produce voltage drops.

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