Gyroscope simulation using State space

I have to simulate a gyroscope using Statespace or TF but I dont get how!

I need to solve this task with the C lvl which is the SS model

Answer 1

[Sam Chak]

Hi @Saleem Jallet,

You didn't provide the transfer function of the gyroscope with sensor dynamics.

In short, you need to provide the mathematical part for the modeling problem, so that we can show you the technical part of MATLAB. Anyhow, here is an example of simulation:

If a system is given by , where , , then the transfer function probably looks like this:

s  = tf('s');
Gp = 1/(s^2 + 2*s + 1)

Gp =
 
        1
  -------------
  s^2 + 2 s + 1
 
Continuous-time transfer function.

step(Gp, 10)

The state-space model can be obtained by making a conversion from the transfer function.

sys = ss(Gp)

sys =
 
  A = 
       x1  x2
   x1  -2  -1
   x2   1   0
 
  B = 
       u1
   x1   1
   x2   0
 
  C = 
       x1  x2
   y1   0   1
 
  D = 
       u1
   y1   0
 
Continuous-time state-space model.

As expected, the simulation of the state-space should produce the same result as the step response of

step(sys)

[Saleem Jallet]

the problem is I dont know the dynamics of the gyroscope sensor

[Saleem Jallet]

from the question I'm thinking that the TF is (K)/(Ts+1) ie the tf = 10/(0.2s+1)

but then the ss is simple

[Sam Chak]

Hi @Saleem Jallet

Based on the "possible sensor parameters", it suggests that a 1st-order system:

s = tf('s');
H = 10/(0.2*s + 1)

H =
 
     10
  ---------
  0.2 s + 1
 
Continuous-time transfer function.

From the "possible noise parameters", the hints suggest the Gaussian Noise Model.

You can check the following:

https://www.mathworks.com/help/comm/ref/wgn.html

https://www.mathworks.com/help/comm/ref/awgn.html

https://www.geeksforgeeks.org/how-to-add-white-gaussian-noise-to-signal-using-matlab/