How to derive the space state form of this system?

[serbring]

Hi all,

I need to derive the space state form of this simple system:

http://imageshack.us/photo/my-images/856/system.png/

The two springs end are moving.

I derived the equation fo motion:

m*ddx_m+k_l*(x_m-x_l)+k_u*(x_m-x_u)+c_l*(dx_m-dx_l)+c_u*(dx_mdx_u)

where ddx_m is the mass acceleration
dx_m is the mass speed
xm is the mass position
x_l is the lower spring end position
dx_l is the lower spring end velocity
x_u is the lower spring end position
dx_u is the lower spring end velocity

My system has two inputs and one output and my problem is to understand how to manage them.

so I changed the variables in this way:
y₁=x_m
y₂=dx_m

and I derived the following equation:

dy₂=-y₁*(k_l/m+k_u/m)-y₂*(c_l/m+c_u/m)+k_l/m*x_l+k_u/m*x_u+c_l/m*x_l+c_u/m*x_u.

And this should be the A matrix:

A=[0 1 ;
-k_l/m-k_u/m -c_l/m-c_u/m]
How should I define the input matrix since I have speed and velocity in the input and they are related each other? Hopefully to have properly explained my doubt, if not don't hesitate to ask me please

 

[serbring]

Hi all,

I need to derive the space state form of this simple system:

http://imageshack.us/photo/my-images/856/system.png/

The two springs end are moving.

I derived the equation fo motion:

m*ddx_m+k_l*(x_m-x_l)+k_u*(x_m-x_u)+c_l*(dx_m-dx_l)+c_u*(dx_mdx_u)

where ddx_m is the mass acceleration
dx_m is the mass speed
xm is the mass position
x_l is the lower spring end position
dx_l is the lower spring end velocity
x_u is the lower spring end position
dx_u is the lower spring end velocity

My system has two inputs and one output and my problem is to understand how to manage them.

so I changed the variables in this way:
y₁=x_m
y₂=dx_m

and I derived the following equation:

dy₂=-y₁*(k_l/m+k_u/m)-y₂*(c_l/m+c_u/m)+k_l/m*x_l+k_u/m*x_u+c_l/m*x_l+c_u/m*x_u.

And this should be the A matrix:

A=[0 1 ;
-k_l/m-k_u/m -c_l/m-c_u/m]



How should I define the input matrix since I have speed and velocity in the input and they are related each other? Hopefully to have properly explained my doubt, if not don't hesitate to ask me please

none can help me?