(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A single wheel cat moving on the plane with linear velocity v angular velocity [tex]\omega[/tex] can be modeled by the nonlinear system:

dpx/dt = v*cos([tex]\theta[/tex])

dpy/dt = v*sin([tex]\theta[/tex])

d[tex]\theta[/tex]/dt = [tex]\omega[/tex]

where (px,py) denote the cartesian coordinates of the wheel and [tex]\theta[/tex] its orientation. The system has input u=[v [tex]\omega[/tex]] '.

Construct a state-space model for this system with state

*note: These are both 3x1 matrixes.

[x1] = [[px*cos([tex]\theta[/tex]) + (py-1)*sin([tex]\theta[/tex])]

[x2] = [-px*sin([tex]\theta[/tex]) + (py-1)*cos([tex]\theta[/tex])]

[x3] = [[tex]\theta[/tex]]]

and output y = [x1 x2] '

2. Relevant equations

dpx/dt = v*cos([tex]\theta[/tex])

dpy/dt = v*sin([tex]\theta[/tex])

d[tex]\theta[/tex]/dt = [tex]\omega[/tex]

3. The attempt at a solution

I don't have much. I'm pretty sure to put the given state into a state-space model I will take the derivative of both sides of the system with respect to t. If that's the correct method, I guess I'm not sure of how to take the derivative of the right side with respect to t since I know the velocity and acceleration functions are functions of time, but the stated system doesn't explicitly show the variable t. Any ideas anyone?

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# Homework Help: Help constructing state-space model of a system

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