
#1
Sep611, 03:23 AM

P: 165

Hi all,
I need to derive the space state form of this simple system: http://imageshack.us/photo/myimages/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_{m}dx_{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: y_{1}=x_{m} y_{2}=dx_{m} and I derived the following equation: dy_{2}=y_{1}*(k_{l}/m+k_{u}/m)y_{2}*(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}/mk_{u}/m c_{l}/mc_{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 



#2
Sep1011, 07:42 AM

P: 165




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