Hi,

Maybe this is a straightforward problem/question, but i am not sure about how to proceed in the modeling of the following problem.
Let's consider the following two-dimensional control problem. There
are two objects, one larger one (M) and a smaller one (m). The large
object is placed at a horizontal surface with the assumption there is
no friction. The smaller object is on top of the larger object and
again friction is zero. However, the smaller mass is connected to the
large mass through a spring and a damper which are in the horizontal
plane. The initial position where also spring force is zero is when
the vertical center of the small mass is aligned with the center of
the large mass. Now, there are only four parameters which define this
system. The absolute position of big mass (M), let's call it (x1), the
absolute position of the small mass (m), which is( x2), the spring
coefficient (k) and the damping coefficient (d).
The input of the system we can control is position x1 and the
objective is to control the absolute position of x2.
The problem is how to write the state space representation and more
specifically what to do with x1, because this is the input to the
system. In case of most of these simple problems which are presented
in text books, the input is NOT position, but force. This would indeed
make the state space representation easy, but in reality (my
experimental setup) this is not the case. I can only feed a position
signal to the linear motor (which is the big mass M in this problem).
If I write the input vector u=[ x1 d/dt(x1)], I also have to control
the input speed d/dt(x1). But is this correct?

I appreciate all input!

Ewoud

Maybe this is a straightforward problem/question, but i am not sure about how to proceed in the modeling of the following problem.

I appreciate all input!

Ewoud