s (4)

1 10

2 t  0, t2 *)

m2  − βt / 2   m20 − m2  ,

, t ≥ t2 *, ,  patV2

m2 m2 RT

m2 (t) 

γ RT , t2 *  2

β  V  p − p  β m20 − m2

20 at

2

However in the considered case the piston is moving and its actual position is not known. Assuming that in initial phase piston is moving very slowly and volumes of both chambers are not changed rapidly, after the time tk, (tk< t1*, tk< t2*), masses of air in both volumes will determine a new balance state for the piston, satisfying the balance conditions. In the case of equal surfaces A1=A2 case the piston stroke will be determined by a relation

x  λL − x , λ  m1(tk )

1  λ 10 m2 (tk ) (5)

xmax  mˆ

1

m2

This relation reflects a general remark: the static fill-ing/emptying action it is not sufficient to achieve any desired stroke x. A more general rule is necessary. The above rela-tions (4), (5) show that some rules for displacement can be derived. After initial displacement above calculation can be repeated for some new piston position x’.

Now let consider a situation, when the cylinder volumes have been filled/emptied by some time t1 and the piston is moving. After a time t2 the piston has achieved a new position x1k and a counter action has to be introduced in time interval <t2 , t3>. A calculation of t3 is necessary. After this time, when both volumes are filled with compressed air, the piston should stop without overshoot. For the filling action of both volumes is used the equation for the first chamber and finally

m1(t)  m*1k −  m*1k − m1 (tk ) − α t − t2 2 ,

m*1k   Pz   A1  x1k