Decomposition:  in  order to handle  the complexity  of  mechatronics systems,  they should  be  decomposed  into  subsystems. This decomposition  is carried  out  on  a multilevel fashion  until we  reach  the  basic elements that constitute the total system. The primitive system model: is a description of  the  system  in the disconnected state.  It expresses  the  relation  between  the variables  in  the  inpidual  elements  when the bonds between these elements are removed. By this model we isolate a specific behavior; static, dynamic,  etc.,  in  each element. A pair of local variables defines the behavior of a given element locally. The  Connected  system  model:  is  a description of the  same system after taking the  internal  constraints  into  account.  The internal constraints  within  the  system are given  by  the  way  the  local  variables are connected  or  related directly as well  as indirectly by the  variables of the connected system. The connected  system  model resembles  the  actual structure of  the real system. 

The applied sources are generated due to interaction  between the  system  and  its environment.  They  could  be  seen as  the external constraints imposed on the system or  even  inherent constraints in the form  of stored energy in system elements.

3.  APPLICATION EXAMPLE 

Consider, the manufacturing system shown in Figure 2. 

 The system consists of a boring spindle powered by  a  direct current  motor. The  feed forward  motion  of the  boring spindle is carried out  by means  of a hydraulic linear actuator.  The  hydraulic actuator is powered by a constant pressure hydraulic pump. The volumetric flow  in the hydraulic  circuit  is  controlled  by  a  servo valve [8].

The  above  manufacturing system has  the following specifications: The  positions of  boring spindle are sensed by three micro breakers. Breaker ( B )  which indicates that the  boring  spindle is  at  the rear position. At  the  rear position the rapid phase valve ( I )  will be switched on in order to allow a rapid forward motion ( F )  and the signal (S) will  switch on the spindle motor. Breaker (M) indicates that the boring spindle has reached  the  feeding  position.  At  this position the rapid phase valve  will  be switched  off  in order  to  start a controlled feed  forward motion. This  motion  is regulated by  the servo valve  (St). Breaker (€) which indicates that the  boring spindle has reached its final position, at this position and the  backward  motion  ( R )  will begin, simultaneously the rapid phase valve ( I )  will be  switched on  in  order to allow  a rapid backward motion. It is also specified that the rotating speed of  the spindle  motor should be kept at 3000 rpm. during boring the work piece and the feed forward speed must be kept at 2cm/sec under all loading conditions. Our objective is to set up a complete model of the given system using multidimensional arrays and  to  carry  out  necessary experiments on  the  model  to  verify  that specifications are satisfied.

3.1  Physical System Modelling 

When  modelling physical  systems,  we  are concerned with modelling the evolution  of the  physical variables that lives within  this system. The  decomposition of the  physical system is shown in Figure 3.