The  functions  of  each subsystem  are described by a set of logical arguments or rules. Each of these logical arguments could be considered as a subsystem that can be decomposed further  into a  number  of factious logical elements.  These elements could be literally anything that could carry a logical variable that assumes either the stateof truth or falsehood (1 0). These elements represent the  primitive system  model of  aspecific control function.The  procedure  of  modelling the  control system  will  also move upward  along  the hierarchy until a total model is obtained  as shown in Figure 6.

 In  the  primitive  system model, the connections between the  logical  variables are defined by three connection objects.  In classical logic, they are referred to as basic logical  connectives.  The  group  of basic logical  connectives includes;  conjunction (AND) ,   disjunction  (OR), and  negation (NOT).  We  propagate  to  the connected system  model  by  aggregating the  logical variables  in the  primitive system  using the above logical connectives. A  connected subsystem is nothing else but the truth table  of a logical argument expressed in a multi-dimensional array form. The number of axes in that array should be equal to the number of variables, therefore all repeated axes must be fused together by the  method  of  colligation. The connected system expresses all the possible states  of the  system  after  imposing the  internal constraints on the  structure  by  connecting its inpidual elements. The behavior of the control system could be represented in the following form s = f( p ,  , i , n )  . Where,  (0) is a set of input variables that is external constraints due to  interaction with the environment. (P,) is the  state transition matrix  of  the  control  system  expressed in multidimensional array format. (s) is a set of output variables. The index ( n )  is analogues to a time index in that it specifies the order of a given state.

3.3  Model of The Total System 

Since both systems utilize different types of signals  internally, then intuitively speaking, the  only  possible  interface between  the physical and  the  control  system model will take place externally, through  the environment  by means of  the  impressed sources.  In  the above  manufacturing system,  we  can  distinguish between  two ways of interface between the  physical and the control system. Discrete interface:  takes place  in  the process controller when the purpose of the control system  is  to  coordinate asynchronous tasks to  satisfy  system requirements. For example,  when an event command "start the spindle motor" is issued by the process controller, the spindle motor starts rotating. The process of rotation itself is controlled  by the  lower level controller (continuos controller). Continuous interface: takes place locally on lower level control  schemes when  the purpose of the control system is to keep the behavior of the physical system within given boundaries such  as  implementing  speed control. The  resultant system model in this case  is said to be a  hybrid  system model. The  identifying  characteristics  of  hybrid systems  are  that  they incorporate  both continuos dynamic  behavior,  i.e.,  the evolution of physical quantities governed by differential and  algebraic equations ( y = f ( A , x , u , r )  ),  and discrete event dynamic behavior  governed  by  logic equations: ( s = f ( p ,  , i , n )  ). A total model can be obtained by generating a  simple interface  between  the  physical system model  and the control system model. The  interface will be  consisting  of two  simple  memoryless  mapping functions ( a  ) and ( p )  [l]. The first map ( a  ) converts the controller output  (s)  into  a  constant incremental input to the physical system as follows:  u ( i )  = a ( s n )  The second map ( p )  converts the  physical system  output  into a  set  of  input logic variables to  the  control system as  follows: i= p ( y ( r ) ) ,  as shown in Figure 7.