The  groups of basic physical elements are classified into three categories: Generalized resistor:  examples  of this category are;  electric resistor,  mechanical damper, and hydraulic resistor. Generalized capacitor:  examples  of this category are; electric capacitor, mechanical spring, and hydraulic reservoir. Generalized  inductor  examples  of  this category are;  electric inductor, mechanical mass, and hydraulic inductor. Breaking  down  the  physical  system into subsystems and further into basic elements will provide us with a sharp insight about the evolution  of  the  physical  quantities within each subsystem,  yielding  to better understanding of the modes and the states that each subsystem would attain.  The advantages  of  having such insight  will become visible during the design phase of a local control system. 

Modelling can be considered as the opposite procedure of decomposition. The difference is that,  in  decomposition,  we  pide  the system into independent  physical  entities, while in modelling we reconnect the models of  these  physical  entities. Therefore, modelling can be seen as the  procedure of connection.

In modelling, we start at the bottom level of this  hierarchy and  move upwards. At  each level, we  propagate from a primitive system model to a connected system model. In the succeeding  level,  the primitive  system model would  then  be  established  by aggregating the  connected system models from the former level as shown in Figure 4.

 At  the bottom level of  each subsystem, the primitive system model will  be  established by  utilizing the governing equation  or  the fundamental law of each inpidual element. That fundamental law, such as Newton's law or Ohm's law,  describes the  local behavior of that  element. Direct  and  indirect connections that resemble  the  internal constraints within the boundaries  of  each subsystem  define the  transformation from the primitive system model to the connected system  model.  For  systems with linear connections such  as  direct current servomotor,  the  internal  constraints  are given by one connection object, the velocity object  (V).  The  velocity object is  a  2- dimensional array, the rows  in  that array correspond to the variables in the  primitive system  (local  variables)  and  the columns correspond to the variables in the connected system (global variables). Thus, the velocity object  is a  transformation  from  the global variables in the connected system model to local  variables  in  the  primitive  system model. 

The model of the physical system is set up by  aggregating diagonally  the  connected system models of the hydraulic subsystem and  the  boring  spindle. Modelling the physical system  resulted in a  set  of different all algebraic equations [7]. In a state space  form,  the  behavior  of  the  physical system is given by: y = ~ ( A , x , u , ~ )  Where ( x )  is the set of initial state variables, ( u )  is the  set  of input  sources,  ( A )  is the state transition  matrix for the physical specific control function of truth or falsehood (1 0). 

3.2  Control System Modelling 

Before a control algorithm can be designed and implemented we  need a description of its required properties or behavior. A precise and comprehensive mathematical model of the properties of the control system could be expressed by employing logic notation. This mathematical model provides us with means to reveal the  inconsistency and conflicts in the control  system  and  to  verify that the control system meets design specifications. In  order  to carry out  all  control functions outlined  in problem description, the control system  should  be  decomposed into three subsystems.  A  process controller subsystem, which  will be  responsible to issue start  and  stop  commands  for  the different physical entities and two continuos controllers. One  controller  for  the servo valve in the hydraulic subsystem in order to regulate  the feed forward motion  of  the hydraulic actuator. The  second controller is for the servomotor  in order to regulate the angular  speed  of the  spindle motor.  The decomposition is shown in Figure 5.