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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.