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. 机电一体化模型英文文献和中文翻译(4):http://www.751com.cn/fanyi/lunwen_63193.html