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You develop Simulink models by constructing a diagram that shows the elements of the problem to be solved. Such diagrams are called simulation diagrams or block diagrams. Consider the equation y = 10f (t). Its solution can be represented symbolically as

This solution can be represented graphically by the simulation diagram shown in Figure 9.1-1 a. The arrows represent the variables y, x, and f. The blocks represent cause-and-effect processes. Thus, the block containing the number 10 represents the process x(t) = 10f(t), where f(t) is the cause (the input) and x(t) represents the effect (the output). This type of block is called a multiplier or gain block. The block containing the integral sign J represents the integration process y(t) = J x(t) dt, where x(t) is the cause (the input) and y(t) represents the effect (the output). This type of block is called an integrator block. There is some variation in the notation and symbols used in simulation diagrams. Figure 9.1-1 b shows one variation. Instead of being represented by a box, the multiplication process is now represented by a triangle like that used to represent an electrical amplifier, hence the name gain block. In addition, the integration symbol in the integrator block has been replaced by the operator symbol 1/ s, which derives from the notation used for the Laplace transform (see Section 10.5 for a discussion of this transform). Thus the equation y = 10f(t) is represented by sy = Wf, and the solution is represented as

Another element used in simulation diagrams is the summer that, despite its SUMMER name, is used to subtract as well as to sum variables. Two versions of its symbol are shown in Figure 9.1-2a. In each case the symbol represents the equation z = x .: y. Note that a plus’ or minus sign is required for each input arrow. The summer symbol can be used to represent the equation y = f(t) – 1Oy,
which can be expressed as y(t) = j[f(t) – lOy]dt
or as 1 y = -(f – lOy) s
You should study the simulation diagram shown in Figure 9.1-2b to confirm that it represents this equation. This figure forms the basis for developing a Simulink model to solve the equation.