The expansion of the transfer function into the simplest units.
In some cases, you want to lay out the transfer function of a dynamic link in the simplest reinforcing links and integrators, for example, to program the ratio denominator in MATLAB Simulink.
Figure 26 shows the decomposition of the transfer function of the second order on 6 amplifier units 3 and 3 integrator adder. In reinforcing the links are written on top of the corresponding coefficients of the numerator, and the bottom - the coefficients of the denominator, with instead of the coefficient of the highest degree of the polynomial is written it the opposite meaning.
Figure 26. Block diagram of the test unit
Solution of the system of differential equations.
The problem solved by this type of transition from the AU to control and block diagram, with its subsequent modeling. To construct the block diagram consistently put combiners that implement the equation, the output of which is considered to be known. Additionally put integrators, allowing to reduce the order of differentiation.
For example, the system controller is specified as (14):
Then the structural diagram of the system takes the following form (see. Figure 27).
Figure 27. Block diagram of implementing a system of differential equations
Obtaining of differential and algebraic equations for 3-order system, the input and output of which are noise.
See part 6 «The matrix mathematical model of the system».
Block diagram of the system model is as follows:
Performed sequentially numbered elements of the system:
Make up matrix mathematical model of the system, with separate columns introduced for the U and V:
Thus, submatrices are obtained by the mathematical model of the matrix:
As a result, the system of differential and algebraic equations using matrices obtained will be: