Example H2.1
MATLAB code for example 2.1 from the book "Regeltechniek voor het HBO"
Find the transferfunction by making a block diagram
- Date : 31/03/2022
- Revision : 1.0
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Table of Contents
Making a block diagram of a first order proces
Often, a block diagram of a control loop is designed so that each block represents an essential part of the total system.
Since a block diagram is a mathematical model, a block diagram can also be used to easily arrive at a transfer function of the total system. This will be explained using the liquid level system of figure 2.23. The corresponding basic equations were:
and 
and also 
is the input signal (the flow) and 
(the level) we consider to be the output signal. Each part of the equations can be "translated" into a part of a block diagram in the form of a block, branch point, or addition or subtraction point. Substraction block
The expression 
is represented in the block diagram by a subtraction point (see figure 2.35a).
is represented in the block diagram by a subtraction point (see figure 2.35a). Multiplication blocks
After multiplying by 
, this gives B(s) (see figure 2.35b). So that is the output signal.
, this gives B(s) (see figure 2.35b). So that is the output signal. Multiplying that in the feedback by the constant 
then gives the signal 
. This is shown in figure 2.35c.
then gives the signal . This is shown in figure 2.35c. Conclusion
Thus, we see that the first-order process
can be constructed from a feedback system, namely that of an integrator.
Indeed, in the time domain, the transfer function
means that the input signal is integrated over time and multiplied by 1/A .
Thus, a first-order process appears to be able to be understood as a feedback-coupled integrator. The final, most simple block diagram, is shown in figure 2.35d.