Download the master file, unzip it to a place on the hard disk easy to find (I recommend the root of the hard disk, or a folder called c:/temp), and from inside the folder run:
ipython notebook
You'll be fine from there...
A system can behave in many ways, output variables can have different goals, for example:
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from IPython.display import SVG
SVG('img/intro_fig1.svg')
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Almost every aspect of everyday life is affected by some kind of control system.
The basic elements of a control system are:
Purpose of the control: To control the outputs c in a predetermined way, by means of the inputs u and the control system.
Feedback: Its function is to reduce the error between the reference input and the output. It also ensures stability.
Plant: is the combination of process and actuator. A plant is often referred to with a transfer function (in the s-domain) which indicates the relation between an input signal and the output signal of a system without feedback, commonly determined by physical properties of the system.
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from IPython.display import SVG
SVG('img/intro_fig2.svg')
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Example: A washing machine. The wash cycle is determined by the user's criteria. There are no sensors that measure the degree of cleaning of clothes.
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from IPython.display import SVG
SVG('img/intro_fig3.svg')
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Uses feedback from the output to the input.
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from IPython.display import SVG
SVG('img/intro_fig4.svg')
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For example, what happens in an elevator in both cases? And in the system of opening and closing of a door?
The feedback has the following goals:
Many times a physical plant can have feedback when analyzed in detail. When the variables of a system exhibit a closed sequence of cause and effect relationships, the system has feedback (input and output are related). For example, for the system:
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from IPython.display import SVG
SVG('img/intro_fig5.svg')
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It can be shown that its transfer function is:
Effect of feedback on gain: From the above equation it is observed that the gain of the system is affected by a factor of $1+GH$. $G$ and $H$ are functions of the frequency, so that the gain can increase in some frequencies and decrease in others.
Effect of feedback on stability: Stability is a concept that indicates the ability of a system to follow a control input. A system is unstable when its output is out of control or increases without limits. Again let's look at the equation when $GH = -1$. The output of the system is infinite for any finite input. Therefore, it can be said that feedback can cause instability in a system. It should be noted that this is not the only condition of instability.
If the plant has $GH = -1$, and it is inevitable, it is possible to add another feedback loop, obtaining a new transfer function. Therefore, the global system can be stable if $F$ is properly selected.
In [6]:
from IPython.display import SVG
SVG('img/intro_fig6.svg')
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In general feedback has effects on performance, bandwidth, impedance, time response and frequency response.