The market is a controlled dynamic system. - page 148
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That's the way it always is. Came in, intrigued and bye.... Intriguer....
Victim of intrigue? Martyr?
A victim of intrigue? A martyr?
Just waiting.
So that there are no difficulties as in the oscilloscope example, this time we will use a domestic single burner tabletop electric cooker as an example.
I hope that everyone is familiar with this device and knows how to use it.
(Now I know that not all are technicians but more humanitarians and that's why for them the oscilloscope example is really difficult to grasp)
.
As you can see from the figure, the regulator on this tile has five positions: 0 - 1 - 2 - 3 - 4. (from "Off" to "Maximum").
Without going into questions of heat exchange with the environment, let's assume for certain that in these five operating modes set by the regulator, the electric heater is heated to a temperature of
0 -- "off"
1 -- 90 С
2 -- 100 С
3 -- 110 С
4 -- 120 С
Information given in the technical data: Warm-up time to operating temperature max. 6 minutes.
.
(I have adopted the heating temperature in various operating modes conditionally, both for convenience and for further actions with the model; the actual heating temperature may be determined experimentally, if necessary; in this case even if there are some differences, they are not very large and not fundamental).
The electric heater of this tile of ours can be described by a first-order differential equation, applying the Laplace transform to which we obtain its representation as a first-order aperiodic link:
here
time constant Te ≈ 2 minutes
gain k depends on the chosen mode of operation
.
Let's assume that the ambient temperature and with it the initial temperature of the heater is 15 °C.
Let us see how the heater heats up in the various modes:
.
0 -- "switched off".
.
1 -- 90 °C
.
2 -- 100 °C
.
3 -- 110 °C
.
4 -- 120 °C
.
We see that in each mode the warm-up time to operating temperature (falling within +/- 5%) is no more than 6 minutes, as specified in the data sheet.
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The electric cooker is decided upon. But the electric cooker is only a tool to achieve the goal. The goal is cooking. Now the next step is to boil potatoes on it.
Now let's get a bigger pot.
Stuff the potatoes so there's enough for the whole family. Fill the potatoes with water. And put the pot with the potatoes in the water on the electric stove.
.
Now let's get a bigger pot.
Stuff the potatoes so there's enough for the whole family. Fill the potatoes with water. And put the pot with the potatoes in the water on the electric stove.
.
And, of course, we remember that the water in the pot will boil when it reaches 100 °C. The water will not rise any higher - it will boil and boil over, but it will not reach more than 100 °C, although the temperature of the heater under the pot will be more than 100 °C. This is a natural temperature limitation.
The pot with water and the potato when heating and cooling down can also be described by a first order differential equation and represented by a first order aperiodic link
but with its own time constant and gain (depending mostly on the volume of the pot).
.
As a result, we have a system "electric stove_with_controller + pot_with_water_and_potatoes".
The following are significant from the potato boiling point of view
1. regulator - set point adjuster
2. electric heater - executing element
3. pan - control object
.
Let us now present this knowledge in the form of a block diagram:
.
Next, consider the process of boiling potatoes.
And, of course, we remember that the water in the pot will boil when it reaches 100 °C. The water will not rise any higher - it will boil and boil over, but it will not reach more than 100 °C, although the temperature of the heater under the pot will be more than 100 °C. This is a natural temperature limitation.
The pot with water and the potato when heating and cooling down can also be described by a first order differential equation and represented by a first order aperiodic link
but with its own time constant and gain (depending mostly on the volume of the pot).
.
As a result, we have a system "electric stove_with_controller + pot_with_water_and_potatoes".
The following are significant from the potato boiling point of view
1. regulator - operation mode selector
2. electric heater - executing element
3. pan - control object
.
Now, let's present our knowledge in the form of a block diagram:
.
Consider the process of boiling potatoes.
All very interesting, we have to go to the sources to remember the concepts:
"The pot of water and potatoes during its heating and cooling can also be described by a first order differential equation, and is represented by a first order aperiodic link
but with its own time constant and gain (depending mainly on the volume of the pot)."
All very interesting, I have to go to the sources to remember the concepts:
"A pot of water and potatoes when heated and cooled can also be described by a first order differential equation, and is represented by a first order aperiodic link
but with its own time constant and gain (depending mainly on the volume of the pot)."
It can be described. But it won't cook any better and it won't add any potatoes.
It can be described. But it won't cook any better and it won't add any potatoes.
If you look (think about it), that's not what we're talking about at all