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Control

One of the most important structures uses feedback along with filters to control the behavior of a process. control

A control loop consists of one or more decisions that test some characteristic of the system against certain limits and redirect the system's processes depending on the outcome of the tests.

Flow control, which is shown here, is a common application. A source sends a flow into a process which outputs another flow, in this case to a sink. The process can be measured ... we might, for example, measure temperature or weight or viscosity.

A set of decisions tests the measurement against certain limits. If the limits are exceeded, then new processes are called into effect. If the limits are not exceeded, nothing needs to be done. The "nil" box in this diagram expresses that condition.

Heating a Room

In this example a furnace produces heat which flows into a room. The room is not completely insulated, and so it steadily leaks heat into its environment. The furnace can be turned on and off. So when the furnace is on, the room gets warmer, and when the furnace is off, the room gets cooler. The control device will monitor the temperature of the room and turn the furnace on and off as needed.

heat

A measuring device in the room communicates the temperature to a pair of control loops. The first loop turns the heat off if the temperature is more than 75 degrees. The second turns the heat on if the temperature is less than sixty degrees. (Since the temperature cannot be both greater than 75 and graph heatless that 60 at the same time, only one control loop can be in effect at any one time.) In this way the control loops monitor the room temperature and use it to direct the behavior of the furnace.

The output of this kind of control mechanism will never get much higher than the first limit, nor will it get much lower than the second limit. As the graphs shows, in this model the temperature of the room will cycle from a low of 60 to a high of 75.

 

Sensitivity

Suppose the lower temperature setting is raised from 60 to 70. How might that change the output of the heating system? graph heat 2The upper limit would stay the same, but the lower limit would rise. This should mean that the graph would show less variation ... the highs and lows should come closer to being on a straight line.

It might seem that we could control this system absolutely. In other words, suppose we raised the lower control setting to 75. Then the high and low would be the same, and the room would always stay at exactly 75 degrees.

But we would be mistaken.

The model is a description of what happens in the room. We can imagine that by changing the model we can also change the room, but that may not be true.

In this case, it takes TIME for the heater to turn itself on and off. And when it does switch on or off, it takes even more time for the flow of heat to build up to its maximum or drop to zero. Because of this, there is a physical limit to our ability to control the system. We can experiment to find out what that limit is, but we cannot arbitrarily dismiss it.

Exercise

The previous diagram shows how the room behaves in the winter when it is colder than 60 degrees outside and heating is needed. Create a new diagram that shows how the room might be air conditioned in the summer when the temperature outside is hotter than 75 degrees. Assume that we are willing to let the room heat up to 85 degrees.

Exercise

If you did not do so already, combine the heating and air conditioning diagrams into one diagram. You can find my diagram of this system here ... but I urge you to draw your own first ... you will learn more by working it out on your own.

Remember This

By measuring a process and testing the measurement against limits, we can control the behavior of a system.

 

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