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Building Controls VProportional and PID Responses

Energy University Course Transcript

Slide 1Welcome to Building Controls Part V: Proportional and PID Responses. This is fifth course in the building controlsseries. If you have not already done so, please participate in Building Controls one through four, prior to taking thiscourse.

Slide 2For best viewing results, we recommend that you maximize your browser window now. The screen controls allow youto navigate through the eLearning experience. Using your browser controls may disrupt the normal play of the course.Click the Notes tab to read a transcript of the narration.

Slide 3At the completion of this course, you will be able to:

Define the proportional control response

Explain the addition of integral and derivative terms to form PI (Proportional + Integral) and PID(Proportional + Integral + Derivative) responses, and you will be able to

Explain the appropriate use of each control response

Slide 4Proportional control is a simple and widely used method of control for many kinds of systems. Proportional Integral- Derivative control, also called PID control, is somewhat more complex and may be suitable in certain situations. It isimportant to note that P, PI, and PID can be used in different applications and using each one has its advantages.

As we will see, there are cases where using all P+I+D is not the best application.

Slide 5Proportional control involves giving a response proportional to the stimulus. To say that less technically, the warmer itgets in a certain range of temperature, the more cool air we put in. So, for instance, looking at this sampleproportional response table for a cooling application, at 22.8oC we might have cool air flowing to a room at 1,360cubic meters per hour. If the room happens to be in the US, at 73oF we would have 800 cubic feet per minute of coolair.


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However, if the temperature were to increase to 23.3oC or 74oF, I might proportionally adjust my air flow to 1,760cubic meters per hour or 1,036 cubic feet per minute.

Each of these steps are at 200 cubic meters per hour or 118 cubic feet per minute, so the higher the temperaturegets, the greater my system responds to it, and the more airflow is produced. Drawing this table as a chart shows youthat the response is proportional to temperature.

Slide 6

You can think of proportional control as control that follows one simple rule, e.g. For every degree of temperaturedifference from the setpoint, increase the airflow by a certain amount.

This equation represents the rule:

Output = [degrees from setpoint] * [amount of air]

Output equals degrees from setpoint multiplied by amount of air

The controller will apply this rule repeatedly by:

Checking the sensor

Changing the airflow if necessary

Waiting a fixed time, and then

Repeating as necessary

Slide 7The control can be adapted by adding more terms. You can think of this as adding more rules to follow. When anintegral component is added, there will now be two parts in the control calculation, the proportional part plus theintegral part.

When a derivative component is added, the control calculation will now have three parts.


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Slide 8Simply put; our proportional control term (Output = [degrees from setpoint]*[amount of air]) has more terms added toit to become this equation:

Output = Pout+ I out+ Dout

Slide 9We already saw the proportional responseit is the simplest to understand. Proportional response is addressinghow far from set-point the variable is.

As already mentioned, the response of the system is proportional with how far the measured variable is from thedesired set-point of that variable. The response increases as the offset increases. The proportional term tells thesystem how much change to make to get back to its setpoint.

Hence, the first rule we mentioned before For every degree of temperature difference from the setpoint, increase theairflow by a certain amount as demonstrated in this equation:

Output = [degrees from setpoint] * [amount of air]

Slide 10The integral, when included, addresses how long the variable has been away from the setpoint. Simply put, in acooling application, if the variable has been above the setpoint too long, more cool air should be delivered than whatthe proportional response is telling the control system to perform.

Slide 11

So, with PI control we now have two rules. The new rule which is added to the first one might be For every minute oftime and degrees of difference from the setpoint, adjust the airflow by a certain amount. Which is demonstrated inthis equation

e.g. Iout= [time and degrees from setpoint calculation] * [air adjustment]

Combining the P and I gives two rules in one control algorithm:Output = ([degrees from setpoint] * [amount of air]) +([time and degrees from setpoint calculation] * [air adjustment])


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Slide 12The [time and degrees from setpoint calculation] is an integral.

The mathematical symbol for it looks like this .

The graph shows you visually how the integral is calculated. It is represented by the yellow filled in area between thetracking of the temperature and the setpoint. At each of these measurement points, the time duration betweenmeasurements is multiplied by how far the variable is from the setpoint, thus giving us the time and the intensity ofseparation between the variable and the setpoint. All of these measurement points are added up and create anadditional load that, when included in calculations, tell the controller that more of a push is needed to get the systemback to setpoint.

Slide 13The derivative component, when included, addresses how fast the variable is approaching its setpoint. It is

compensating for the speed of response. If we were measuring temperature, this would be how fast the temperatureis falling per second.

So, with PID control we would have a third rule to add to the first two. Something like If the temperature is rising at 2degrees per minute, add a certain amount of more airflow. Or If the temperature is falling at 4 degrees per minute,decrease a certain amount of airflow. A more general way to say that might be For every degree per minute ofchange, adjust the air flow by a certain amount.

The derivative

component


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Here is how it would look in an equation:

Dout= [rate of change calculation] * [another air adjustment]

Slide 14Combining the P, I and D gives three rules in one control algorithm:Output = ([degrees from setpoint] * [amount of air]) +([time and degrees from setpoint calculation] * [air adjustment amount]) +([rate of change calculation] * [another air adjustment amount]).

Whats the value of adding the derivative? The derivative calculation might notice that the temperature was fallingquickly, and the system is approaching its setpoint, so it would reduce the total to make the change more gradual andavoid overshooting the setpoint. Avoiding overshoots can be important in a system where only heating or cooling isenabled.

Slide 15Imagine that it is the summer, and the heating system for the building is completely turned off. You enter a room thathas been too hot for quite a while. Someone turns the control system on. The proportional and integral terms willdrive a lot of cold air to the zone.

If the zone becomes overcooled due to overshooting the setpoint, you will need to wait for it to heat back uppassively. You will not be able to force the temperature variable upward.

Slide 16In general, P relates to the present offset, I relates to the accumulation of past offsets, and D predicts future offsetsbased on the current rate of change. By tuning the three terms in the P-I-D controller you can provide control actions

that are adapted for the requirements in terms of responsiveness when an offset is detected and the degree to whichthe controller overshoots the setpoint.

Slide 17Adding integral and derivative components is only necessary if there is a need that is calling for it. We need toanalyse what type of control is needed, and then select the relevant response terms, proportional, integral orderivative, to give the required control of the system.

Lets begin with deciding what kind of control response is needed.

Slide 18The key component that defines what we need to use is time-in other words; once an adjustment is made, how long

does it take my control system to properly detect the result of the change that has been made. Lets consider threeterms to define the responsiveness of the system being controlled:

Slow, being 1 to 2 minutes,

Moderate, being 20 to 30 seconds, and

Fast, being 3 to 5 seconds.


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Slide 19It is important to point out that when we use the term system in this discussion, it doesn't mean an ent ire building'scontrol system. Here we mean one room with a temperature sensor, flow sensor on the VAV, VAV damper actuator,and variable speed drive controlling a fan. A building control system may have many smaller systems it is controlling.

A slow responding system would be best fit with a proportional response.

A moderate system would be best fit with a proportional + integral or a proportional + integral + derivative response

Lastly, a fast responding system would be best fit with a floating response.

Slide 20You may have heard that PID control is the most expensive and best solution, but there are good reasons whyfloating control should be used for fast responding systems. In our next class, we will look in more detail at slow,

medium and fast responding systems, and see why each is best served by a different control response. In addition,we will show step-by-step how the three terms of P I D function together and provide you with an interactive exampleto help you understand the concepts.

Slide 21Lets summarize some of the information that we have learned in this course.

Proportional control is a simple control method that provides a response proportional to the stimulus. It iscalculated from the difference between the actual and set-point. An integral term can be added, which is driven bythe amount of time that the measured variable has been offset from the setpoint. On a graph of actual versus setpointover time, it is calculated from the area under the graph. A derivative term can also be added, which is driven by therate of change of the measured variable. This is useful to prevent overshoots. On a graph of actual over time, it

is calculated from the slope of the line.

Finally, also we identified which response was appropriate to a slow responding system, which response wasappropriate for a moderate and fast responding system.

Slide 22Thank you for participating in this course.

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