Interactive Illustration of PID Response Part 7 – Building Automation Systems Training
Interactive illustration of pid response this is the seventh course in the building control series if you have not already done so please participate in building controls one through six prior to taking this course for best viewing results at the completion of this course you will be able to see how proportional control may oscillate and stabilize at a point above the set point show how an integral term helps a control loop to achieve a result closer to the set point and you will be able to illustrate how a derivative term helps to prevent overshoots.
In the previous classes we have explored the definition of each of the terms in a pid controller p for proportional control to deliver more or less response according to the stimulus.
I for integral control to adjust the response depending on how long the actual has been away from the set point and d for derivative control to adjust the response depending on the rate of change to help avoid overshooting the set point now we’ll walk through an example and use an interactive simulation to see how these terms combine in a control loop let’s see why proportional control achieves stability with an offset imagine a room where the temperature has stabilized and it is the same as the set point.
The controller is providing 800 units of air per minute keeping in mind that for the purposes of this example it doesn’t matter what the units are now a group of people enter and start having a meeting the temperature in the room climbs so the controller implements its proportional rule as shown here in this equation we can now change the language we use in this rule to use the terms we learned in previous classes as shown here in this equation as the temperature climbs the error or offset also goes up and the gain setting will cause more air to enter the room let’s say the temperature climbs by 2 degrees and the amount of air supplied is now 1050 units per minute if this increased air supply is enough to stop the temperature increasing anymore the system will now stabilize at this point even though it is offset by two degrees above the set point the controller will go on providing 1050 units per minute and that will only change when some people leave the room or more people come in if the offset of 2 degrees is acceptable this system is adequately tuned but if 2 degrees is not tolerable.
This system will not meet requirements in its current setup let’s go back to the point where the people first enter the room what if we had set the gain differently so that the 2 degree temperature increase made the controller supply 1200 units per minute then the additional air might be enough to reduce the temperature in the room when the temperature drops the supply will also drop according to the tuning of the system
since the air output has been reduced the temperature may go up again and cause another increase in the output the output may go up and down for a while as the temperature in the room is changed by the output and is fed back to the system to create a new output level but as long as the gain is not set too high it will find stability although probably at a point which is not the room set point this oscillation is a typical shape for a proportional response over time how does the shape differ when we add integral and derivative terms these three curves illustrate the different responses from p i and pid control.