基于matlab的pid-閱讀頁
2025-07-12 18:18本頁面
【正文】 the PV is close to the setpoint.Note that the output often goes past (over shoots) the steadystate output to get the process back to the setpoint. For example, a cooler may normally have its cooling valve open 34% to maintain zero degrees (after the cooler has been closed up and the temperature settled down) . If someone opens the cooler, walks in, walks around to find something, then walks back out, and then closes the cooler door－the PID controller is freaking out because the temperature may have raised 20 degrees! So it may crank the cooling valve open to 50, 75, or even 100 percent－to hurry up and cool the cooler back down－before slowly closing the cooling valve back down to34 percent. [3]Let’s think about how to design a PID controller.We focus on the difference (error) between the process variable (PV) and the setpoint (SP). There are three ways we can view the error.The absolute errorThis means how big is the difference between the PV and SP. If there is a small difference between the PV and the SP－then let’s make a small change in the output. If there is a large difference in the PV and SP－then let’s make a large change in the output. Absolute error is the “proportional” (P) ponent of the PID controller.The sum of errors over timeGive us a minute and we will show why simply looking at the absolute error (proportional) only is a problem. The sum of errors over time is important and is called the “integral” (I) ponent of the PID controller. Every time we run the PID algorithm we add the latest error to the sum of errors. In other words Sum of Errors＝Error1＋Error2＋Error3 ＋Error4＋….The dead timeDead time refers to the delay between making a change in the output and seeing the change reflected in the PV. The classical example is getting your oven at the right temperature. When you first turn on the heat, it takes a while for the oven to “heat up”. This is the dead time. If you set an initial temperature, wait for the oven to reach the initial temperature, and then you determine that you set the wrong temperature－then it will take a while for the oven to reach the new temperature setpoint. This is also referred to as the “derivative” (D) ponent of the PID controller. This holds some future changes back because the changes in the output have been made but are not reflected in the process variable yet.Absolute Error/ProportionalOne of the first ideas people usually have about designing an automatic process controller is what we call “proportional”. Meaning, if the difference between the PV and SP is small－then let’s make a small correction to the output. If the difference between the PV and SP is large－then let’s make a larger correction to the output. This idea certainly makes sense.We simulated a proportional only controller in Microsoft Excel. Fig. is the chart showing the results of the first simulation (DEADTIME＝0, proportional only) :Proportional and Integral ControllersThe integral portion of the PID controller accounts for the offset problem in a proportional only controller. We have another Excel spreadsheet that simulates a PID controller with proportional and integral control. Here (Fig. ) is a chart of the first simulation with proportional and integral (DEADTIME＝0, proportional＝) .As you can tell, the PI controller is much better than just the P controller. However, dead time of zero (as shown in the graph) is not mon..Fig. The simulation chartDerivative ControlDerivative control takes into consideration that if you change the output, then it takes time for that change to be reflected in the input (PV) . For example, let’s take heating of the oven. [4]Fig. The simulation chartIf we start turning up the gas flow, it will take time for the heat to be produced, the heat to flow around the oven, and for the temperature sensor to detect the increased heat. Derivative control sort of “holds back” the PID controller because some increase in temperature will occur without needing to increase the output further. Setting the derivative constant correctly allows you to bee more aggressive with the P
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