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 Тема повідомлення: Understanding Derivative in PID Control
ПовідомленняДодано: 18 серпня 2014, 17:09 
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З нами з: 29 листопада 2013, 17:11
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Understanding Derivative in PID Control
The third factor in PID is the least understood. Derivative action can do good things, but when used improperly, it causes headaches.
http://www.controleng.com/single-articl ... 35e3d.html
http://e-ditionsbyfry.com/Olive/ODE/CTL ... w=document
Цитата:
You’ve probably heard the expression, “a little knowledge is dangerous.” This certainly applies to PID loops, especially when you try to dabble with the derivative factor. This element of the control strategy can improve performance, but only in the right situations and when applied properly. Understanding those situations begins with a quick basic review of how PID operates.
Proportional control applies an effort in proportion to how far you are from the setpoint. It’s main drawback is that the closer you get to the setpoint, the less it pushes. Eventually it doesn’t push hard enough to move the variable, so the process can run continuously close to the setpoint, but not quite there.
Integral control tries to even out the difference of the time spend on both sides of the line. If you’ve spent a minute running at 98%, it will try to push you over to 102% for similar amount of time. This action compensates for P’s inability to make that last effort.
Many, if not most, control applications can run perfectly well with just P and I control. (See sidebar.) Ziegler-Nichols tuning produces the traditional curve where the process variable oscillates briefly but settles onto the line with each cycle reducing amplitude by 75%. For applications that require the fastest possible response, seeing that kind of action after a setpoint change would be hugely rewarding to a control engineer.
But let’s say the process in your case is a tank of liquid product that you’re trying to heat. If the process variable (temperature) goes above the setpoint, the product may be ruined or catch on fire. So, how do you get the process variable to move, but not overshoot the setpoint excessively? One answer is introducing a derivative factor.
Derivative acts as a brake or dampener on the control effort. The more the controller tries to change the value, the more it counteracts the effort. In our example, the variable rises in response to the setpoint change, but not as violently. As it approaches the setpoint, it settles in nicely with a minimum of overshoot. It doesn’t move as quickly as the PI-only effort, but without the oscillations, the right amount of derivative action can stabilize the process variable at the setpoint sooner.
Bob Rice, Ph.D., director of solutions engineering for Control Station, sums up the three elements: “The proportional term looks at where my value is currently. Integral looks at where I’ve been over time, and derivative tries to predict where I’m going. Derivative tries to work opposite of where proportional and integral are trying to drive the process. P and I are trying to drive one way, and D is trying to counteract that. Derivative has its largest effect when the process is changing rapidly in one direction. The P and I terms are saying, 'Keep going.’ The derivative catches it and says, 'You’re going too fast. You need to slow down.’”

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