Greetings to all,
several weeks ago I started
another thread about the Proportional component of PID control and used a gasfired oven as a example ... Ayman Metwally posted
this reply and said that he fully understood how the oven would not be able to reach the desired setpoint using only Proportional action for its controller ... but then he asked a perfectly valid (and very common) question about why other types of systems (level, flow, pressure, etc.) might not be able to reach the desired setpoint when using Proportionalonly control ...
paraphrasing slightly, he asked:
Quote:
I understand that the oven system achieves a steady state condition, but what would keep other PVs from just climbing until they reached the setpoint using Proportional only? Can you give me another example?

personally, I can remember having exactly the same questions when I first started learning about PID control ... I had already accepted the textbook’s “rule” which says that Proportionalonly control cannot maintain a desired setpoint ... but still, in the back of my mind, was always the nagging question: “but WHY won’t it work?” ... it seemed quite simple ... the controller sees a small error ... it makes a small correction ... the process moves closer to the target and gives an even smaller error ... the controller gives a smaller correction ... and so on ... eventually we SHOULD be right on target and the Proportionalonly controller SHOULD be able to maintain the setpoint ... but it doesn’t work that way ... or does it? ... as most experienced technicians know, there ARE some exceptions to the “rule” ...
the fact is that SOME systems CAN reach the setpoint using only Proportional action ... but only under certain conditions ... my own personal word for this type of situation is a “sealed system” ... the basic idea is that if there is NO LOSS from the system, then Proportional action alone might be enough to reach the setpoint ... let’s use an example ...
Figure 1 shows manual control (not automatic control) being used to control what I would call a “sealed system” ... a compressor keeps the pressure inside a reservoir (C) at a constant value of 100 psi ... we want to control the pressure in tank (T) ... suppose that we close the outlet valve completely so that there is NO WAY for any air to leave the tank ... then we crack the inlet valve open just a tiny amount ... in our example, we’re using a valve setting of 1% ... but ANY amount of opening would give the same final results ... specifically, the pressure in tank (T) will eventually rise to the full supplied pressure of 100 psi ... as I said, if we wait long enough the final resulting pressure will always be the same ... the only difference would be that smaller valve openings would take longer to reach the full pressure ... and larger valve openings would reach the full pressure quicker ... but the final pressure would ALWAYS eventually be the same ... notice that there is no time scale on the graph ... since we aren’t told how large the tank is, or how much air will transfer through our 1% open inlet valve, then there is no way for us to predict just how long it will take tank (T) to reach the full supplied pressure ... maybe minutes ... maybe hours ... maybe years ... but EVENTUALLY the pressure in tank (T) WILL reach the full pressure of the compressor reservoir (C) ...
now let’s look at the graph in Figure 1 ... notice that when the graph starts, the inlet valve is fully closed ... the pressure in tank (T) is zero psi ... shortly into the graphing period, the inlet valve is cracked open 1% as shown by the red trace ... the pressure in the tank starts to rise rapidly at first ... but then it begins to rise less rapidly as the test continues ... until finally it is rising VERY slowly as the pressure makes its final approach to the full supplied value ...
the basic shape of this curve should be familiar to everyone who has ever studied electronics ... it’s basically the same curve followed by a capacitor being charged through a resistor ... the main idea is that as the pressure in tank (T) rises, the higher pressure opposes a further rise in pressure ... said another way, when the pressure in tank (T) is very low (at the beginning), then it’s very easy for more air to flow into the tank and quickly raise the pressure ... but ... when the pressure in tank (T) is very high (at the end), then it’s much harder for more air to flow into the tank ... and so the pressure rises much more slowly ...
the most important thing to notice is that regardless of how small a setting we use for our inlet valve, if we leave it cracked open long enough (even if just a pinhole), then the pressure in tank (T) will EVENTUALLY rise all the way up to the full supplied pressure ... just as long as there is NO leakage from the tank ...