# basics of PID control

Discussion in 'Mathematics and Physics' started by PG1995, Jun 12, 2013.

1. ### PG1995Active Member

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Thank you, Steve, NG.

Taking the previous two messages together means that having an inner PID loop makes the system more stable. But the question is how stable does it make the system.

Suppose P&O outer loop updates, say, every one minute, and the inner PID loop updates at a very fast rate. If a cloud is passing above and it takes only 20 seconds to get the sky clear again then inner loop might be able to maintain the input voltage and hence temporary changing conditions doesn't disturb the system and hence a comparatively stable system. But what if the sky takes just more than a minutes to clear, the system will definitely be disturbed because inner P&O loop will change the input voltage. After that the system will stay at this non-optimum input voltage until the inner P&O loop gets updated again. Thank you.

Best wishes
PG

2. ### atferrariWell-Known Member

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What does "P&O" in this context mean? Perturb and observe?

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Yes.

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5. ### NorthGuyWell-Known Member

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Including inner loop will not make P&O better. But it'll let you select the time scale for P&O where it is the least harmful. Without inner loop, P&O has to run relatively fast.

For example, you connect a load to the battery, voltage drops, inner loop adjusts voltage quickly and returns the system to MPPT. P&O is not affected. If not for the inner loop, P&O would have to work on adjusting voltage.

6. ### MrAlWell-Known MemberMost Helpful Member

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Hello,

I see we are talking about MPPT again. It's not always about MPP accuracy as i will try to explain here.

The perturbed system is interesting, but as NorthGuy pointed out it is not very stable when there is variable cloud cover. That's because a cloud moving overhead tends to look like a perturbation itself. It does work, but what will happen is there will be times when the system does not put out much power because the system gets a little lost.

This is typical behavior in a system that is (or would be) designed based on feedback that includes only the derivative, and that's just about what the perturbed system is because it is much like solving for a wave maximum by setting the first derivative to zero:
y=f(x)
max y:
0=f'(x)
solve for x, double check solutions.

In the perturbed system we force two different x's so what we are doing is the above but using a numerical approach instead of a purely algebraic approach:
f'(x)=(f(x+h)-f(x))/h

where h is the perturbing increment in x. We then evaluate f'(x) and see if it is positive, and if it is positive then we assume the power went up and if negative then it went down.

A way to help the situation is to make h smaller, so that the change is smaller and this means it will take longer to react to a changing condition. This is like using a damping factor in a numerical method. The drawback is that if a cloud comes quickly overhead the system may not be able to react fast enough and so again we end up putting out little power for a while.

So we have the two evils, making h large causes the unit to put out little power sometimes, and making it small does the same. What matters now is how the unit will be used and what for. If it is used as a one only unit that you use for powering your battery charger it may not matter because the system would come back up to normal power eventually, and it may not take that long. But if it is part of a bigger system such as when it is to be line tied to the grid, that's another story. The power company can not always tolerate power coming and going especially when you might not be the only one generating.
There could be possibly thousands of users in the future, and if we had thousands of units delivering power that keeps jumping up and down, it could cause problems.

Back in the 80's when i was working with Sandia Labs on a solar project, they decided that it would be better to use feedback based on a measurement rather than a change in control signal. Using a measurement here is then just like any other system that uses a sensor to measure a quantity and it is then able to make adjustments very rapidly. Because the measurement is monotonically increasing (or decreasing) for a change in measured parameter, there is never a problem with stability. This is unlike the perturbed system, where increasing and decreasing can switch roles without the system having that knowledge.
The main criterion for them was stability over accuracy of MPP because thinking ahead the systems that come on line must be stable at all costs.

The measurement this time comes in the form of a single solar cell. If i remember right, the open circuit voltage is measured and that provides the feedback signal. A percentage of that voltage will indicate the relative level of sunlight reaching the solar panels at the given time. I went thought the numbers and found that this will cause some inaccuracy, but that is acceptable for the sake of stability when there could potentially be a million units coming on line in the years ahead.

In the years ahead we might be able to join satellite weather tracking to MPPT per region, but im not sure how long that will take.

Last edited: Aug 20, 2014
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