,there is a gain of high gain feedback implicitly generates the inverse of G(s) without having to actually carry the inversion. I do agree that if the controller H(s) very high (i.e. >> 1), the ratio between U(s) and R(s) is 1/G(s). But is the reciprocal function of G (s) equivalent to an inversion operation of G(s)?
2) I've seen a few different models where only measurement noise + output disturbance, or input and output disturbance are considered. Typically, what are the disturbances and erroneous inputs considered in this type of a model?
3) Regarding control system sensitivity
, there is a claim that says reducing the sensitivity function and the input/output disturbances would result in a close to perfect setpoint tracking. My question is how are the disturbances usually reduced?
Yes, in theory. In the real world there are a host of factors that must be considered; primarily the fact that if you build that system your G(s) won't necessarily match the plants, the fact that the scheme doesn't work for a metastable (i.e. integrating) or unstable G(s), and the fact that for a G(s) with poles close to the stability boundary (i.e. if it has resonances or if it responds very slowly) the disturbance rejection of the system will be poor.
Do a web search on "pole-zero cancellation".
That's a loaded question. Typically one considers the disturbances that may make a difference for the system at hand, and that can cover a lot of ground.
By changing the plant. The most valuable lesson I ever learned as a control system engineer is that there's only so much performance improvement that you can squeeze out of any given plant, even with the best controller. Once you've reached that, you're done until you change the plant.
Note, too, that their last bullet point is incorrect, in a way that could be considered to be wildly optimistic. Sensitivity does not _typically_ increase in one frequency range when you reduce it in another. In this fallen and imperfect world we live in, sensitivity _must_ increase in one frequency range when you reduce it in another, unless you're fixing a (very) badly implemented controller. Look up the "Bode Sensitivity Integral" for more information.
You _cannot_ reduce a systems sensitivity to disturbance across the board; all you can do is shove that sensitivity to frequency ranges that you (or your customer) cares less about, from ones that you care more about.
I'll strengthen that, control engineers often have the job of applying controls to work around problems caused by poorly designed plant. Many times I've made that point to plant designers, then acceeded to their request under sufferance and implemented a configuration that may or may not have ameliorated the situation. The solution then is to keep lobbying, so that next time there are funds available such as during a major revamp, the core problem can be resolved.
Me, too. You get the same situation in product design, by the way -- the mechanical design gets finalized, it works marginally, but no one wants to change it because that opens up a huge can of worms. I seem to end up getting called in to help at that stage a lot. I do what I can, and I can often get significant improvement for a customer, but it's often frustrating all around. You just can't get silk out of a sow's ear, even if you're a control system designer.
Some of the most valuable work that I've done (IMHO) wasn't diddling with a control loop -- rather, it was working with the mechanical design team from Day 1 on a project, to make sure that the plant's own inherent disturbance rejection, stemming from its mechanical design, was as good as possible.
Or maybe it was making it clear that the attention needed to be paid up front in the first place.
A typical scenario: The mechanical guys have finished their machine. Motors are mounted (often steppers where analog servos would be better, or vice-versa) and the structural parts are anodized. I'm invited to a meeting to tell them how long my group will need to "wire it up". I ask where the limit switches will go, how the wires will get from here to there, and how the connectors will attach. You know the reaction: "We can't drill it now! it's all anodized! (or plated, ir irridited, whatever.) At that point, I say, "Here's the list of what I need to go where. You figure out how to arrange for it. If you don't want holes, decide where the cables will wrap around the outside. Next time, call me when it's still on paper. Really, fellas, I can read a print." I know that next time will be exactly like this time.
I spent a whole project once asking "Where are the cables going to go? Where are the cables going to go?".
When it came time to put the two major assemblies together -- assemblies that had to move freely with respect to each other for the machine to perform -- guess who got to route the cables?
They still use essentially the same sheet metal brackets that I came up with, just laser cut and bent on a brake instead of hacked out with snips, cleaned with a file, bent on the edge of a desk and held in with double-stick tape.
I still contract with that company part-time -- now they actually discuss cable routing in conceptual-level design reviews.
If OLTF(s)=3DK/(tau*s+1) then the feed forwards are 1/OLTF(s) or 1/K and tau/K Start with the feed forwards and add the closed loop control.
What is an output disturbance? A log falling on a actuator is not an output disturbance. Perhaps we are using different names for the same thing.
I never have used your type of control. I don't see why your model would be much different from any other form of control. I look at feedback quantizing errors first but that is because feedback in motion control systems is usually pretty clean otherwise.
My usual case is a log dropping on a log carriage. The actuators will move but will recover quickly. I don't do temperature systems but if I were controlling an oven I would consider any rate of change in product going through the oven to be a disturbance. The higher the rate of going through the oven the more heat required. If I can control the conveyor or can detect the product going into the furnace I should be able to work out a feed forward to estimate the load. If the amount product in the oven changes the time constant I should be able to compute that too. The speed of the conveyor might affect the dead time. If I can do system identification on this adjust my feed forwards and closed loop gains to compensate for the changes. If the dead time is severe then a Smith Predictor may be necessary. All of this requires a bit of work for average joe but I were making ovens I would have it all worked out.
I don't think of this as reducing disturbances but rather compensating for them. Reducing disturbance is limiting the rate of change in product in the oven or not letting the logs drop to far before they hit the carriage knees. Now you are getting into performance limitations or the mechanical design issues discussed above.
Thanks for your in-depth response. I'm clearer on the responses to the first two questions. While the third question has a ridiculously optimistic assumption to it, I'm just going to take its word with respect to this course. Your conversation with other community members on this newsgroup gave me perspective on how control system design functions in the real world. Looking forward to talk to you more about controls in the near future.