Double integrator, PD control: stability analysis (theory)

[@rezah336]

why do control theorists put input disturbance as disturbance instead of output disturbance? input disturbance means that the actuation that you are giving the system doesnt happen as wished and this is considered a hardware error in real life and the control algorithms are not expected to handle that before output disturbances.
output disturbances are realistic and should be handled before input disturbances, input disturbances are usually handled with fault detection of the hardware because usually control algorithms cant handle it

[@ASalaControlEN]

Thanks for your comment.
You shouldn't take the word "input" literally. What you are referring to is an "actuator hardware fault" which, indeed, may be catastrophic for a control algorithm.
What I understand as input "disturbance" is, say, an abstraction/simplification of a wind gust on a drone, opening your fridge's door, opening the faucet to drink water from a level-controlled tank... let me explain: you have a manipulated "actuator input" variable that can exert, say, a force on something you are moving in the direction and magnitude you wish... that's good; however, other guys may also be exerting unexpected/unmodelled forces (wind on a drone, augmented friction on a mechanical system, somebody pushing...) the end result is that the resultant force is not what you think it will be, and the difference is abstracted in the concept of "input disturbance". There is no "hardware fault" in there: on the contrary, your drone control must be there in order to avoid the drone drifting because of air currents and propeller miscalibration.
In general, you may be providing a "manipulated, known" amount of "power" or "inflow" to move/heat/charge some system but the resultant power is not 100% what you thought you were providing; no problem because you get informed of that situation with sensing, nothing is wrong/faulty there: if your sensors detect that the drone is moving left when you thought it should remain motionless, your controller will react and push it rightwards just a little, in order to compensate for that "unknown thing", i.e., disturbance that seems to be moving it. No fault is happening in your propellers, it's just the wind.
So, "input disturbance" is the "theoretical abstraction" of these issues when we are not interested in the actual "physics" or "technological detail" of what is causing them/how they happen:
the most simple way of simulating the above kind of events to validate a PID behaviour is to add, say, a step on the input side, to see how the PID reacts to compensate for it.

[@rezah336]

@@ASalaControlEN
drone:
input disturbance: the motors dont go to the rpm set by the controller
output disurbance: wind or a push on the drone out of position
fridge:
input disturbance: the cooling circuit does not give the cooling it is supposed to
output disturbance: opening the door
level controlled tank (assuming constant flow out of tank, controlled by water being added):
input disturbance: the water being added is not what is expected by the controller
output disturbance: opening faucet to empty faster or less flow out of the tank
input: actuation
output: result
input disturbance: error on the actuation
output disturbance: error on the result

[@ASalaControlEN]

Dear Rezah,
Well, it seems that what I call "manipulated input" or "manipulated actuator" you name it, plainly, "input". And "everything else", you name that as "output".
Well, if that's what you understand, that's not what I understand... No problem, we have different opinions, but we can live on our lives happily.
My opinion in systems-theory jargon:
INPUT: anything that can change the "internal state/energy/mass" of the process I am interested in controlling.
There are TWO classes of inputs: the "manipulated ones" in which I can decide its value (manipulated actuation) and the "non-manipulated inputs", which come in as they wish and I must counteract.
OUTPUT: what my sensors tell me about the internal state/stored energy/stored mass in my process.
Then, in "generic systems theory" there is no such thing as "output disturbance". Disturbances may affect internal states in many ways, so we need to discuss controllability, observability, etc. for each input and sensor.
Now, terminology in "single-input single-output process control simplifications" of the above general setup:
INPUT DISTURBANCE: any "disturbance input" whose effect is (maybe approximately) equal to that of my "manipulated input"... any "external force" to my drone, any "thermal power drain" in my fridge, etc.
OUTPUT DISTURBANCE: any "disturbance input" whose effect on my output of interest might be "faster" than that of my actuator, of which affects other subsystems/states different to those that my actuator is able to change, and important for my control tasks (target motion in tracking, measurement noise, ...).
If my system is stable, slow input disturbances can be converted to output ones via a block diagram transformation. Fast output disturbances cannot be converted onto input ones.
But, as I said, we are not starting a war here... Just note that classifying everything into "either input or output" is a simplification just as naming a color "either black or white"... there are "grey" things.. and in full-fledged system theory there are inputs, states, outputs, and controllable subsets of states for a given input, and observable subsets of states for a given sensor, and quantitative measures of controllability and observability... so there are many terminology nuances which are needed for a correct formal analysis apart from "input" versus "output".
Best regards.

[@rezah336]

@@ASalaControlEN
your definition is so complicated 🙂
it was very interesting to read how theorists view things, if anything that affects the internal states is an input disturbance isn't everything an input disturbance?
also when you put the disturbance in front of the system in the block diagram, that is the input of the system, which is the actuation signal
anyway, we disagree, no war, in the middle east we argue about everything but as long as there is no insults, everyone is friends

[@ASalaControlEN]

" if anything that affects the internal states is an input disturbance isn't everything an input disturbance?"
In an abstract sense, yes: disturbances are always "inputs" to a system. The actuation signal is "just one of the possible inputs" affecting the energy/mass balances of my process. Disturbances "added at the input" or "added at the output" of block diagrams are simplifications for a first approach to testing PID control performance.
And, yes, you have many more important issues to discuss in middle East than what is the meaning of "input". Best wishes, my friend.