Dear Michael Short

Thank you for your answer. It was a fair answer presented by you, but still I think the revamped control strategy works well. I can present you some examples in aerospace and mechanical engineering for such controller to succeed, however, through your ResearchGate profile, I guess you are more focused on electronic systems, while I am more focused on mechanical systems. Anyway, to my humble knowledge on electronic circuitry, assume you want to stabilize the light intensity of a lamp by sensing its brightness through a sensor. In my revamped controller design, you need to only regulate the voltage of the light wire (Tungsten) which is more convenient to be measured than the brightness intensity. Here, the actuator could be considered as the Tungsten voltage, and the plant could be the light (brightness) intensity, while the controller is the voltage source and its variation.

In an aircraft, such a controller could be analogous to employing the servo-motor to regulating only flap (moving wing/elevator) position which is itself an actuator, by sensing its position by a sensor, which is more convenient than to sense aircraft aerodynamic states. I think it is a subtle point, however, a mechanical engineering viewpoint could be more illustrative on the revamped control idea. It needs a bit more careful ponder on the strategy to reveal its possible novelty as I claim.

warning: I am discussing only one control-loop with one feed-back path and one feed-forward path. There isn't any other interfering and jamming signal or blocks to make the system untidy. It is SISO.

Dear Saeb,

In the block diagrams, you can play with the internal blocks. However, if you think about the real system, you have the real plant and you want its “output” (such as position, velocity, etc.) to do something that you want. Yes, you do measure the output through a sensor, yet you assume that this sensor indeed gives you the measure of the actual output that you are interested to control. The actuator, however, is supplying something else.

“Through this revamped controller design, instead of measuring and regulating aircraft states as pitch-rate, we only measure and regulate actuator (elevator) deflection.”

The role of this actuator deflection must be such that the plant output does what you intend it to do (and that you decide through some command generator).

The basic idea of closed-loop control is that you supply some command, the plant responds with some output that you measure and then you use their difference (the error) to generate the proper signals that will force the plant to move such that the error tends to end being zero. This requires generating the signals that can activate the actuator, which in turn makes the plant move in the desired direction. The actual value of the actuator is secondary, and it is relevant only as far as it makes the plant output behave the way you decide through your command.

(A “small” issue that I don‘t understand: Is the plant supposed to actuate the actuator?)

I hope it helps,

Thanks,

Itzhak

Dear Michael Short

In double-integrator system, the position-rate is usually inaccessible, hence there have been some steadfast trend to look for control-laws with only position feedback and time, without any rate measurement by sensor.

see the paper:

On hyper-exponential output-feedback stabilization of a double integrator by using artificial delay

https://ieeexplore.ieee.org/document/8550196

Hence, it seems, although position-rate (which is a state) is not simply observable and not involved in the control-law, but the double-integrator system is controllable. This contradicts your viewpoint that:

"For me, if a state is not observable, it is not controllable."

I have also some other evidence for my claim. Assume the aircraft becomes very small and the rudder becomes too large, I mean the rudder becomes in size of the large fuselage, and the fuselage becomes in size of the small rudder. Now, the small fuselage is going to control the giant rudder, and this is like a jack-knife movement in a truck. Only artificially change your imagination of a real aircraft as the size of rudder and fuselage are interchanged. Then you can spot what I mean by my claim.

Thanks,

Saeb

The double integrator is actually observable, let assume a continuos double integrator for the sake of simplicity, though the same result can be applied to sampled form.

A = [0 0; 1 0], B = [0;1], C = [0 1], D = [0]

the observability space:

obs = [CA^0;CA^1] = [0 1; 1 0], whose rank is 2, thus the system is observable.

In other words it means system state can be determinated in a finite time relying only on output measurements, this implies the possibility to create state observers (e.g. Luenberger observer or Kalman filters).

A common misconception is the pratical usage of stabilizability, which means uncontrollable states are stable on their own, thus you can "control" (actually "stabilize") partially non-observable systems.

Dear Itzhak Barkana

Thank you for your comment. As you said, I meant actually the plant is supposed to actuate the actuator.

Consider a truck in a jack-knife movement. It does not differ you actuate the cabin to control the trailer, or actuate the trailer to control (steer) the cabin. The same happens in an aircraft as I exemplified for Mr. Short.

A trailer capable of steering the cabin (honestly I've never heard of) is a different physical system than a cabin steering a trailer. Controllers are designed taking into account a certain mathematical description of physical systems, but any mathematical description implies a series of assumptions which should be true in order for the controller to have the expected behaviour.

So, I may assume there can be systems where you can replace actuator and plant, but I can imagine this as a pure theoretical exercise.

For example, you can imagine to use a PID to control a boost converter's output and, let's say, you can find a boost converter which forces a given PID to behave in some way, but honestly this wouldn't make much sense in practical terms.

Dear Vito Antonio Nardi

Thanks for your comment. Notice that, in a truck, the trailer is connected to cabin most probably through a circular joint. The whole dynamics of the truck is similar to a jack-knife movement. So to steer the truck, it does not differ to rotate the cabin around the circular joint, or to rotate the trailer around the circular joint. Both are good steering strategies, although they may differ in hardware implementation. But in some systems, particularly in aerospace engineering and aircrafts, such a flip of roles between plant and actuator could benefit to a high extent, as aerodynamic parameters of fuselage are much difficult to be determined than aerodynamic parameters of the actuator (rudder, elevator or aileron) around the hinge-line of the control-surface.

The truck example is only for a better understanding of the revamped control strategy, not to specifically build such a truck.

The concept is a bit hardly tangible but I stand by my claim.

Hi Saeb

In any control system, we present the input and output relationship (response) of the entire system. At the initial stage of the deriving transfer function, you need to consider how each section related to each other. For the mathematical analysis, you can manipulate the system parameters without affecting it to the hole function of the system.

Nelaka

Hi Saeb AmirAhmadi Chomachar , this is true for a kinematic description of trailer and cabin, but from a physical point of view you need a trailer which has steering wheels, in other words you'd need a different physical system. By chance it may be possible to control this new physical system with the same mathematical rules which allow the control of the "similar" one.

Dear Vito Antonio Nardi

Although for a truck, such modified controller, requires new physical system, whereas, for an aircraft this is not binding, while only sensors location should be repositioned. Ground vehicles are different from flight vehicles, however my truck example was only to give an evidence for such revamped controller, not to necessarily design and built such a truck, even though I think for a driver-less truck, the auto-driver (controller) would behave better if steering commands are generated directly from the revolving circular joint which connects cabin to trailer, no matter which one is to be steered.

The main application of my revamped control strategy, is for systems where plant model could not be highly reliable, but actuator model is. As in aircrafts, where identifying aerodynamic parameters of aircraft wing and fuselage are much difficult to be gleaned than the aerodynamic model of the actuator (rudder, elevator, aileron).

Dear Saeb and All,

I would not like to add to an eternal argument.

Again, if you have an LTI system and you know that it is stable, changing the order of the internal blocks does not affect its stability.

However, you write “The main application of my revamped control strategy, is for systems where plant model could not be highly reliable, but the actuator model is.”

This is exactly why people developed closed-loop control:

You have a command and want the plant to track the command. So, you measure the desired command and the plant output that you want to control and then use their difference, i.e., the error signal, to force the plant to move towards zero error. You do this through some control algorithms, actuators, etc. However, what you want to control, despite the poor model, is the plant output. If the plant model is bad, this is even more important, because the fact that you can control the actuator, does not say much about the plant.

Dear Itzhak Barkana

I proposed my control strategy only for stabilization (nullify the output). Hence, if actuator out-put is nullified, then the plant output is also nullified, due to signal-flow rule in a block-diagram, although plant is before actuator, but they are mathematically flipped, hence if one block has zero out-put, the other would be certainly so.

But in case of control (command-following), I had modified my plant in my original question post as:

G(s)=Gcontroller(s)*Gactuator(s)*[Gplant(s)/Gactuator(s)]*Gactuator(s),

it means the new controller block would be:

Gcontroller[new]=Gcontroller[old]*Gactuator

and the new plant block would be:

Gplant[new]=Gplant[old]/Gactuator,

and then we again implement the modified control strategy I claimed as a proposal.

Thanks

I have been playing Prof and Dr., yet I am first of all an Engineer and I care about the real plant performance.

IMHO, when your plant must reach that angle or that height at that precise time, the fact that you measure and control the actuator position may not only be imprecise but even dangerous.

Thanks,

Itzhak

Dear Itzhak Barkana

Please notice the image attached here.

If it does not differ, it doesn't matter.

Still, when we want to control a plane, I would make sure that we measure and control what we want to control, not some other value, actuator or so.

It is only my opinion, so I will end with Good Luck.

Itzhak

Which jack-knife model are you assuming?

I don't want to make too much philosophy but I think we take a different perspective, I'm an engineer too (though with far far less experience than Itzhak's) so I tend to always relate anything to its physical significance and reality.

When designing control strategies we make a series of assumptions, the most common, the strongest and most useful is linearity. Linearity doesn't actual esist in reality, as soon as you have a saturation, a failure threshold or any of the simplifications which allow us to deal with a real-world problems, then you are assuming linearity.

But we're not crazy, we are (or at least try being) smart, so we assume linearity under a series of assumptions: non saturated (by far) actuators, robust joints, phase margins, magnitude margins, emergency shutoffs, blinking alarms.

Any control strategy is then closely coupled with a certain set of hypothesis. You can surely use the same control strategy for different systems, but you must be sure these hypothesis are still valid.

Dear Vito Antonio Nardi

I have been studying mechanical engineering for almost 20 years so far.

My M.Sc. thesis has been on one of the most challenging systems at the cutting edge interaction of aerospace and mechanical engineering.

It is available at:

https://ieeexplore.ieee.org/document/7118932

I am not proposing this revamped control strategy at a glance. I have thought of it for too many years.

I didn't mean to undervalue your background, I simply mistakenly assumed it was different from mine. I'm sorry.

Dear Vito Antonio Nardi

It's O.K.

No need to be sorry. The discussions below this post, including your comments, have been constructive to give me a better judgement about my revamped controller strategy. However, I do not claim that, the strategy is completely correct. Hence, any criticism about the strategy, would be valuable and welcomed.

Could that mean replacing output with process?

Dear Uchenna Godswill Onu

Please, notice the discussion Q&A, above , where you can find the answer to your question and some other similar questions already discussed recently.