Surreal Stability and Control thread -- abstract continued

[Martin Taylor 2013.12.29.09.46]

[previously]

[Martin Taylor 2013.12.26.12.03]

This is a very strange thread, almost surreal. Here's my brief abstract of how we got from Bruce's link to show CSGnet readers what is meant by classical control theory to here (or at least "here" as of a couple of days ago. I've been almost incommunicado since an ice storm knocked out our power and cold temperatures induced us to go and stay with our son in an unaffected part of Toronto.

BA: Here's a link if you want to know about classical control theory.

RM: I stopped looking at it very shortly because they talked about "stability" which has nothing to do with control.

BA and MT: "Stability" is nothing to do with control. Control is a way of achieving stability.

BA also: What distinguishes control from self-restoring systems like the ball-in-a-bowl is that the disturbance provides the energy that allows the ball to reach its stable position whereas a control system provides the energy separately.

MT: Bruce is right.

RM: Bruce is wrong. Control is ... (a subthread ensued on different possible definitions of "control").

BA stays silent.

MT. Stability and control are quite different concepts.

RM: Wrong. Control and stability are quite different concepts. To know whether control is happening you have to use the TCV.

MT: Shows pictures of two of the three kinds of dynamical attractors that represent the three kinds of stability (fixed point, and oscillator, leaving "strange" aside), and points out that by looking at the orbit one could not tell whether the stability is due to a control system or a ball-in-bowl kind of system.

RM: Wrong. Looking at the orbits one can't tell whether the stability is due to a control system or a ball-in-bowl kind of system. To know whether control is happening you have to use the TCV.

MT: We were talking about whether "stability" can be applied to control systems.

RM: No we weren't. We were talking about how to tell whether control is happening.

MT: Stability and control are concepts in a different domain, like "cold" and "ice cream".

As of Xmas Eve:

> Martin Taylor (2013.12.24.16.34)--

> MT: I don't remember anyone claiming that all systems that exhibit stability are
> control systems.

RM: Me neither. I believe the claim was that all control systems exhibit stability. And in my last post I think I showed that this is not the case; a very good control system can appear to be highly unstable.

That was never the claim. The claim was that all control systems are dynamical systems, and all dynamical systems have the _property_ of "stability".

[continuation]

RM: OK, so all dynamical systems have the property of stability. Could you tell me what that property -- how to measure it -- is so that I can see if, indeed, it is a property of control systems.

MT produces a tutorial explaining the property of stability, using simple control system as an example, to show how it applies and how it implies the need for the TCV to determine whether a system is a control system, ending with "Does this answer your question, at least conceptually?"

RM: No. I just want a formula and a definition of the variables that go into the formula so I can measure the stability of an equilibrium system. I can give you the formula for the stability of a simple control system. [MT: Having said a little earlier that he did not understand whether the property of "stability" could apply to control systems.]

MT: But do you understand the concept? That's all I tied to get across.
MT: I seriously doubt you can give a formula for the stability of a control system. But go ahead and try it (proposing the simplest control loop with specified output gain and loop transport lag as the type example).

RM responds with a formula for the Control Ratio !!! Clearly, what little he may have read of the tutorial did not answer the question conceptually. Without having the concept, there's not much point in a measure.

[This thread is pure Magritte in text form -- to be continued, no doubt, with other red herrings and dead horses thrown into the blue sky to float along with all the unread messages on which Rick has offered critical comment].

Martin